35002 lines
3.1 MiB
35002 lines
3.1 MiB
[
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as \"x + 1 = 10\".",
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"gt_answers": "\\frac { 5 } { 1 4 } = \\frac { 1 } { x }\n",
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"image_path": "./data/HME100K/test_images/test_2.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
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"gt_answers": "- 2 x ^ { 4 } - x ^ { 2 } + 5 = ( - x ^ { 2 } + 1 ) ( x + a ) + b = x ^ { 2 } + a x + 3 x - 3 a - b\n",
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"image_path": "./data/HME100K/test_images/test_3.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as follows:\n\n\\(S_{AB} = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left",
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"gt_answers": "S _ { \\Delta D B F } = \\frac { 3 } { 8 } S _ { \\Delta A B C } = \\frac { 3 } { 8 } \\times \\frac { 1 5 } { 2 } = \\frac { 4 5 } { 1 6 }\n",
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"image_path": "./data/HME100K/test_images/test_5.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x} + \\frac{1}{y} = \\frac{1}{x + y}\n\\end{equation}\n\nThis is a basic algebraic equation that demonstrates the commutative property of addition.",
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"gt_answers": ": x _ { 1 } = - \\frac { 3 } { 5 }\n",
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"image_path": "./data/HME100K/test_images/test_6.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as follows:\n\n\\(15\\left(100 - 75\\right) = 100\\left(100 - 75\\right) - 75\\left(100 - 75\\right) = 100\\left(100 - 75\\right) - 75\\left(100 - 75\\right) = 0\\)",
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"gt_answers": "7 5 \\div ( 7 5 + 2 5 ) = 7 5 \\div 1 0 0 = 7 5 \\%\n",
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"image_path": "./data/HME100K/test_images/test_7.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as y = 3x - 1.",
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"gt_answers": "y = 3 . y = - 1\n",
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"image_path": "./data/HME100K/test_images/test_8.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as \"6x^2 - 4x + 1 = 0.\"",
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"gt_answers": "x _ { 1 } = - 6 x _ { 2 } = 4\n",
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"image_path": "./data/HME100K/test_images/test_9.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(25.6\\times 10^{3} + 13.8\\times 10^{2} + 1.2\\times 10^{1} + 1.3\\times 10^{0} = 26.9\\times 10^{3}\\)",
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"gt_answers": "2 3 . 5 + \\frac { 1 } { 2 } x = 1 3 + x\n",
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"image_path": "./data/HME100K/test_images/test_10.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)\n\nThis is a quadratic equation in the form of a formula, where x is the unknown variable.",
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"gt_answers": "\\frac { 9 } { 1 0 } \\div \\frac { 3 } { 5 } = \\frac { ( 9 ) } { ( 1 0 ) } \\textcircled { \\times } \\frac { ( 5 ) } { ( 3 ) } = ( \\frac { 2 } { 3 } )\n",
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"image_path": "./data/HME100K/test_images/test_13.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is:\n\n\\(x^2 + y^2 + 3xy + 4x + 5y + 6 = 0\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\nx^2 + y^2 + 3xy + 4x + 5y + 6 = 0\n\\end{equation}\n\nThe LaTeX code for the equation is:\n\n\\begin{equation}\nx^2 + y^2 + 3xy + 4x + 5y + 6 = 0\n\\end{equation}\n\nThe equation is written in the form of an equation with two variables, x and y, and the expression is enclosed within the parentheses. The equation is also written in the form of an equation with two terms, the first term being the sum of the squares of the variables, and the second term being the sum of the products of the variables.",
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"gt_answers": "= \\frac { ( 7 + 1 8 ) + ( 9 - 1 4 ) i } { 5 } = \\frac { 2 5 - 5 i } { 5 } = 5 - i\n",
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"image_path": "./data/HME100K/test_images/test_14.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as \"LCpB = 90\u00b0.\"",
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"gt_answers": "\\angle C P Q = \\angle B = 9 0 ^ { \\circ }\n",
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"image_path": "./data/HME100K/test_images/test_16.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as a-4b+1.",
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"gt_answers": "a - 4 b = - 1\n",
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"image_path": "./data/HME100K/test_images/test_17.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as \"a^2 + b^2 = c^2.\"",
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"gt_answers": "a \\neq \\frac { 3 } { 2 }\n",
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"image_path": "./data/HME100K/test_images/test_18.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as \"abla\" using LaTeX format.",
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"gt_answers": "a \\bot b\n",
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"image_path": "./data/HME100K/test_images/test_19.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as: OE + AB = AC.",
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"gt_answers": "\\frac { O E } { A C } = \\frac { O B } { A B }\n",
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"image_path": "./data/HME100K/test_images/test_20.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x + 2y = 10\\)\n\nThis formula represents the relationship between the variables x and y, where 3x + 2y = 10.",
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"gt_answers": "\\frac { \\frac { 8 } { 3 } } { 2 \\times \\frac { 4 } { 9 } } = - \\frac { - \\frac { 8 } { 3 } } { \\frac { 8 } { 9 } } = \\frac { 8 } { 3 } \\times \\frac { 9 } { 8 } = 3\n",
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"image_path": "./data/HME100K/test_images/test_21.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as y = 3x - 2.",
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"gt_answers": "y = \\frac { 7 } { 3 }\n",
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"image_path": "./data/HME100K/test_images/test_23.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
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"gt_answers": "( - 1 + 0 ) ^ { 2 } = ( - 1 ) ^ { 2 } = 1\n",
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"image_path": "./data/HME100K/test_images/test_24.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as follows:\n\n\\(4 \\times 5 \\times 6 \\times 7 \\times 8 \\times 9 \\times 10 \\times 11 \\times 12 \\times 13 \\times 14 \\times 15 \\times 16 \\times 17 \\times 18 \\times 19 \\times 20 \\times 21 \\times 22 \\times 23 \\times 24 \\times 25 \\times 26 \\times 27 \\times 28 \\times 29 \\times 30 \\times 31 \\times 32 \\times 33 \\times 34 \\times 35 \\times 36 \\times 37 \\times 38 \\times 39 \\times 40 \\times 41 \\times 42 \\times 43 \\times 44 \\times 45 \\times 46 \\times 47 \\times 48 \\times 49 \\times 50 \\times 51 \\times 52 \\times 53 \\times 54 \\times 55 \\times 56 \\times 57 \\times 58 \\times 59 \\times 60 \\times 61 \\times 62 \\times 63 \\times 64 \\times 65 \\times 66 \\times 67 \\times 68 \\times 69 \\times 70 \\times 71 \\times 72 \\times 73 \\times 74 \\times 75 \\times 76 \\times 77 \\times 78 \\times 79 \\times 80 \\times 81 \\times 82 \\times 83 \\times 84 \\times 85 \\times 86 \\times 87 \\times 88 \\times 89 \\times 90 \\times 91 \\times 92 \\times 93 \\times 94 \\times 95 \\times 96 \\times 97 \\times 98 \\times 99 \\times 100 \\times 101 \\times 102 \\times 103 \\times",
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"gt_answers": "x _ { 3 } = \\frac { - 5 + \\sqrt { 4 1 } } { 4 }\n",
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"image_path": "./data/HME100K/test_images/test_25.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b^2 - 4ac = 0\\)\n\nThis formula is a quadratic equation, which can be solved using the quadratic formula.",
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"gt_answers": "b ^ { 2 } \\dot { = } a ^ { 2 } + c ^ { 2 } - 2 a c \\cdot \\cos B\n",
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"image_path": "./data/HME100K/test_images/test_26.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as \"14x + 10 = 100.\"",
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"gt_answers": "1 0 \\sqrt { 1 0 x - x ^ { 2 } } = 1 4\n",
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"image_path": "./data/HME100K/test_images/test_27.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as \"4x5 + 8y = 480.\"",
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"gt_answers": "5 . 5 - 2 . 5 ) x + 4 8 \\times 5 . 5 = 4 8 0\n",
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"image_path": "./data/HME100K/test_images/test_28.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 5x + 4 = 10\\)",
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"gt_answers": "4 . 5 8 5 > 4 . 6 5 > 4 . 5 6 > 4 . 5 0 6\n",
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"image_path": "./data/HME100K/test_images/test_29.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as \"L + L' + L\" and is a mathematical formula involving three variables.",
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"gt_answers": "\\angle D O E = \\angle D B E = \\angle A E B = 7 5 ^ { \\circ }\n",
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"image_path": "./data/HME100K/test_images/test_30.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as K = 12 - 5.",
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"gt_answers": "x = \\frac { 1 7 } { 5 }\n",
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"image_path": "./data/HME100K/test_images/test_31.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2\\pi r^2 + 2\\pi r\\cos(\u03b8) = 4\\pi r^2\\)\n\nThis formula relates the area of a circle to its radius and the angle it makes with the x-axis. The area of the circle is given by the formula \\(A = \\pi r^2\\), where r is the radius and \u03c0 is the constant pi. The formula in the image adds the terms \\(2\\pi r^2\\) and \\(2\\pi r\\cos(\u03b8)\\) together to obtain the total area of the circle.",
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"gt_answers": "\\frac { 1 } { 3 } \\times \\frac { 1 } { 4 } = \\frac { 1 } { 1 2 } = 1 2 ( c m )\n",
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"image_path": "./data/HME100K/test_images/test_32.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as 2x^2 - 2b^2 = 4b^2.",
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"gt_answers": "\\frac { 2 x - 6 } { 2 } = 6\n",
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"image_path": "./data/HME100K/test_images/test_33.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{x^2 + 2x + 1}{x^2 - 2x + 1}\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\ny = \\frac{x^2 + 2x + 1}{x^2 - 2x + 1}\n\\end{equation}\n\nThe LaTeX code for the equation is as follows:\n\n\\begin{equation}\ny = \\frac{x^2 + 2x + 1}{x^2 - 2x + 1}\n\\end{equation}\n\nThe equation is written using the `\\( ... \\)` and `\\( ... \\)` LaTeX commands to indicate the beginning and end of the equation, respectively. The `\\frac` command is used to indicate a fraction, and the `\\( ... \\)` command is used to indicate the beginning and end of the numerator and denominator, respectively.",
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"gt_answers": "y = \\frac { x ( x - 2 ) } { ( x - 1 ) ^ { 2 } }\n",
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"image_path": "./data/HME100K/test_images/test_34.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as 1/x + 1/y = 1/z.",
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"gt_answers": "x _ { 1 } = \\frac { 1 } { 9 }\n",
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"image_path": "./data/HME100K/test_images/test_35.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x^2 + 3y + 4\\)",
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"gt_answers": "y _ { 1 } = 0 , y _ { 2 } = \\frac { 8 } { 3 } \\cdot\n",
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"image_path": "./data/HME100K/test_images/test_36.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as follows:\n\n\\(2^{12} + 2^{11} + 2^{10} + 2^{9} + 2^{8} + 2^{7} + 2^{6} + 2^{5} + 2^{4} + 2^{3} + 2^{2} + 2^{1} + 2^{0} = 2^{12} \\cdot 2^{11} \\cdot 2^{10} \\cdot 2^{9} \\cdot 2^{8} \\cdot 2^{7} \\cdot 2^{6} \\cdot 2^{5} \\cdot 2^{4} \\cdot 2^{3} \\cdot 2^{2} \\cdot 2^{1} \\cdot 2^{0} = 2^{12} \\cdot 2^{11} \\cdot 2^{10} \\cdot 2^{9} \\cdot 2^{8} \\cdot 2^{7} \\cdot 2^{6} \\cdot 2^{5} \\cdot 2^{4} \\cdot 2^{3} \\cdot 2^{2} \\cdot 2^{1} \\cdot 2^{0} = 2^{12} \\cdot 2^{11} \\cdot 2^{10} \\cdot 2^{9} \\cdot 2^{8} \\cdot 2^{7} \\cdot 2^{6} \\cdot 2^{5} \\cdot 2^{4} \\cdot 2^{3} \\cdot 2^{2} \\cdot 2^{1} \\cdot 2^{0} = 2^{12} \\cdot 2^{11} \\cdot 2^{10} \\cdot 2^{9} \\cdot 2^{8} \\cdot 2^{7} \\cdot 2^{6} \\cdot 2^{5} \\cdot 2^{4} \\cdot 2^{3} \\cdot 2^{2} \\cdot 2^{1} \\cdot 2^{0} = 2^{12} \\cdot 2^{11} \\cdot 2^{10} \\cdot 2^{9} \\cdot 2^{8} \\cdot 2^{7} \\cdot",
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"gt_answers": "( 2 ) \\vert A B \\vert = \\vert - 1 - 5 \\vert = 6\n",
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"image_path": "./data/HME100K/test_images/test_39.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 10\\)",
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"gt_answers": "\\frac { 4 x } { 3 } + \\frac { 3 } { 2 } > - \\frac { x } { 6 }\n",
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"image_path": "./data/HME100K/test_images/test_40.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as follows:\n\n(2x + 3) \\* (13 - 2x) = 8",
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"gt_answers": "( \\frac { ( 2 \\times 4 ) } { 8 } + 1 3 = 2 1 > 2 0 )\n",
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"image_path": "./data/HME100K/test_images/test_41.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} = \\frac{1}{15}\n\\end{equation}\n\nThis equation represents the sum of three fractions, each with a denominator of 5, and the numerator of 1. The result is a fraction with a denominator of 15.",
|
|
"gt_answers": "n = \\frac { 1 } { 2 } \\div \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_42.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\times 3 \\times 6 + \\frac { 1 } { 2 } \\times ( 6 + 8 ) \\times 1 1 + \\frac { 1 } { 2 } \\times 2 \\times 6 = 9 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_43.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"X2(x-4) = 0.\"",
|
|
"gt_answers": "x = 2 ( \\frac { 5 x - 1 7 } { 4 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_44.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 5 = 0\\)",
|
|
"gt_answers": "P ( x = 0 ) : \\frac { C _ { 4 } ^ { 3 } } { C _ { 7 } ^ { 3 } } = \\frac { 4 } { 3 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_45.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BQAbTana = 2018 - 2010 = 8 years.\"",
|
|
"gt_answers": "B Q = A B \\tan A = 2 0 \\tan 6 0 ^ { \\circ } = 2 0 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_46.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x3 - 9 = 9 - 3x3.",
|
|
"gt_answers": "\\frac { 1 } { 3 } \\times \\frac { 1 } { 3 } = \\frac { 1 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_47.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(19.22 \\times 147.95 \\div 195.6 = 14.44\\)",
|
|
"gt_answers": "1 9 6 . 2 6 \\times \\frac { 3 } { 4 } = 1 4 7 . 1 9 5 ( m l )\n",
|
|
"image_path": "./data/HME100K/test_images/test_48.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\sin(z) = \\frac{a \\sin(x) + b \\sin(y)}{c \\sin(x) + d \\sin(y)}\n\\end{equation}\n\nThe variables a, b, c, d, x, and y are defined as follows:\n\na = 1, b = 2, c = 3, d = 4, x = 5, and y = 6.",
|
|
"gt_answers": "\\sin \\angle 3 = \\frac { A D } { A C } = \\frac { A O } { O C } = \\frac { 5 } { 5 \\sqrt { 5 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_49.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 538-384=154.",
|
|
"gt_answers": "5 \\frac { 1 } { 2 } - 3 x = a + \\frac { 1 } { 4 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_50.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\vert \\overrightarrow { b } \\vert = \\sqrt { \\vert \\overrightarrow { b } \\vert ^ { 2 } } = \\sqrt { \\overrightarrow { b } \\cdot \\overrightarrow { b } } = \\sqrt { x _ { 2 } ^ { 2 } + y _ { 2 } ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_51.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "1 + a ^ { 2 } b ^ { 2 } - a ^ { 2 } - b ^ { 2 } > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_52.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"225x10^2 + 12x10^1 + 5x10^0 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "x = \\frac { 2 2 5 } { 2 } \\times \\frac { 1 0 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_53.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SQRT(x^2 + y^2 - 2xy) = 2x + y.\"",
|
|
"gt_answers": "S _ { \\Delta A O V } = \\frac { 1 } { 2 } \\times 4 \\times 6 = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_54.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(A + B = C\\)\n\nThis is a basic algebraic equation that represents the addition of two numbers.",
|
|
"gt_answers": "A H = 3 k B H = 4 k\n",
|
|
"image_path": "./data/HME100K/test_images/test_55.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 4\\)",
|
|
"gt_answers": "\\frac { x ^ { 2 } } { 4 } + \\frac { y ^ { 2 } } { 2 } = 1 ( \\vert x \\vert \\neq 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_61.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(3x^2 + 2x - 9 = 0\\)\n\nThis formula can be written using LaTeX as follows:\n\n\\(3x^2 + 2x - 9 = 0\\)\n\nThe LaTeX code for the formula is:\n\n\\begin{equation}\n3x^2 + 2x - 9 = 0\n\\end{equation}\n\nThe equation is written in the form of an equation with the variable x on the left side and the expression on the right side. The equation is also written in the form of an equation with the variable x squared on the left side and the expression on the right side.",
|
|
"gt_answers": "\\frac { 2 x } { 3 } = \\frac { 4 x - 8 } { 9 } - 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_62.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 3x^2 - 6x + 1.",
|
|
"gt_answers": "x = - \\frac { 6 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_64.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2} + \\frac{3x}{2} + 1\\)",
|
|
"gt_answers": "( x + 1 ) ^ { 2 } - 4 = ( x + 1 ) ( x - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_65.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(x^2 + 2x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x ^ { 2 } + a x ^ { 2 } + a ^ { 2 } x - a x ^ { 2 } - a ^ { 2 } x - a\n",
|
|
"image_path": "./data/HME100K/test_images/test_66.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 6 0 0 0 c m ^ { 3 } = 3 6 d m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_67.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/2 + 1/3 = 1/6.\"",
|
|
"gt_answers": "x - y = - \\frac { 1 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_68.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 0.055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555",
|
|
"gt_answers": "0 . 5 < 0 . 5 0 1 < 0 . 5 1 < 0 . 5 1 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_70.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 8/3 = 2.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666",
|
|
"gt_answers": "\\frac { 8 } { 8 } - \\frac { 7 } { 8 } = \\frac { 1 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_71.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 28 - 14 x 2 = 42.",
|
|
"gt_answers": "\\frac { 2 8 } { 4 2 } = \\frac { 1 4 \\times 2 } { 1 4 \\times 3 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_72.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{9.216}{22.6} = 0.429\n\\end{equation}\n\nThis equation is a fraction with the numerator being 9.216 and the denominator being 22.6. The result of the equation is 0.429.",
|
|
"gt_answers": "9 x - 5 , 2 = 2 1 . 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_73.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\nW = 120 - 2(a + b) + 2(c + d) + 2(e + f) + 2(g + h) + 2(i + j) + 2(k + l) + 2(m + n) + 2(o + p) + 2(q + r) + 2(s + t) + 2(u + v) + 2(w + x) + 2(y + z)\n\nThis formula can be used to calculate the total distance traveled by a car along a road with 20 turns, where each turn is 10 meters long.",
|
|
"gt_answers": "W = ( 1 2 0 - a ) m + 1 0 0 ( 3 0 0 - m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_74.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x _ { 1 } = \\sqrt { 2 } x _ { 2 } = - \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_75.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = a + bx + cx^2 + dx^3 + ex^4 + fx^5 + gx^6 + hx^7 + ix^8 + jx^9 + kx^{10} + lx^{11} + mx^{12} + nx^{13} + ox^{14} + px^{15} + qx^{16} + rx^{17} + sx^{18} + tx^{19} + ux^{20} + vx^{21} + wx^{22} + wy^{23} + x^{24} + y^{25} + z^{26} + x^{27} + y^{28} + z^{29} + x^{30} + y^{31} + z^{32} + x^{33} + y^{34} + z^{35} + x^{36} + y^{37} + z^{38} + x^{39} + y^{40} + z^{41} + x^{42} + y^{43} + z^{44} + x^{45} + y^{46} + z^{47} + x^{48} + y^{49} + z^{50} + x^{51} + y^{52} + z^{53} + x^{54} + y^{55} + z^{56} + x^{57} + y^{58} + z^{59} + x^{60} + y^{61} + z^{62} + x^{63} + y^{64} + z^{65} + x^{66} + y^{67} + z^{68} + x^{69} + y^{70} + z^{71} + x^{72} + y^{73} + z^{74} + x^{75} + y^{76} + z^{77} + x^{78} + y^{79} + z^{80} + x^{81} + y^{82}",
|
|
"gt_answers": "\\therefore F 1 8 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_76.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(100 \\text{kg} \\cdot 200 \\text{kg} = 20,000 \\text{kg} \\cdot \\text{m}^2\\)\n\nThis formula calculates the mass of a cube with a side length of 200 meters. The mass of the cube is equal to the product of the cube's volume (20,000 m^3) and its mass per unit volume (100 kg/m^3).",
|
|
"gt_answers": "1 0 0 = 2 0 0 k + b\n",
|
|
"image_path": "./data/HME100K/test_images/test_77.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4 - 2 = 2\".",
|
|
"gt_answers": "x _ { 3 } = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_78.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 1 } { 5 } \\times 1 0 0 0 = 2 0 0 ( g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_79.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. In this case, the variable is a, which is the square of the first term in the equation. The other two terms are b and c, which are the squares of the second and third terms respectively. The equation states that the sum of the squares of the first two terms (a and b) is equal to the square of the third term (c).",
|
|
"gt_answers": "\\angle A E D = \\angle D A E = \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } -\n",
|
|
"image_path": "./data/HME100K/test_images/test_80.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { x ^ { 2 } + 1 } { x + 1 } - \\frac { 2 } { x + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_81.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(30 \\times 30 \\times 30 = 27000\\)",
|
|
"gt_answers": "3 0 - 3 = 2 7 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_82.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3y^2 + 9b^2 + 3y + 3b + 3 = 0\\)",
|
|
"gt_answers": "3 y - 2 = 9 - 6 \\sqrt { y + 3 } + y + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_83.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 3.1415926535897932384626433832795028841971693993751058209749445923078163978418157067982148481117530248967187537679867938564821185679323076793176679381968428810975665933446482534211706798271260967932772413766034861274809628848111753024896718753767938564821185679323076793176679381968428810975665933446482534211706798271260967932772413766034861274809628848111753024896718753767938564821185679323076793176679381968428810975665933446482534211706798271260967932772413766034861274809628848111753024896718753",
|
|
"gt_answers": "3 . 1 4 \\times 5 \\times 8 = 1 2 5 . 6 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_85.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "v = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_86.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as Fe(OH)4 + 2H2O = Fe(OH)2 + 2H2O.",
|
|
"gt_answers": "F e + H _ { 2 } S O 4 = F e _ { 5 } S O _ { 4 } + H 2 \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_87.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"443 + 234 = 677\" using LaTeX format.",
|
|
"gt_answers": "\\angle 2 + \\angle 3 = \\angle E B F = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_88.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 5x3x4x60 = 1800.",
|
|
"gt_answers": "5 \\times 3 \\times 4 = 6 0 ( d m ) ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_89.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "a m + b n > a n + b m > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_90.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 7y = 14.\"",
|
|
"gt_answers": "2 x = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_91.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `x^2 + 5x + 8 = 0`.",
|
|
"gt_answers": "x = \\frac { 5 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_92.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x + 2y = 10\\)\n\nThis formula represents the relationship between the variables x and y, where 3x + 2y = 10.",
|
|
"gt_answers": "\\frac { 1 } { 4 } \\div \\frac { 3 } { 2 } = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_93.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n3x + y = 12\n\nThe equation is written in the form of an algebraic equation, with the variables x and y on the left side and the constant 12 on the right side.",
|
|
"gt_answers": "3 x _ { ( g ) } + y _ { ( g ) } \\rightleftharpoons 2 z ( g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_94.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which are not supported by LaTeX. However, I can provide a rough translation of the characters into English: \"The sum of the squares of the first 100 natural numbers is equal to the sum of the squares of the first 100 even numbers.\"",
|
|
"gt_answers": "x + 1 = \\pm \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_95.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(K = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "\\frac { 2 x } { x - 2 } = \\frac { 2 - x } { 2 - x } - \\frac { 1 } { 2 - x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_96.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4^{4} \\cdot 5^{5} \\cdot 6^{6} \\cdot 7^{7} \\cdot 8^{8} \\cdot 9^{9} \\cdot 10^{10} \\cdot 11^{11} \\cdot 12^{12} \\cdot 13^{13} \\cdot 14^{14} \\cdot 15^{15} \\cdot 16^{16} \\cdot 17^{17} \\cdot 18^{18} \\cdot 19^{19} \\cdot 20^{20} \\cdot 21^{21} \\cdot 22^{22} \\cdot 23^{23} \\cdot 24^{24} \\cdot 25^{25} \\cdot 26^{26} \\cdot 27^{27} \\cdot 28^{28} \\cdot 29^{29} \\cdot 30^{30} \\cdot 31^{31} \\cdot 32^{32} \\cdot 33^{33} \\cdot 34^{34} \\cdot 35^{35} \\cdot 36^{36} \\cdot 37^{37} \\cdot 38^{38} \\cdot 39^{39} \\cdot 40^{40} \\cdot 41^{41} \\cdot 42^{42} \\cdot 43^{43} \\cdot 44^{44} \\cdot 45^{45} \\cdot 46^{46} \\cdot 47^{47} \\cdot 48^{48} \\cdot 49^{49} \\cdot 50^{50} \\cdot 51^{51} \\cdot 52^{52} \\cdot 53^{53} \\cdot 54^{54} \\cdot 55^{55} \\cdot 56^{56} \\cdot 57^{57} \\cdot 58^{58} \\cdot 59^{59} \\cdot 60",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_97.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 100 - 0.05x^2 + 0.005x^3 + 0.0005x^4 + 0.00005x^5 + 0.000005x^6.",
|
|
"gt_answers": "- 1 0 - \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_98.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5x + 2.\"",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = \\frac { 2 } { 3 } \\times 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_101.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `a^2 + b^2 = c^2`.",
|
|
"gt_answers": "1 0 a + 1 5 0 - 1 5 a \\geq\n",
|
|
"image_path": "./data/HME100K/test_images/test_102.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "B D ^ { 2 } - A B ^ { 2 } - A D ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_103.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `y = a + bx + c(x^2 + y^2)`.",
|
|
"gt_answers": "( 1 ) a ^ { x } _ { 2 } = a _ { 1 } + ( 2 - 1 ) d\n",
|
|
"image_path": "./data/HME100K/test_images/test_105.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is represented by the letter \"c,\" the side opposite the right angle is represented by \"a,\" and the side adjacent to the right angle is represented by \"b.\"",
|
|
"gt_answers": "2 ^ { 2 } + b ^ { 2 } = a ^ { 2 } + b ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_106.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2NaCl + 2H2SO4 \\rightarrow 2NaHSO4 + Cl2 + H2O\\)",
|
|
"gt_answers": "2 N a O H + C u S O _ { 4 } = C u ( O H ) _ { 2 } \\downarrow + N a _ { 2 } S O _ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_109.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x + 2 = 12.",
|
|
"gt_answers": "\\frac { x } { 3 } + \\frac { a + x } { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_110.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `a^2 + b^2 = c^2`.",
|
|
"gt_answers": "a = - 7 - ( 2 , s )\n",
|
|
"image_path": "./data/HME100K/test_images/test_111.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBOC = 120\u00b0.\"",
|
|
"gt_answers": "\\angle B O C = 1 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_112.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 2x - 1 = 0\\)",
|
|
"gt_answers": "a _ { 2 } = 3 b _ { 2 } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_113.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1500x300x500x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000x1000",
|
|
"gt_answers": "1 5 0 0 \\times \\frac { 1 } { 5 } = \\frac { 1 5 0 0 \\times 1 } { 5 } = \\frac { 1 5 0 0 } { 5 } = \\frac { 3 0 0 } { 5 } =\n",
|
|
"image_path": "./data/HME100K/test_images/test_114.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x + 3y = 5\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 c } + \\frac { 1 } { 2 a } \\geq \\frac { 2 } { c + a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_115.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(L_{RT} = \\frac{RT}{R_{T} + R_{S}}\\)\n\nwhere RT is the resistance of the thermistor, RS is the resistance of the sensor, and L is the total resistance of the circuit.",
|
|
"gt_answers": "l = R + R \\sin 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_116.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"X2 + 7x - 9 = 420.\"",
|
|
"gt_answers": "x - 5 - 2 x + 7 - 4 \\sqrt { 2 x - 7 } - 4 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_117.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a + b = c\\)\n\nThis is a basic algebraic equation that represents the addition of two numbers, a and b, to equal a third number, c.",
|
|
"gt_answers": "a n c = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_118.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "k > 0 E ( - \\infty , - \\frac { 1 } { k } ) \\downarrow ( - \\frac { 1 } { k } , - \\infty ) \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_119.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, but it can be translated to English as follows:\n\n\\(4x^2 + 3x - 1 = 0\\)",
|
|
"gt_answers": "x = \\frac { B E } { A B } = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_120.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 c m : 6 0 0 m = 2 c m : 6 0 0 0 0 c m = 1 : 3 0 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_121.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2m + 1 = 3m\".",
|
|
"gt_answers": "\\frac { m ^ { 2 } + 4 } { m ^ { 2 } - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_122.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a + b = c\\)\n\nThis formula represents the basic algebraic equation of addition, where a, b, and c are variables and represent the values of the terms on the left and right sides of the equation.",
|
|
"gt_answers": "+ a _ { 6 } + ( a _ { 3 } + a _ { 8 } ) = 5 + 5 + 5 + 5 + 5 = 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_124.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{x^2 + 3x + 4}{2x + 3} + 1\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(y = \\frac{x^2 + 3x + 4}{2x + 3} + 1\\)\n\nThe formula is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "x _ { 1 } = n + 2 , x _ { 2 } = 2 ( n + 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_125.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is the equation of energy, also known as the mass-energy equivalence formula. It states that the energy (E) of an object is equal to the mass (m) of the object multiplied by the speed of light squared (c^2).",
|
|
"gt_answers": "- x = m + 1 , y = - m - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_126.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 4x12 + 4x18 + 3x24 + 3x30 + 6x36 + 6x42 + 8x48 + 8x54 + 10x60 + 10x66 + 12x72 + 12x78 + 14x84 + 14x90 + 16x96 + 16x102 + 18x108 + 18x114 + 20x120 + 20x126 + 22x132 + 22x138 + 24x144 + 24x150 + 26x156 + 26x162 + 28x168 + 28x174 + 30x180 + 30x186 + 32x192 + 32x198 + 34x204 + 34x210 + 36x216 + 36x222 + 38x228 + 38x234 + 40x240 + 40x246 + 42x252 + 42x258 + 44x264 + 44x270 + 46x276 + 46x282 + 48x288 + 48x294 + 50x300 + 50x306 + 52x312 + 52x318 + 54x324 + 54x330 + 56x336 + 56x342 + 58x348 + 58x354 + 60x360 + 60x366 + 62x372 + 62x378 + 64x384 + 64x390 + 66x396 + 66",
|
|
"gt_answers": "\\frac { 4 \\times 1 2 } { 4 8 } + \\frac { ( 8 - 4 ) } { 4 } \\times 3 = 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_127.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3 = 2 + 1.",
|
|
"gt_answers": "\\frac { 3 } { 2 } = \\frac { 2 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_128.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 4x + 24 = 0`.",
|
|
"gt_answers": "x = \\frac { 2 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_129.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible for me to accurately transcribe it into LaTeX format. However, I can provide a rough translation of the expression: \"The sum of the squares of the first 100 natural numbers.\"",
|
|
"gt_answers": "x = \\frac { 2 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_130.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2H2O + CO2 + Li2CO3 + 2H2O.",
|
|
"gt_answers": "2 L i O H + C O _ { 2 } = L i _ { 2 } C O _ { 3 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_131.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(3p + 3q = 9\\)",
|
|
"gt_answers": "\\therefore D P = \\frac { - 3 + \\sqrt { 6 9 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_132.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6x + 2y = 12.\"",
|
|
"gt_answers": "\\sin \\alpha x = \\alpha\n",
|
|
"image_path": "./data/HME100K/test_images/test_133.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x + 4 = 4x + 4.",
|
|
"gt_answers": "3 x - \\frac { 3 } { 4 } = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_134.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 22 - 6 + 55 - 3 = 10.",
|
|
"gt_answers": "\\frac { 2 7 } { 2 } - 6 + 3 \\sqrt { 3 } + \\frac { 9 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_135.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "y ( 2 y + x ) = 0 \\cdot \\therefore y\n",
|
|
"image_path": "./data/HME100K/test_images/test_136.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(x^2) + 2(y^2) = 1000.",
|
|
"gt_answers": "1 0 0 y \\times 2 \\times 2 = 1 0 0 x \\times 1 \\times 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_137.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: y = 3x^2 + 2x + 1.",
|
|
"gt_answers": "y = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_139.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"R(D)K(r) + K(r)D(r) + K(r)K(r)\".",
|
|
"gt_answers": "k \\geq 0 . k \\geq \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_140.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ADLBBL.\"",
|
|
"gt_answers": "A D \\bot B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_141.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a Chinese character in the middle, which could be a symbol or a word.",
|
|
"gt_answers": "2 t - \\frac { 2 5 } { 2 4 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_143.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x - 5 = 0\\)",
|
|
"gt_answers": "I _ { 1 } : I _ { 2 } = 3 : 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_144.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4} \\).",
|
|
"gt_answers": "\\cdot E G = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_145.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Rethold = 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/2 + 1/2 * (1/",
|
|
"gt_answers": "F e + H _ { 2 } S O _ { 4 } = F e S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_146.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x + 4 = 12.",
|
|
"gt_answers": "x = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_148.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(y = 27.44 + 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "( y - 2 ) ( y + 1 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_149.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4-2\\sqrt{2} = 2\\sqrt{2} - 2\\sqrt{2} = 0\\)",
|
|
"gt_answers": "4 - 2 h = \\sqrt { h ^ { 2 } + r ^ { 2 } } . \\textcircled { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_151.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "\\sqrt { x + 4 5 } - 2 x + 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_153.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x10y = 100.",
|
|
"gt_answers": "\\frac { 1 } { 4 } x + \\frac { 3 } { 1 0 } y = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_154.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis equation represents the basic mathematical operation of multiplication, where the first term is multiplied by the second term, resulting in a fraction with a denominator of 4.",
|
|
"gt_answers": "x = \\frac { 3 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_155.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
|
|
"gt_answers": "( 8 9 9 9 ) < ( 9 0 0 1 ) < ( 9 8 9 9 ) < ( 9 9 9 9 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_156.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LPF(x) = 0.5x^2 + 0.5x - 100\".",
|
|
"gt_answers": "\\angle P F E = 1 8 0 ^ { \\circ } - \\angle 1 - 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_158.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SOA: if(a, b, c)\".",
|
|
"gt_answers": "S _ { \\Delta } A F C = \\frac { 1 } { 2 } A F \\cdot B C = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_159.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3(60x3) + 180(60x3) + 45(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3(60x3) = 180(60x3) + 45(60x3) + 3",
|
|
"gt_answers": "6 0 \\times \\frac { 3 } { 4 } = \\frac { 6 0 \\times 3 } { 4 } = \\frac { 1 8 0 } { 4 } = 4 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_161.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 4 0 ^ { \\circ } - 5 m + 5 m - 5 0 ^ { \\circ } = 9 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_163.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 - 7x + 5 = 0`.",
|
|
"gt_answers": "x > - \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_164.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "\\frac { x + 2 } { 3 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_165.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "E H = \\sqrt { x ^ { 2 } - x ^ { 2 } + 5 x - \\frac { 2 5 } { 4 } } =\n",
|
|
"image_path": "./data/HME100K/test_images/test_166.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 4\\)\n\nThis formula represents the relationship between two variables, x and y, where the sum of their values is equal to 4.",
|
|
"gt_answers": "I = \\frac { Q } { t } = \\frac { 2 } { 4 } = 0 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_167.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LAOFEL3-40=0\" using the LaTeX formula notation.",
|
|
"gt_answers": "\\angle A O F = \\angle 3 = 4 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_168.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2(x+2) = 4(x+1) + 2(x+1) = 4x + 4 + 2x + 2 = 4x + 6\\)",
|
|
"gt_answers": "( 4 2 \\div 2 ) + 2 = 2 3 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_169.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2H2O + O2 = 2H2O + 2H2O.",
|
|
"gt_answers": "2 N a O H + C O _ { 2 } = O N a _ { 2 } C O _ { 3 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_170.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(n^2 + n + 1 = 2n^2 + 2n + 1\\)",
|
|
"gt_answers": "n ( n + 2 ) + 1 = ( n + 1 ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_171.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\left(LBAC + 48\\right) = 100\\)\n\nThe formula is a simple algebraic equation that involves the variables LBAC (left-hand side) and 48 (right-hand side). The equation states that the sum of the left-hand side and the right-hand side is equal to 100.",
|
|
"gt_answers": "\\angle P A C = \\frac { 1 } { 2 } \\angle B A C = 4 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_172.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\nLbod + Lcop = 0.5Lbodcos(90\u00b0 - \u03b8) + 0.5Lcopcos(\u03b8)\n\nwhere Lbod is the length of the body, Lcop is the length of the cop, and \u03b8 is the angle between the body and the cop.",
|
|
"gt_answers": "\\angle B O D + \\angle C O D = 6 0 ^ { \\circ } + 3 0 ^ { \\circ } = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_173.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: `x^2 + 108x + 13 = 0`.",
|
|
"gt_answers": "x = \\frac { 1 0 8 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_174.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so I cannot provide a LaTeX representation of it. However, the formula is likely a mathematical expression involving the number 3.",
|
|
"gt_answers": "x = 3 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_175.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(30h = 30\\cdot 2^{2} = 30\\cdot 4 = 120\\)",
|
|
"gt_answers": "3 0 h = 2 7 \\Delta h - 8 \\Delta h\n",
|
|
"image_path": "./data/HME100K/test_images/test_176.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 30.4d9 - 10.",
|
|
"gt_answers": "3 a _ { 1 } + 9 d = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_177.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"I.B.B.D.C.R.A.B.B.D.C.R.A.B.B.D.C.R.A.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.B.D.C.R.A.B.B.",
|
|
"gt_answers": "1 \\sim 5 : B B D C B\n",
|
|
"image_path": "./data/HME100K/test_images/test_178.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"Cb = 255 - Cg\".",
|
|
"gt_answers": "\\angle B = \\angle C ^ { \\prime }\n",
|
|
"image_path": "./data/HME100K/test_images/test_179.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{1 + \\left( \\frac{1}{2} \\right)^2} = \\frac{1}{3}\n\\end{equation}\n\nThis formula can be simplified further to:\n\n\\begin{equation}\n\\frac{1}{3} = \\frac{1}{1 + \\left( \\frac{1}{2} \\right)^2}\n\\end{equation}\n\nThe equation is written using the `\\frac` command to indicate a fraction, and the `\\left( \\frac{1}{2} \\right)^2` expression is enclosed within parentheses to indicate that it is a square of a fraction.",
|
|
"gt_answers": "d = \\sqrt { a ^ { 2 } - 1 - \\frac { a ^ { 2 } - 1 } { 4 } } = \\frac { \\vert a ^ { 2 } - 1 \\vert } { \\sqrt { a - 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_180.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"B0-Dm, Omini\".",
|
|
"gt_answers": "B D = D M , D H \\bot B M\n",
|
|
"image_path": "./data/HME100K/test_images/test_181.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1}\\)",
|
|
"gt_answers": "( y + 1 ) ^ { 2 } + ( y + 1 ) y + y ^ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_182.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3(y-7) = 2(y-7) + 1(y-7) = 2y-14.",
|
|
"gt_answers": "\\frac { 1 } { 3 } + 1 1 y = 1 0 y - 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_183.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\sqrt { 1 3 ^ { 3 } - 5 ^ { 2 } } - \\sqrt { ( \\sqrt { 2 } - 1 ) ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_184.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(x - 1) - 3(x - 2) = 0.",
|
|
"gt_answers": "\\frac { 6 + a - 5 } { 5 } = \\frac { 1 0 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_185.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 64u^2 = 3`.",
|
|
"gt_answers": "x = \\frac { 6 4 0 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_186.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 1 7 } { 2 0 } > \\frac { 1 6 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_188.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "= s h = 1 . 0 \\times 1 0 ^ { - 3 } m ^ { 2 } \\times 0 . 2 m = 2 \\times 1 0 ^ { - 4 } m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_189.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444",
|
|
"gt_answers": "4 x ^ { 2 } - y ^ { 2 } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_190.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = \\frac{1}{2}mv^2\\)\n\nThis formula states that the energy (E) of an object is equal to one-half the product of its mass (m) and its velocity squared (v^2).",
|
|
"gt_answers": "I = \\frac { U } { R } = \\frac { 1 2 V } { 3 0 \\Omega } = 0 . 4 A\n",
|
|
"image_path": "./data/HME100K/test_images/test_192.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x + 20 = 20x + 20.",
|
|
"gt_answers": "\\frac { 7 } { + 7 + 3 } \\times 3 6 0 ^ { \\circ } = 2 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_193.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 15000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 . 5 < 0 . 5 0 1 < 0 . 5 1 < 0 . 5 1 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_194.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Lopa = LABC/60\" where Lopa is the length of the side of a square, LABC is the length of the side of a cube, and 60 is the number of minutes in an hour.",
|
|
"gt_answers": "\\angle O B A = \\angle A B C = 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_195.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `6x^2 + 10x - 30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "6 0 \\times 6 0 \\times 1 0 = 3 6 0 0 0 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_196.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x ^ { 2 } + ( 2 x - 1 ) ^ { 2 } + 3 ( 2 x - 1 ) + x + 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_197.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Noah's formula\" and is given as follows:\n\n\\(N = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) \\right) = \\frac{1}{4} + \\frac{1}{4} = \\frac{3}{4} \\text{, where N is the number of people in a group of four.}",
|
|
"gt_answers": "F _ { 1 } = 1 0 0 0 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_198.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3.6 - 4 = 0.4.",
|
|
"gt_answers": "\\frac { 3 . 6 } { 4 . 5 } = \\frac { 4 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_200.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x = \\frac{180\u00b0 - 20\u00b0}{180\u00b0 - 40\u00b0} \\times 180\u00b0 + 20\u00b0\\)\n\nThis formula can be rewritten as follows:\n\n\\(x = \\frac{160\u00b0}{180\u00b0 - 40\u00b0} \\times 180\u00b0 + 20\u00b0\\)\n\nThe result of this formula is the angle x in degrees, given the angles 180\u00b0 and 20\u00b0.",
|
|
"gt_answers": "\\angle 1 = 1 8 0 ^ { \\circ } - \\angle B A E = 1 8 0 ^ { \\circ } - 4 6 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_201.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `x^2 + 3x - 4 = 0`.",
|
|
"gt_answers": "x = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_202.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A = 486 - 861.\"",
|
|
"gt_answers": "a = \\frac { 9 5 } { 8 6 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_203.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. In this case, the variable is x, and the square of x is x^2. The variable y is also involved in the equation, and its square is y^2. The equation is solved by setting the two sides equal to each other, which results in the equation x^2 + y^2 = 1.",
|
|
"gt_answers": "2 4 0 \\times 3 = 7 2 0 2 4 0 \\times 4 = 9 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_204.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( x - ) ( 3 x + 2 ) - 3 x ( x + 3 ) + 1 0 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_205.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{4} + \\frac{1}{4} + \\frac{1}{4} + \\frac{1}{4} = \\frac{1}{2}\n\\end{equation}\n\nThis equation represents the sum of four identical fractions, each with a denominator of 4. The numerator of each fraction is 1, resulting in a total of four equal fractions. The sum of these fractions is equal to the numerator of the first fraction, which is 1, divided by the denominator of the first fraction, which is 4. Therefore, the sum of the four fractions is equal to 1/2.",
|
|
"gt_answers": "\\frac { 1 } { 6 } < \\frac { 4 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_206.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(J_b = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "y = \\pm \\frac { \\sqrt { b ^ { 2 } + 1 } } { b ^ { 2 } + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_207.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2(3-2) + 3(2-1) + 4(1-0) = 12.",
|
|
"gt_answers": "\\frac { 2 } { 2 } - \\frac { 6 } { 2 } + 2 = 1 - 3 + 2 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_208.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: Zn(OH)2 + H2SO4 + 2H2O --> ZnSO4 + 2H2O + 2OH.",
|
|
"gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_209.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{",
|
|
"gt_answers": "x = - \\frac { 5 } { 1 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_210.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a = \\frac{b^2}{2c}\\)",
|
|
"gt_answers": ". a _ { 1 } = - \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_211.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x = 30/4\".",
|
|
"gt_answers": "x _ { 2 } = \\frac { 3 \\sqrt { 6 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_212.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "\\frac { 5 } { 1 4 } - \\frac { 1 } { 6 } = \\frac { 2 } { 2 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_213.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x + 2y = 16.",
|
|
"gt_answers": "\\frac { 1 6 } { 3 } x = \\frac { 3 2 } { 3 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_214.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SNS + WO = O2.\"",
|
|
"gt_answers": "2 N O + O _ { 2 } \\rightarrow 2 N O _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_215.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(0.064444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444",
|
|
"gt_answers": "0 . 6 6 > 0 . 6 4 > 0 . 6 0 6 > 0 . 6 0 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_218.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 - 2x + 1 = 0\\)",
|
|
"gt_answers": "\\rho _ { N A } : y = \\frac { 3 } { 2 } x - 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_219.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x^2 - 3x + 1.",
|
|
"gt_answers": "x + y - \\sqrt { x + y } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_221.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 5\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } ( 3 0 \\% x - 4 ) = 2 0 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_222.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(cos(B) = \\frac{a^2 + b^2 - 2ab \\cos(C)}{2ab} \\tag{1}\\label{formula1}`",
|
|
"gt_answers": "\\cos \\beta = \\frac { 3 } { 2 } \\cos \\alpha\n",
|
|
"image_path": "./data/HME100K/test_images/test_223.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"C2H4O2 + 2H2O --> 2CO2 + 4H2O + 2O2.\"",
|
|
"gt_answers": "C Q = B C - B Q = 6 0 - 2 0 \\sqrt { 3 } ( m\n",
|
|
"image_path": "./data/HME100K/test_images/test_224.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"500 + 480 = 980\".",
|
|
"gt_answers": "5 0 0 \\approx 4 8 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_225.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 21x2 - 21x1 - 21x0.",
|
|
"gt_answers": "3 - 1 - 2 \\times \\frac { 1 } { 2 } = 3 - 1 - 1 = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_226.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Nazco4H2SO4\" using LaTeX format.",
|
|
"gt_answers": "N a _ { 2 } C O _ { 3 } + H _ { 2 } S O _ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_228.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 - y^2}{x^2 + y^2} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{y^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^2 + y^2}}{1 + \\frac{x^2}{x^2 + y^2}} = \\frac{1 - \\frac{y^2}{x^",
|
|
"gt_answers": "( x - 1 ) ( 3 a x ^ { 2 } - 3 a x - 1 ) \\geqslant 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_231.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2n + 17 = 100.",
|
|
"gt_answers": "\\frac { 2 n } { 2 n + 1 } = \\frac { 1 7 } { 3 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_232.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\sqrt{3} \\cdot 11 = 22.66\\)",
|
|
"gt_answers": "2 \\sin ( A - \\frac { \\pi } { 6 } ) = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_233.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 1/2 x^2 + 3/4 x + 1.",
|
|
"gt_answers": "y _ { 1 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_234.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "( t ^ { 2 } - \\sqrt { 2 } ) ( t ^ { 2 } + \\sqrt { 2 } t + 1 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_235.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\( \\sin(x) = \\frac{ADC}{BC} \\cdot \\sin(y) \\cdot \\cos(z) \\)\n\nThe formula is a trigonometric function that calculates the sine of an angle in terms of the sides of a triangle. The sides of the triangle are represented by the letters A, B, and C, and the angle is represented by the letter x. The formula uses the ratio of the side lengths ADC to the side length BC to calculate the sine of the angle.",
|
|
"gt_answers": "\\angle A D C = 1 8 0 ^ { \\circ } - 6 0 ^ { \\circ } = 1 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_237.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - 1) - 2(m - 1) = 2(7 - 2) + 3(m - ",
|
|
"gt_answers": "\\frac { x } { x - 3 } - 2 m = \\frac { 3 m - 1 } { x - 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_239.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBossts = 180\u00b0 - 20\u00b0\".",
|
|
"gt_answers": "\\angle B O S + \\angle S = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_240.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(3x^2 + 4x + 5 = 10\\)",
|
|
"gt_answers": ". ( - 4 ) + 7 + ( - 9 ) + 8 + 6 + ( - 4 ) + ( - 3 ) = 1 k m\n",
|
|
"image_path": "./data/HME100K/test_images/test_242.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(12 \\times 11 = 132\\)",
|
|
"gt_answers": "\\frac { 1 } { \\sqrt { 2 } - 1 + 1 } = \\frac { 1 } { \\sqrt { 2 } } = \\frac { \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_243.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"280-506-300\".",
|
|
"gt_answers": "2 8 0 \\div 5 0 = 6 \\cdots 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_244.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 100.\"",
|
|
"gt_answers": "x - a ^ { 5 } = - \\frac { 1 } { b \\sqrt { 1 0 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_248.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{a^2 + b^2}{2} + \\frac{a^2 - b^2}{2} = a^2 + b^2\n\\end{aligned}\n\\end{equation}\n\nThis equation is a simple algebraic expression that shows the relationship between the square of the sum of two numbers and the square of the difference between those numbers.",
|
|
"gt_answers": "\\frac { 1 } { a + b } = - \\frac { 1 } { 2 - 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_251.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(cos(5\\pi/6) = \\cos(3\\pi/4) \\cos(1\\pi/4) \\cos(1/4) \\cos(1/16) \\cos(1/32) \\cos(1/64) \\cos(1/128) \\cos(1/256) \\cos(1/512) \\cos(1/1024) \\cos(1/2048) \\cos(1/4096) \\cos(1/8192) \\cos(1/16384) \\cos(1/32768) \\cos(1/65536) \\cos(1/131072) \\cos(1/262144) \\cos(1/524288) \\cos(1/1048576) \\cos(1/2097152) \\cos(1/4194304) \\cos(1/8388608) \\cos(1/16777216) \\cos(1/33554432) \\cos(1/67108864) \\cos(1/134217728) \\cos(1/268435456) \\cos(1/536870912) \\cos(1/1073741824) \\cos(1/2147483648) \\cos(1/4294967296) \\cos(1/8589934592) \\cos(1/17179869184) \\cos(1/34359738368) \\cos(1/687194767368) \\cos(1/137438958792) \\cos(1/275879987768) \\cos(1/5517",
|
|
"gt_answers": "\\cos \\angle A B C = \\frac { 5 } { 1 3 } = \\frac { B D } { A B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_252.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x2 + 2x2 = 4x2.\"",
|
|
"gt_answers": "x - \\frac { x - 1 } { 4 } = 2 \\times \\frac { x - 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_253.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 112 + 44 = 888.",
|
|
"gt_answers": "\\frac { 1 1 7 } { 4 9 } = \\frac { y } { 8 . 8 y }\n",
|
|
"image_path": "./data/HME100K/test_images/test_254.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 2 = 7.\"",
|
|
"gt_answers": "\\frac { 5 } { 6 } \\times \\frac { 6 } { 5 } \\textcircled { = } \\frac { 3 } { 7 } \\times \\frac { 7 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_256.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"y = 2x^2 + 3x + 4.\"",
|
|
"gt_answers": "y = \\frac { 1 } { 3 } x ^ { 2 } + b x + c\n",
|
|
"image_path": "./data/HME100K/test_images/test_257.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac",
|
|
"gt_answers": "6 x - 1 0 - 7 x - 6 x + 2 x + 2 = 3 x - 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_258.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 11x^2 + 384x + 11 = 0.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x - 1 1 1 + x = 8 3 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_259.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 6299 + 3x5 = 13x5.",
|
|
"gt_answers": "6 2 9 \\div 1 3 = 4 8 \\cdots 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_262.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 8x - 4 = 0\\)",
|
|
"gt_answers": "\\frac { 1 } { 3 } [ \\frac { 1 } { 4 } ( \\frac { 1 } { 5 } x - 2 ) - 8 ] = - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_263.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(3.141592653589793238462643383279502884197169399375105820974944592307816406286208998629489549303844609550588270277815948309171679811326072643383279502884197169399375105820974944592307816406286208998629489549303844609550588270277815948309171679811326072643383279502884197169399375105820974944592307816406286208998629489549303844609550588270277815948309171679811326072643383279502884197169399375105820974944592307816406286208998629489549303844609550588270277815948309171679811326072643383279502884",
|
|
"gt_answers": "3 . 1 4 \\times 4 0 = 1 2 5 . 6 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_264.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(a^2 + b^2 = c^2\\)\n\nwhere a, b, and c are real numbers.",
|
|
"gt_answers": "a \\geq - \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_265.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 179.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
|
|
"gt_answers": "v = \\frac { m } { \\rho } = \\frac { 1 0 2 7 k g } { 7 . 9 g / c m ^ { 3 } } = 1 3 0 0 0 0 c m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_266.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 80\\)",
|
|
"gt_answers": "8 0 \\% x + 1 5 0 = 5 0 0 \\times 6 0 \\% + 3 0 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_267.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x _ { 1 } = \\sqrt { 5 } + 1 , x _ { 2 } = 1 - \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_268.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Detect(C) = DC/3.5cm\".",
|
|
"gt_answers": "D E + E C = D C = 3 . 5 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_269.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Arabic script, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Arabic.",
|
|
"gt_answers": "1 = - 1 , x _ { 2 } = \\frac { 5 \\cdot } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_270.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\nBE = DF \\times Y\n\\end{equation}\n\nThe equation represents the relationship between the beam's bending moment (BE), deflection (DF), and Young's modulus (Y).",
|
|
"gt_answers": "\\therefore B E = D F = y\n",
|
|
"image_path": "./data/HME100K/test_images/test_271.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 100/111 = 0.8889.",
|
|
"gt_answers": "\\frac { 1 0 6 } { x } = \\frac { \\cdot 1 0 0 } { 2 0 3 } = \\frac { 1 1 7 } { y }\n",
|
|
"image_path": "./data/HME100K/test_images/test_272.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 15x4 = 60kg.",
|
|
"gt_answers": "1 5 \\times 4 = 6 0 ( k g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_273.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(x^2 + 2x + 3 = 0\\)\n\nThis formula represents a quadratic equation in the variable x.",
|
|
"gt_answers": "8 ( 7 x - 1 ) - 1 2 ( 5 x + 1 ) = 4 8 - 6 ( 3 x + 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_276.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LBLC_{8-10}LBAC_{8-10} = 8.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
|
|
"gt_answers": "\\cdot \\angle B = ^ { \\prime } \\angle C = \\frac { 1 8 0 ^ { \\circ } - \\angle B A C } { 2 } = \\frac { 8 0 ^ { \\circ } } { 2 } = 4 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_278.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as CD = 400 + 500.",
|
|
"gt_answers": "C D = 4 \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_279.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(N_A = \\frac{N_A^0}{1 + \\left(\\frac{N_A^0}{N_A^1}\\right)^2}\\)\n\nThe formula is a mathematical expression that describes the relationship between the number of atoms in a molecule and the number of atoms in a cluster of molecules. The first term on the left-hand side represents the number of atoms in a single molecule, which is denoted by \"N_A^0.\" The second term on the left-hand side represents the number of atoms in a cluster of molecules, which is denoted by \"N_A^1.\" The right-hand side of the equation represents the ratio of the number of atoms in the cluster to the number of atoms in a single molecule, which is given by the exponent of the second term. The exponent is squared, which means that the number of atoms in the cluster is multiplied by itself twice. The result of this multiplication is then divided by the number of atoms in a single molecule, which is represented by the first term. The overall expression can be interpreted as the ratio of the number of atoms in a cluster to the number of atoms in a single molecule, which is a measure of the size of the cluster compared to the size of the molecule.",
|
|
"gt_answers": "N a O H + H _ { 2 } O + C l _ { 1 } = Z N a C l + H C l O\n",
|
|
"image_path": "./data/HME100K/test_images/test_280.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 14.",
|
|
"gt_answers": "\\frac { 3 6 } { 4 } = \\frac { x } { 2 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_281.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = r^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is represented by the letter \"r,\" and the two sides are represented by the letters \"x\" and \"y.\"",
|
|
"gt_answers": "\\sin ( - \\frac { 8 7 } { 4 } \\pi ) = s i\n",
|
|
"image_path": "./data/HME100K/test_images/test_282.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 996^2\\)",
|
|
"gt_answers": "1 6 \\times 6 = 9 6 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_283.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "y = \\frac { 9 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_285.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 150(100x1) + 100(100x2) + 100(100x3) + 100(100x4) + 100(100x5) + 100(100x6) + 100(100x7) + 100(100x8) + 100(100x9) + 100(100x10) + 100(100x11) + 100(100x12) + 100(100x13) + 100(100x14) + 100(100x15) + 100(100x16) + 100(100x17) + 100(100x18) + 100(100x19) + 100(100x20) + 100(100x21) + 100(100x22) + 100(100x23) + 100(100x24) + 100(100x25) + 100(100x26) + 100(100x27) + 100(100x28) + 100(100x29) + 100(100x30) + 100(100x31) + 100(100x32) + 100(100x33) + 100(100x34) + 100(100x35) + 100(100x36) + 100(100x37) + 100(100x38) + 100(100x39) +",
|
|
"gt_answers": "7 5 0 + 1 5 0 ( x - 1 ) = \\frac { 3 0 0 x } { 2 } + \\frac { 1 0 0 x } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_287.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(7 - 42) = 14.",
|
|
"gt_answers": "\\frac { 7 } { 8 } = \\frac { 4 2 } { 4 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_288.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x + 3 = 6\\)",
|
|
"gt_answers": "\\frac { 1 2 } { 1 6 } = \\frac { 9 } { 1 2 } \u3001 \\frac { 4 } { 1 2 } > \\frac { 5 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_289.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Bd+1 = 2Bd-1\" using LaTeX format.",
|
|
"gt_answers": "\\frac { B D } { C P } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_290.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\" in LaTeX format.",
|
|
"gt_answers": "5 x = \\frac { 1 } { 2 } x + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_291.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"H2O + CO2 = H2CO3 + heat.\"",
|
|
"gt_answers": "C O _ { 2 } + C a ( O H ) _ { 2 } = C a C O _ { 3 } \\downarrow + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_292.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 4y = 16.",
|
|
"gt_answers": "x = \\frac { 1 6 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_293.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x + 3 x = 2 + 1 - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_294.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "P = e g h = 1 \\times 1 0 ^ { 3 } k g / m ^ { 3 } \\times 0 . 1 m \\times 9 . 8 N / k g = 9 8 0 P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_295.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { O E } { O B } = \\frac { O F } { O C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_296.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac",
|
|
"gt_answers": "x ^ { 2 } + x + 1 = ( x + \\frac { 1 } { 2 } ) ^ { 2 } + \\frac { 3 } { 4 } \\in [ - 1 , 1 ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_297.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(n \\ln(n) + n^2 \\ln(n) + n^3 \\ln(n) + n^4 \\ln(n) + n^5 \\ln(n) + n^6 \\ln(n) + n^7 \\ln(n) + n^8 \\ln(n) + n^9 \\ln(n) + n^{10} \\ln(n) + n^{11} \\ln(n) + n^{12} \\ln(n) + n^{13} \\ln(n) + n^{14} \\ln(n) + n^{15} \\ln(n) + n^{16} \\ln(n) + n^{17} \\ln(n) + n^{18} \\ln(n) + n^{19} \\ln(n) + n^{20} \\ln(n) + n^{21} \\ln(n) + n^{22} \\ln(n) + n^{23} \\ln(n) + n^{24} \\ln(n) + n^{25} \\ln(n) + n^{26} \\ln(n) + n^{27} \\ln(n) + n^{28} \\ln(n) + n^{29} \\ln(n) + n^{30} \\ln(n) + n^{31} \\ln(n) + n^{32} \\ln(n) + n^{33} \\ln(n) + n^{34} \\ln(n) + n^{35} \\ln(n) + n^{36} \\ln(n) + n^{37} \\ln(n) + n^{38} \\ln(n) + n^{39} \\ln(n) + n^{40} \\ln(n) + n^{41} \\ln(n) + n^{42} \\ln(n) + n^{43} \\ln(n) + n^{44} \\ln(n) + n^{45} \\ln(n) + n^{46} \\ln(n) + n^{47} \\ln(",
|
|
"gt_answers": "\\sin ( \\frac { \\pi } { 6 } + x ) = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_298.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 6 = 10\\)",
|
|
"gt_answers": "\\frac { 6 } { x + 1 } = \\frac { x - 8 } { 3 } + 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_299.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Lacobac-Tb0\" using the LaTeX formula notation.",
|
|
"gt_answers": "\\angle A C D + \\angle B A C = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_300.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 78.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.166.128.168 + 68.16",
|
|
"gt_answers": "x + 8 2 \\times 6 . 2 + 6 8 \\times 6 . 2 = 1 2 6 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_301.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{24\\times 32 \\times 56 \\times 78 \\times 100 \\times 112 \\times 123 \\times 134 \\times 145 \\times 156 \\times 167 \\times 178 \\times 189 \\times 190 \\times 201 \\times 212 \\times 223 \\times 234 \\times 245 \\times 256 \\times 267 \\times 278 \\times 289 \\times 290 \\times 301 \\times 312 \\times 323 \\times 334 \\times 345 \\times 356 \\times 367 \\times 378 \\times 389 \\times 390 \\times 401 \\times 412 \\times 423 \\times 434 \\times 445 \\times 456 \\times 467 \\times 478 \\times 489 \\times 500 \\times 511 \\times 522 \\times 533 \\times 544 \\times 555 \\times 566 \\times 577 \\times 588 \\times 599 \\times 600 \\times 611 \\times 622 \\times 633 \\times 644 \\times 655 \\times 666 \\times 677 \\times 688 \\times 699 \\times 700 \\times 711 \\times 722 \\times 733 \\times 744 \\times 755 \\times 766 \\times 777 \\times 788 \\times 799 \\times 800 \\times 811 \\times 822 \\times 833 \\times 844 \\times 855 \\times 866 \\times 877 \\times 888 \\times",
|
|
"gt_answers": "2 . 4 \\times ( 1 0 - 3 ) + 3 . 6 ( x - 1 0 ) + 1 2 = 3 2 . 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_302.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 7-445-00.",
|
|
"gt_answers": "x - 4 y + 5 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_303.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "y = - \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_304.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 + 100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 119 + 120 + 121 + 122 + 12",
|
|
"gt_answers": "\\frac { 4 } { 5 } S _ { A B C D } = 2 ( S _ { D B _ { 1 } C _ { 1 } } + S _ { B _ { 1 } C D _ { 2 } } + S _ { D _ { 2 } B A _ { 4 } } + S _ { C _ { 1 } A A _ { 4 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_306.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as NaOH + KOH = Na+ + K+ + OH-",
|
|
"gt_answers": "N a O H + K N O _ { 3 } = N a N O _ { 3 } + K O H\n",
|
|
"image_path": "./data/HME100K/test_images/test_307.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is: BD-ODE(BC).",
|
|
"gt_answers": "B D = O D = \\frac { 1 } { 2 } B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_308.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the chemical formula notation, which is a standard way to represent chemical compounds. The formula is written as CaCO3, which represents calcium carbonate, a compound that is commonly found in rocks, minerals, and shells.",
|
|
"gt_answers": "C a ( O H ) _ { 2 } + k _ { 2 } C O _ { 3 } = C a C O _ { 3 } \\downarrow + 2 k O H\n",
|
|
"image_path": "./data/HME100K/test_images/test_310.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 26.5 - 76.120 = 59.600.",
|
|
"gt_answers": "1 7 6 + 1 2 0 - 2 6 . 5 = 2 6 9 . 2 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_311.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"DE = 3D/O\" using LaTeX format.",
|
|
"gt_answers": "\\frac { D E } { O D } = \\frac { B D } { D E }\n",
|
|
"image_path": "./data/HME100K/test_images/test_312.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(6x^2 + 6x + 6 = 36x^2 + 12x + 6\\)",
|
|
"gt_answers": "\\pm \\sqrt { ( - 6 ) ^ { 2 } } = \\pm 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_313.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2 = 10.DB\".",
|
|
"gt_answers": "D E ^ { 2 } = D O \\cdot D B\n",
|
|
"image_path": "./data/HME100K/test_images/test_314.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n2x3 - 3x2 + 2x1 - 3x0 = 0",
|
|
"gt_answers": "2 x + y = 3 x + 6 y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_315.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "( 1 4 0 0 ) \\times ( 1 0 0 ) \\times ( 3 5 0 ) \\times ( 2 5 ) = ( 1 8 7 5 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_316.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBG = 2LBAC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2LBACC + 2",
|
|
"gt_answers": "\\angle B A G = \\frac { 1 } { 2 } \\angle B A C = 9 0 ^ { \\circ } - 2 \\alpha\n",
|
|
"image_path": "./data/HME100K/test_images/test_317.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": ". O A = \\sqrt { 1 ^ { 2 } + 4 ^ { 2 } } = \\sqrt { 1 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_318.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( 2 n + 1 ) b _ { n + 1 } - b _ { n + 1 } = n b _ { n }\n",
|
|
"image_path": "./data/HME100K/test_images/test_320.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "2 1 \\times 2 1 = 4 6 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_321.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: K = 19/199.",
|
|
"gt_answers": "k = \\frac { 1 9 } { 2 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_322.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(A + B + C = AD + BC + AB + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC + AD + BC +",
|
|
"gt_answers": "\\cdot \\frac { D C } { A O } = \\frac { A D } { B O } = \\frac { A C } { A B } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_323.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(F = \\frac{mg}{r^2}\\)\n\nThis formula represents the force of gravity acting on an object of mass m, which is proportional to the object's weight (mg) and inversely proportional to the square of its distance from the center of the Earth (r^2).",
|
|
"gt_answers": "V = \\frac { F + ( n + \\frac { 3 } { 4 } ) } { M } = W R\n",
|
|
"image_path": "./data/HME100K/test_images/test_324.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(K_a = \\frac{1}{2} \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{R_1} + \\frac{1}{R_2} \\right) \\left( \\frac{1}{",
|
|
"gt_answers": "x = ( 5 0 + k _ { 1 } \\times 5 0 ) c m ( k _ { 1 } = 1 , 2 , 3 \\cdots )\n",
|
|
"image_path": "./data/HME100K/test_images/test_325.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 144 - 3 = 141.",
|
|
"gt_answers": "1 4 \u3001 - \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_326.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\times k + 16\\times l + 72\\times m + 128\\times n = 1000\\)",
|
|
"gt_answers": "\\beta + \\alpha = 2 k \\pi + \\frac { \\pi } { 2 } ( k \\in z )\n",
|
|
"image_path": "./data/HME100K/test_images/test_327.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x _ { 1 } = - 5 x _ { 2 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_328.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x _ { 1 } = 0 x _ { 2 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_329.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(3\\cdot 4\\cdot 5\\cdot 6\\cdot 7\\cdot 8\\cdot 9\\cdot 10\\cdot 11\\cdot 12\\cdot 13\\cdot 14\\cdot 15\\cdot 16\\cdot 17\\cdot 18\\cdot 19\\cdot 20\\cdot 21\\cdot 22\\cdot 23\\cdot 24\\cdot 25\\cdot 26\\cdot 27\\cdot 28\\cdot 29\\cdot 30\\cdot 31\\cdot 32\\cdot 33\\cdot 34\\cdot 35\\cdot 36\\cdot 37\\cdot 38\\cdot 39\\cdot 40\\cdot 41\\cdot 42\\cdot 43\\cdot 44\\cdot 45\\cdot 46\\cdot 47\\cdot 48\\cdot 49\\cdot 50\\cdot 51\\cdot 52\\cdot 53\\cdot 54\\cdot 55\\cdot 56\\cdot 57\\cdot 58\\cdot 59\\cdot 60\\cdot 61\\cdot 62\\cdot 63\\cdot 64\\cdot 65\\cdot 66\\cdot 67\\cdot 68\\cdot 69\\cdot 70\\cdot 71\\cdot 72\\cdot 73\\cdot 74\\cdot 75\\cdot 76\\cdot 77\\cdot 78\\cdot 79\\cdot 80\\cdot 81\\cdot 82\\cdot 83\\cdot 84\\cdot 85\\cdot 86\\cdot 87\\cdot 88\\cdot 89\\cdot 90\\cdot 91\\cdot 92\\cdot 93\\cdot 94\\cdot 95\\cdot 96\\cdot 97\\cdot 98\\cdot 99\\cdot 100\\cdot 101\\cdot 102\\",
|
|
"gt_answers": "( a + 1 ) ^ { 2 } + ( a - 1 ) ^ { 2 } = 3 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_330.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "\\sqrt { 5 x - 4 } = - x + 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_331.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 1.\"",
|
|
"gt_answers": "x _ { 2 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_332.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2 \\times 2 = 4 \\times 1\\)",
|
|
"gt_answers": "1 \\div 2 = \\frac { 1 } { 2 } ( k g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_333.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2.141592653589793238462643383279502884197169399375105820974944592307816406286208998629489549303844609550582231679687249147688481117159265358979323846264338327950288419716939937510582097494459230781640628620899862948954930384460955058223167968724914768848111715926535897932384626433832795028841971693993751058209749445923078164062862089986294895493038446095505822316796872491476884811171592653589793238462643383279502884197169399375105820974944592307816406286208998629489549303844609550582231679",
|
|
"gt_answers": "- q _ { 1 } B V _ { 1 } = m \\frac { V _ { 1 } ^ { 2 } } { R }\n",
|
|
"image_path": "./data/HME100K/test_images/test_334.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x + 2y = 5\\)\n\nThis formula represents the relationship between the variables x and y, where x is equal to 3 and y is equal to 2. The result of the equation is 5.",
|
|
"gt_answers": "x ^ { . } + \\frac { \\sqrt { 6 } } { 4 } = - \\frac { 3 } { 4 } \\sqrt { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_335.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "s x = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_336.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4HCl = 90\u00b0.\"",
|
|
"gt_answers": "\\angle A H C = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_337.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x = 2 \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_338.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 30 + 77 + 43 + 100 = 57.",
|
|
"gt_answers": "\\frac { 3 0 + 2 7 + 4 3 } { 5 7 } = 1 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_339.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "2 x - 2 5 = \\frac { x + 1 2 } { 4 } 2 x - x = 2 8 \\times 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_340.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 3(24x4) + 8(24x4) = 36(24x4) + 8(24x4) = 36(96) + 8(96) = 36(192) + 8(192) = 36(384) + 8(384) = 36(768) + 8(768) = 36(1536) + 8(1536) = 36(3072) + 8(3072) = 36(6144) + 8(6144) = 36(12288) + 8(12288) = 36(24576) + 8(24576) = 36(49152) + 8(49152) = 36(98304) + 8(98304) = 36(196608) + 8(196608) = 36(393216) + 8(393216) = 36(786432) + 8(786432) = 36(1572864) + 8(1572864) = 36(3145728) + 8(3145728) = 36(6291456) + 8(6291456) = 36(12582912) + 8(12582912) = 36(25165824) + 8(25165824) = 36(50331648) + 8(50331648) = 36(100663320) + 8(100663320) = 36",
|
|
"gt_answers": "\\frac { 1 } { 3 } S _ { \\Delta } A B O = 2 4 \\times \\frac { 1 } { 3 } = 8 = S _ { \\Delta } A B P\n",
|
|
"image_path": "./data/HME100K/test_images/test_341.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 2x - 1 = 0\\)",
|
|
"gt_answers": "a = \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_343.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "9 x + G = 3 x + G\n",
|
|
"image_path": "./data/HME100K/test_images/test_344.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `x^2 + y^2 = 25`.",
|
|
"gt_answers": "( x - 2 b ) ( y - 2 a ) = x y - 2 a x - 2 b y + 4 a b\n",
|
|
"image_path": "./data/HME100K/test_images/test_345.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: (x + y)2 = (x2 + y2) - 2xy.",
|
|
"gt_answers": "( x _ { 0 } - m ) y = y _ { 0 } ( x - m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_346.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nX2 - 2X + 2 = 0\n\nThis is a quadratic equation in the variable X.",
|
|
"gt_answers": "x > 2 x < - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_348.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Japanese.",
|
|
"gt_answers": "x = \\frac { 1 } { 6 } \\div \\frac { 3 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_349.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\sin C = \\frac { A B } { A C } = \\frac { C } { 2 R }\n",
|
|
"image_path": "./data/HME100K/test_images/test_350.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LA = 60\u00b0 cosh(mB)\".",
|
|
"gt_answers": "\\angle A = 6 0 ^ { \\circ } , \\frac { \\cos B } { \\sin C } \\overrightarrow { A B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_351.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{a^2 + b^2}{c^2 + d^2} = \\frac{a^2 + b^2}{c^2 + d^2}\n\\end{equation}\n\nThis is a simple algebraic equation that states that the square of the sum of two numbers is equal to the square of the sum of their squares, when the square of the sum of the squares of the two numbers is equal to the square of the sum of the squares of the two numbers.",
|
|
"gt_answers": "( 2 ) \\because a = \\frac { 1 } { 3 } , c = \\frac { \\sqrt { 2 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_352.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/4 + 1/4 = 1/2.\"",
|
|
"gt_answers": "x _ { 2 } = \\frac { 1 } { - 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_354.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"S = S + 10m\".",
|
|
"gt_answers": "S _ { a } = S = 1 0 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_355.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(4 \\times 2 = 8 + 2 \\times 2 = 8 + 4 = 12\\)",
|
|
"gt_answers": "\\frac { 4 } { B D } = \\frac { 8 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_356.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "y _ { 2 } = - \\frac { 2 \\sqrt { 7 } } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_357.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{10} \\cdot 3^{10} \\cdot 4^{10} \\cdot 5^{10} \\cdot 6^{10} \\cdot 7^{10} \\cdot 8^{10} \\cdot 9^{10} \\cdot 10^{10} = 10^{30} \\cdot 10^{30} \\cdot 10^{30} \\cdot 10^{30} \\cdot 10^{30} \\cdot 10^{30} \\cdot 10^{30} \\cdot 10^{30} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = 10^{120} = ",
|
|
"gt_answers": "\\Delta = b ^ { 2 } - 4 a c \\div ( - 1 ) ^ { 2 } - 4 \\times 1 \\times 2 = - 7 < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_358.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x + 1 = 3\" using LaTeX format.",
|
|
"gt_answers": "x _ { 1 } = 1 + \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_359.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"L2-L1 = 2(L1-L3) + 3(L3-L4) + 4(L4-L5) + 5(L5-L6) + 6(L6-L7) + 7(L7-L8) + 8(L8-L9) + 9(L9-L10) + 10(L10-L11) + 11(L11-L12) + 12(L12-L13) + 13(L13-L14) + 14(L14-L15) + 15(L15-L16) + 16(L16-L17) + 17(L17-L18) + 18(L18-L19) + 19(L19-L20) + 20(L20-L21) + 21(L21-L22) + 22(L22-L23) + 23(L23-L24) + 24(L24-L25) + 25(L25-L26) + 26(L26-L27) + 27(L27-L28) + 28(L28-L29) + 29(L29-L30) + 30(L30-L31) + 31(L31-L32) + 32(L32-L33) + 33(L33-L34) + 34(L34-L35) + 35(L35-L36) + 36(L36-L37) + 37(L37-L38) + 38(L38-L39) + 39(L39-L40) + 40(L40-L41) + 41(L41-L42)",
|
|
"gt_answers": "\\angle 2 = 6 0 ^ { \\circ } 3 0 ^ { \\circ } \\because \\angle A B C = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_360.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 = 1.",
|
|
"gt_answers": "1 \\div 9 = \\frac { 1 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_362.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + 3x - 1 = 0\n\\end{aligned}\n\\end{equation}\n\nThis is the quadratic equation in the form of a polynomial equation.",
|
|
"gt_answers": "\\frac { 2 x - 1 } { 3 } = \\frac { 3 } { 4 } x - 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_364.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 1 } { 2 } ( x - t ) ( x - t + 4 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_365.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4x^2 - 4x + 1}{x^2 - 4x + 1} = \\frac{4",
|
|
"gt_answers": "4 x ^ { 4 } - 5 x ^ { 2 } - 4 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_368.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written in the form of a mathematical equation, with the letters \"a\" and \"b\" representing variables, and the letter \"d\" representing a constant. The formula is written in the form of a function, with the function name \"f\" and the function arguments \"a\" and \"b\". The function is defined as \"f(a,b) = a^2 + b^2\".",
|
|
"gt_answers": "A B ^ { 2 } - A D ^ { 2 } = D B\n",
|
|
"image_path": "./data/HME100K/test_images/test_369.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 16 - 5 = 11.",
|
|
"gt_answers": "1 5 - 5 = 1 0 ^ { \\circ } C\n",
|
|
"image_path": "./data/HME100K/test_images/test_370.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 2 = 0\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } [ x - ( k \\times 2 2 - 1 ) ] = \\frac { 2 } { 3 } ( 2 2 - x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_372.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as follows:\n\n\\(P = \\frac{V^2}{R + \\left( \\frac{L}{C} \\right)^2}\\)\n\nwhere P is the power, V is the voltage, R is the resistance, L is the inductance, and C is the capacitance.",
|
|
"gt_answers": "P 2 = U _ { 2 } I = 2 . 5 v \\times \\frac { 1 . 6 5 w } { U R } = \\frac { 2 . 5 V \\times 1 . 6 5 W } { u _ { 2 } - 2 . 5 V }\n",
|
|
"image_path": "./data/HME100K/test_images/test_375.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 4 } { 5 } x = \\frac { 4 } { 5 } + \\frac { 2 5 } { 5 . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_376.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"H2O = 90\u00b0.\"",
|
|
"gt_answers": "\\angle D O H = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_378.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(W = \\frac{V^2}{R} + \\frac{I^2}{C} + \\frac{P^2}{L}\\)\n\nThis formula represents the power dissipated in a resistor, where W is the power dissipated, V is the voltage across the resistor, I is the current through the resistor, P is the power supplied to the resistor, and L is the resistance of the resistor.",
|
|
"gt_answers": "W _ { 1 } = V _ { 1 } I _ { 1 } t = V I _ { 1 } t = 6 v \\times 0 . 6 A \\times 1 0 s = 3 6 J\n",
|
|
"image_path": "./data/HME100K/test_images/test_379.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x2 - 2x4.",
|
|
"gt_answers": "4 x + 2 x - 2 = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_380.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"mg = gmg\" using LaTeX format.",
|
|
"gt_answers": "m g = G \\frac { M m } { R ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_382.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4.50454556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556556",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_383.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(O + 1 = 3\\cdot 0.5 + 1\\)\n\nThis formula represents the relationship between the total load (O) and the number of objects (OB) in a container. The total load is calculated as the sum of the weight of each object multiplied by its volume. The number of objects is represented by the variable OB. The formula states that the total load (O) is equal to 3 times the volume of the container (0.5) plus 1.",
|
|
"gt_answers": "\\tan \\angle O A B = \\frac { O B } { O A } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_384.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"bom = 6000 im\" using the LaTeX format.",
|
|
"gt_answers": "6 0 m = 6 0 0 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_385.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(5d = 47 - 34 \\cdot 5\\)\n\nThe formula uses the variables \"d\" and \"5\" and the numbers \"47\" and \"34\". The equation is written in the form of an algebraic expression, where the variable \"d\" is multiplied by the number \"5\" and then subtracted from the number \"47\". The result is then multiplied by the number \"34\".",
|
|
"gt_answers": "\\overrightarrow { E D } = ( 0 . 4 , - 3 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_386.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-24-S-2",
|
|
"gt_answers": "S = 2 4 . 5 \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_387.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(t^2 + 3t + 4 = 0\\)",
|
|
"gt_answers": "t _ { 1 } = \\frac { V _ { 1 } } { a _ { 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_388.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 0 0 0 c m ^ { 2 } = ( 1 2 0 ) d m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_389.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(L_{BDE-90} = \\frac{L_{BDE-60}}{1.25} \\times 0.85\\)\n\nThe formula is a ratio of two lengths, where the first length is the length of the BDE-90 beam at a specific angle, and the second length is the length of the BDE-60 beam at a different angle. The ratio is calculated by dividing the first length by the second length, multiplying the result by 1.25, and then dividing the result by 0.85.",
|
|
"gt_answers": "\\angle B D E = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_391.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 227888 - 8540.",
|
|
"gt_answers": "( \\frac { 2 2 + 1 8 } { 4 0 } ) \\div 8 = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_392.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"L = 100\u00b0\".",
|
|
"gt_answers": "\\angle C = 1 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_395.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(MU021 = \\frac{p \\times q}{2 \\times 10^{5}} \\times 10^{2} \\times 10^{3} \\times 10^{6} \\times 10^{7} \\times 10^{8} \\times 10^{9} \\times 10^{10} \\times 10^{11} \\times 10^{12} \\times 10^{13} \\times 10^{14} \\times 10^{15} \\times 10^{16} \\times 10^{17} \\times 10^{18} \\times 10^{19} \\times 10^{20} \\times 10^{21} \\times 10^{22} \\times 10^{23} \\times 10^{24} \\times 10^{25} \\times 10^{26} \\times 10^{27} \\times 10^{28} \\times 10^{29} \\times 10^{30} \\times 10^{31} \\times 10^{32} \\times 10^{33} \\times 10^{34} \\times 10^{35} \\times 10^{36} \\times 10^{37} \\times 10^{38} \\times 10^{39} \\times 10^{40} \\times 10^{41} \\times 10^{42} \\times 10^{43} \\times 10^{44} \\times 10^{45} \\times 10^{46} \\times 10^{47} \\times 10^{48} \\times 10^{49} \\times 10^{50} \\times 10^{51} \\times 10^{52} \\times 10^{53} \\times 10^{54} \\times 10^{55} \\times 10^{56} \\times ",
|
|
"gt_answers": "2 1 0 \\times \\frac { 5 } { 7 } = 1 5 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_398.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2}",
|
|
"gt_answers": "C E ^ { 2 } = E A \\cdot E B = 2 k\n",
|
|
"image_path": "./data/HME100K/test_images/test_399.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"b1:b2:b3:b4:b5:b6:b7:b8:b9:b10:b11:b12:b13:b14:b15:b16:b17:b18:b19:b20:b21:b22:b23:b24:b25:b26:b27:b28:b29:b30:b31:b32:b33:b34:b35:b36:b37:b38:b39:b40:b41:b42:b43:b44:b45:b46:b47:b48:b49:b50:b51:b52:b53:b54:b55:b56:b57:b58:b59:b60:b61:b62:b63:b64:b65:b66:b67:b68:b69:b70:b71:b72:b73:b74:b75:b76:b77:b78:b79:b80:b81:b82:b83:b84:b85:b86:b87:b88:b89:b90:b91:b92:b93:b94:b95:b96:b97:b98:b99:b100:b101:b102:b103:b104:b105:b106:b107:b108:b109:b110:b111:b112:b113:b114:b115:b116:b117:b118:b119:b120:b121:b122:",
|
|
"gt_answers": "b \\neq - 1 \\therefore b + 1 \\neq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_400.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 120 = 25 + 48.",
|
|
"gt_answers": "1 2 0 \\div 2 5 = 4 . 8 ( d m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_401.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2876 - 404 = 2472 km.\"",
|
|
"gt_answers": "8 7 + ( 1 0 4 + 9 6 ) = 2 8 7 k m\n",
|
|
"image_path": "./data/HME100K/test_images/test_403.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LEO3 L444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444",
|
|
"gt_answers": "\\angle E O B = \\angle 3 + \\angle 4 + \\angle 5 = 1 1 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_404.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 2(1/2) + 3(1/3) + 4(1/4) + 5(1/5) + 6(1/6) + 7(1/7) + 8(1/8) + 9(1/9) + 10(1/10) + 11(1/11) + 12(1/12) + 13(1/13) + 14(1/14) + 15(1/15) + 16(1/16) + 17(1/17) + 18(1/18) + 19(1/19) + 20(1/20) + 21(1/21) + 22(1/22) + 23(1/23) + 24(1/24) + 25(1/25) + 26(1/26) + 27(1/27) + 28(1/28) + 29(1/29) + 30(1/30) + 31(1/31) + 32(1/32) + 33(1/33) + 34(1/34) + 35(1/35) + 36(1/36) + 37(1/37) + 38(1/38) + 39(1/39) + 40(1/40) + 41(1/41) + 42(1/42) + 43(1/43) + 44(1/44) + 45(1/45) + 46(1/46) + 47(1/47) + 48(1/48) + 49(1/49) + 50(1/50) + 51(1/51) + 52(1/52) + 53(1/5",
|
|
"gt_answers": "2 \\times 0 . 3 \\times 0 . 1 5 = 0 . 0 9 m ^ { 3 } = 9 0 d m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_405.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4(a+b) - 2(c+d) + 8(e+f) - 28(g+h) + 70(i+j) - 288(k+l) - 880(m+n) - 2880(o+p) - 7000(q+r) - 28800(s+t) - 88000(u+v) - 288000(w+x) - 700000(y+z) - 2880000(aa+bb) - 8800000(cc+dd) - 28800000(ee+ff) - 70000000(gg+hh) - 28800000(ii+jj) - 88000000(kk+ll) - 288000000(mm+nn) - 880000000(oo+pp) - 700000000(qq+rr) - 2880000000(ss+tt) - 8800000000(uu+vv) - 28800000000(ww+xx) - 70000000000(yy+zz) - 288000000000(aaa+bbb) - 880000000000(ccc+ddd) - 288000000000(eee+fff) - 700000000000(ggg+hhh) - 288000000000(iii+jjj) - 880000000000(kkk+lll) - 288000000000(mmm+nnn) - 880000000000",
|
|
"gt_answers": "b ^ { 2 } - 4 a c = 8 + 2 0 = 2 8 > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_408.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2mf = 600.",
|
|
"gt_answers": "\\angle M C F = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_409.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 1 = 3.",
|
|
"gt_answers": "\\frac { x + 1 } { x ^ { 2 } } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_410.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55\\)",
|
|
"gt_answers": "\\frac { 3 } { 1 4 } + \\frac { 5 } { 1 4 } - \\frac { 1 } { 1 4 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_411.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A = \\frac{1}{2} \\left( \\sqrt{a^2 + b^2} + \\sqrt{c^2 + d^2} \\right)\\)",
|
|
"gt_answers": "A E = \\frac { 1 } { n } A O\n",
|
|
"image_path": "./data/HME100K/test_images/test_412.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(n^2 - nf^2 = (n-f)^2\\)",
|
|
"gt_answers": "\\frac { 1 } { x + y } = n \\frac { 1 } { x - y } = m\n",
|
|
"image_path": "./data/HME100K/test_images/test_413.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{1}{1",
|
|
"gt_answers": "S ( x - 3 y ) ( x - y ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_414.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"99x-19\".",
|
|
"gt_answers": "x = \\frac { 9 9 } { 1 9 } \u3002\n",
|
|
"image_path": "./data/HME100K/test_images/test_415.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "+ 3 x + 2 ( 3 - x ) + ( 3 + x ) ( - 2 ) = - x < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_416.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2 + 2ab + bc\\)",
|
|
"gt_answers": "a c + 1 = 2 a + 2 c \\geq 2 \\sqrt { 4 a c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_417.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + y^2 = 100\\)\n\nThis is a quadratic equation in two variables, where x and y represent the two unknowns. The equation states that the sum of the squares of the two variables is equal to 100.",
|
|
"gt_answers": "6 0 0 0 0 0 \\times \\frac { 1 } { 6 0 0 0 0 0 } = 1 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_420.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 - 3x + 4 = 0.",
|
|
"gt_answers": "5 \\frac { 1 } { 2 } - 3 x = a + \\frac { 1 } { 4 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_421.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x _ { 1 } = \\sqrt { 2 } - 1 , x _ { 2 } = 1 - \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_422.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: `6x^2 + 2x - 22 = 0`.",
|
|
"gt_answers": "[ x + ( x + \\frac { 1 } { 4 } ) ] \\times 6 \\div 2 = 2 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_423.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"PBE = 30\u00b0.\"",
|
|
"gt_answers": "\\angle D B E = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_424.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given by:\n\n\\(y = \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b}{a} + \\frac{b}{a} \\cdot \\frac{b}{a} \\cdot \\frac{b",
|
|
"gt_answers": "y _ { 1 } = \\frac { \\sqrt { b ^ { 2 } + 1 } } { b ^ { 2 } + 1 } . y _ { 2 } = - \\frac { \\sqrt { b ^ { 2 } + 1 } } { b ^ { 2 } + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_426.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x + 3y = 5.",
|
|
"gt_answers": "y _ { 2 } = - \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_428.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{1}{1",
|
|
"gt_answers": "\\frac { \\frac { 4 } { 5 } x - \\frac { 1 } { 8 } } { \\frac { 5 } { 8 } x } = \\frac { y } { 5 x y - \\frac { 5 } { 8 } x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_429.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is the famous equation of energy, which states that the total energy of an object is equal to its mass multiplied by the square of its speed of light.",
|
|
"gt_answers": "\\rho = \\frac { m } { V }\n",
|
|
"image_path": "./data/HME100K/test_images/test_430.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten format, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a negative sign in front of the expression, which can be represented in LaTeX as follows:\n\n\\(-\\frac{x}{y}\\)",
|
|
"gt_answers": "y = \\frac { 1 7 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_431.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"m = 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "m = 6 0 \\times 0 . 1 = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_432.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"b^2 - 4ac = 0.\"",
|
|
"gt_answers": "\\Delta = m ^ { 2 } - 1 6 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_433.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 160x(160-60) = 3600.",
|
|
"gt_answers": "1 6 0 x = 1 6 0 \\times \\frac { 4 } { 3 } = \\frac { 6 4 0 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_434.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "5 0 + 5 x = 7 5 - 2 5 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_435.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2^{22} - 2^{21} + 2^{20} - 2^{19} + 2^{18} - 2^{17} + 2^{16} - 2^{15} + 2^{14} - 2^{13} + 2^{12} - 2^{11} + 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{22} - 2^{21} + 2^{20} - 2^{19} + 2^{18} - 2^{17} + 2^{16} - 2^{15} + 2^{14} - 2^{13} + 2^{12} - 2^{11} + 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{22} - 2^{21} + 2^{20} - 2^{19} + 2^{18} - 2^{17} + 2^{16} - 2^{15} + 2^{14} - 2^{13} + 2^{12} - 2^{11} + 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{22} - 2^{21} + 2^{20} - 2^{19} + 2^{18} - 2^{17} +",
|
|
"gt_answers": "5 0 0 - 2 2 2 < 2 5 7 + 2 2 5 < 9 0 6 - 3 4 5 < 2 7 8 + 6 2 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_436.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(S_{BDC} = \\frac{1}{2} \\left(S_{AB} + S_{CD}\\right) - \\frac{1}{2} \\left(S_{BA} + S_{DC}\\right)\\)\n\nThis formula represents the surface area of a triangle with vertices A, B, and C, where S_{AB} is the area of the triangle formed by the sides AB and BC, S_{CD} is the area of the triangle formed by the sides CD and AC, and S_{BA} is the area of the triangle formed by the sides BA and AC.",
|
|
"gt_answers": "S _ { \\Delta B D C } = \\frac { 1 } { 2 } B D \\cdot C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_437.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x - 1 = 0\\)",
|
|
"gt_answers": "f ( x ) \\leq \\vert 2 x - 6 \\vert\n",
|
|
"image_path": "./data/HME100K/test_images/test_438.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 2(x + 1) - 4(x - 2) = 6x - 8.",
|
|
"gt_answers": "1 2 \\times 1 2 = 1 4 4 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_439.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mixture of Greek and Latin characters, which can be difficult to read and understand. Here is a transcription of the formula in LaTeX format:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\Delta B D P \\sqrt { 2 } + \\sqrt { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_440.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as y = 3 - 2x.",
|
|
"gt_answers": "y _ { 1 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_441.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 500\\)\n\nThis formula represents the equation of a circle with a center at the origin (0, 0) and a radius of 500 units.",
|
|
"gt_answers": "0 . 8 5 \\times 1 0 0 0 = 8 5 0 ( k g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_442.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 99.\"",
|
|
"gt_answers": "\\angle N D E = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_443.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 5x^2 + 3x - 10 = 0.",
|
|
"gt_answers": "5 \\times \\frac { 9 } { 5 } = 9 ( t )\n",
|
|
"image_path": "./data/HME100K/test_images/test_444.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 2x + 1 = 3x^2 + 3x + 1\\)\n\nThis formula can be rewritten as:\n\n\\(2x^2 + 2x + 1 = (3x + 1)(x + 1)\\)\n\nThe formula can also be written as:\n\n\\(2x^2 + 2x + 1 = (x + 1)(3x + 1)\\)\n\nThe formula is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "\\frac { 1 } { x + 1 } + \\frac { 2 } { x - 2 } = - \\frac { 8 } { ( x + 2 ) ( x - 2 ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_445.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Am-Jab-BM-2.0\" using LaTeX format.",
|
|
"gt_answers": "A M = \\sqrt { A B ^ { 2 } - B M ^ { 2 } } = 2 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_447.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(z = \\sqrt{x^2 + y^2 + z^2}\\)",
|
|
"gt_answers": "\\sqrt { 2 5 - x ^ { 2 } } = x - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_448.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/2 x (1/2 x 3) + 1/2 x (1/2 x 2) + 1/2 x (1/2 x 1) = 1/2 x 3 + 1/2 x 2 + 1/2 x 1 = 3/2 + 2/2 + 1/2 = 6/2 = 3.",
|
|
"gt_answers": "\\frac { 8 } { 9 } \\times \\frac { 3 } { 1 6 } = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_449.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\therefore O B \\bot A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_450.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3x + 2y = 10\\)\n\nThis is a simple algebraic equation that can be solved using the addition and subtraction operations.",
|
|
"gt_answers": "y _ { 1 } = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_451.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.5) - 0.5(PCO2 + 0.5) - 0.5(PO2 + 0.",
|
|
"gt_answers": "P Q = ( Q \\cdot \\sin C = ( 6 0 - 2 0 \\sqrt { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_452.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 4.\"",
|
|
"gt_answers": "\\frac { 1 } { x - y } = b\n",
|
|
"image_path": "./data/HME100K/test_images/test_453.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a \\times 10^{2} = 100\\)\n\nThis formula represents the relationship between the number a and the power of 10, where a is multiplied by 10 to the power of 2. The result is 100.",
|
|
"gt_answers": "a = \\frac { 7 x } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_454.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A0 = O0 + B0,\" where A0 and O0 represent the initial values of the variables A and O, respectively, and B0 represents the initial value of the variable B.",
|
|
"gt_answers": "A O = O C = O B = O D\n",
|
|
"image_path": "./data/HME100K/test_images/test_455.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3x + 1 - 1 = 2x - 1\\)",
|
|
"gt_answers": "\\frac { x + 4 } { 3 } - \\frac { 3 x - 1 } { 2 } \\geq 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_457.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\frac { x } { a } + \\frac { x } { - a } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_458.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1/2(x^2 + 4x - 10) + 1/2(x^2 - 4x + 10) = 0.",
|
|
"gt_answers": "\\Delta = ( - 1 ) ^ { 2 } - 4 ( a - 1 ) \\leq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_459.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as Fe(OH)3(s) + 3HCl(aq) = FeCl3(aq) + 3H2O(l).",
|
|
"gt_answers": "F e _ { 2 } O _ { 3 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_460.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x + 3y = 5\\)",
|
|
"gt_answers": "\\frac { x } { 2 } + \\frac { 2 y } { 5 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_461.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: K(G-8) = 1.",
|
|
"gt_answers": "k _ { 2 } = \\frac { 9 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_462.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as H2O + HCl --> H3O+ + Cl-.",
|
|
"gt_answers": "\\frac { D H } { H C } = \\frac { A H } { D H }\n",
|
|
"image_path": "./data/HME100K/test_images/test_463.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{A}{B} + \\frac{C}{D} + \\frac{E}{F} + \\frac{G}{H} + \\frac{I}{J} + \\frac{K}{L} + \\frac{M}{N} + \\frac{O}{P} + \\frac{Q}{R} + \\frac{S}{T} + \\frac{U}{V} + \\frac{W}{X} + \\frac{Y}{Z} = 1\n\\end{aligned}\n\\end{equation}\n\nThis equation represents a sum of 15 terms, each of which is a fraction of two numbers. The numbers are written in the form of letters, with the first letter representing the numerator and the second letter representing the denominator.",
|
|
"gt_answers": "A > B > C B > A > C \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_464.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "( \\frac { 2 } { 3 } x + \\frac { 1 } { 2 } ) = \\frac { 3 } { 4 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_465.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 14 = 0\\)",
|
|
"gt_answers": "\\frac { m + 1 8 } { 1 4 } > 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_467.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3",
|
|
"gt_answers": "\\frac { 2 } { 3 } = \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_468.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"y = 1/x + 1/x^2 + 1/x^3 + 1/x^4 + 1/x^5 + 1/x^6 + 1/x^7 + 1/x^8 + 1/x^9 + 1/x^10 + 1/x^11 + 1/x^12 + 1/x^13 + 1/x^14 + 1/x^15 + 1/x^16 + 1/x^17 + 1/x^18 + 1/x^19 + 1/x^20 + 1/x^21 + 1/x^22 + 1/x^23 + 1/x^24 + 1/x^25 + 1/x^26 + 1/x^27 + 1/x^28 + 1/x^29 + 1/x^30 + 1/x^31 + 1/x^32 + 1/x^33 + 1/x^34 + 1/x^35 + 1/x^36 + 1/x^37 + 1/x^38 + 1/x^39 + 1/x^40 + 1/x^41 + 1/x^42 + 1/x^43 + 1/x^44 + 1/x^45 + 1/x^46 + 1/x^47 + 1/x^48 + 1/x^49 + 1/x^50 + 1/x^51 + 1/x^52 + 1/x^53 + 1/x^54 + 1/x^55 + 1/x^56 + 1/x^57 + 1/x^58 + 1/x^59 + 1/x^60 + 1/x^61 + 1/x^62 + 1/x^63 + 1/x^64",
|
|
"gt_answers": "y = - \\frac { 1 5 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_470.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"M(a,b) = a^2 + b^2\".",
|
|
"gt_answers": "M ( a , - a ^ { 2 } + 2 a + 3 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_472.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(f(x) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2}",
|
|
"gt_answers": "C u S O _ { 4 } + F e ( O H ) _ { 2 } = F e S O _ { 4 } + C u ( O H ) _ { 2 } \\downarrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_473.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "a < \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_474.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(16 + 17) - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17 - 16 - 17",
|
|
"gt_answers": "3 0 \\div 7 2 = \\frac { 3 0 } { 7 2 } = \\frac { 5 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_475.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(P = \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{4} \\cdot \\left( \\frac{1}{2} \\cdot \\left(",
|
|
"gt_answers": "P > \\frac { 1 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_476.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LVED2LER2R2S2\".",
|
|
"gt_answers": "\\angle B D E = \\angle E D O ^ { , } \\angle D O E = \\angle D E B = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_477.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "5 1 2 \\div 6 3 = 8 \\cdots 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_478.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mixture of Korean and English, but it can be rewritten in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\",
|
|
"gt_answers": "\\frac { A H } { 2 } = \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_479.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "1 \\div ( \\frac { 1 } { a } + \\frac { 1 } { b } ) = \\frac { a b } { a + b } h\n",
|
|
"image_path": "./data/HME100K/test_images/test_480.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = 2x^2\n\\end{equation}\n\nThis formula can be simplified further to:\n\n\\begin{equation}\nx^2 + y^2 = 2x^2\n\\end{equation}\n\nThis is the Pythagorean theorem, which states that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the hypotenuse.",
|
|
"gt_answers": "\\frac { x } { x - 7 } + \\frac { 1 } { x - 7 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_481.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55\\)",
|
|
"gt_answers": "\\frac { 1 } { 3 } : \\frac { 1 } { 2 } = \\frac { 1 } { 6 } : \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_482.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4}",
|
|
"gt_answers": "3 . 1 4 \\times 0 . 2 ^ { 2 } \\times 4 = 0 . 5 0 2 4 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_483.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Hebrew, and it is a formula for calculating the area of a circle. The formula is written in a script-like font, and the letters are arranged in a way that makes it easy to read.",
|
|
"gt_answers": "\\sqrt { 3 x } > \\sqrt { 5 } x - \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_484.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"180/100 = 1.8\" using LaTeX format.",
|
|
"gt_answers": "\\angle D C A + \\angle E C F = 1 8 0 ^ { \\circ } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_485.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{4x^2 + 4x + 1}{4x^2 + 4x + 1} = \\frac{1}{4x^2 + 4x + 1}\n\\end{equation}\n\nThis is a simple algebraic equation that can be solved by dividing both sides by the numerator and simplifying the denominator. The result is:\n\n\\begin{equation}\n\\frac{1}{4x^2 + 4x + 1} = \\frac{1}{4x^2 + 4x + 1}\n\\end{equation}\n\nThis is the same expression as the original equation.",
|
|
"gt_answers": "4 x ^ { 2 } + ( 4 n - 4 ) x + n ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_486.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"216 + 162 = 378.\"",
|
|
"gt_answers": "< 2 > . \\frac { 7 } { 1 6 } \\textcircled { < } \\frac { 1 1 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_487.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 30\u00b0 - 76\u00b0 = 45\u00b0.",
|
|
"gt_answers": "\\angle O E D = 7 5 ^ { \\circ } - 4 5 ^ { \\circ } = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_488.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"OB = BD + CD + OC.\"",
|
|
"gt_answers": "O B = B D = C D = O C\n",
|
|
"image_path": "./data/HME100K/test_images/test_489.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis equation is a simple algebraic expression that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "2 [ \\frac { 4 } { 3 } x - ( \\frac { 2 } { 3 } x - \\frac { 1 } { 2 } ) ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_490.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 12x^2 + 3xy + 4x + 5\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(y = 12x^2 + 3xy + 4x + 5\\)",
|
|
"gt_answers": "( 1 2 + 3 y ) ^ { 2 } - 5 y ( 1 2 + 3 y ) + 6 y ^ { 2 } = a\n",
|
|
"image_path": "./data/HME100K/test_images/test_491.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: A-2x + 3y = 10.",
|
|
"gt_answers": "a = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_492.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(F = mg \\cdot sin(\\theta)\\)\n\nwhere F is the force, m is the mass, and g is the acceleration due to gravity. The angle \u03b8 is the angle between the force and the horizontal axis.",
|
|
"gt_answers": "V = \\frac { m } { \\rho } = \\frac { 9 k g } { 0 . 9 \\times 1 0 ^ { 3 } k g / m ^ { 3 } } = 1 0 ^ { - 2 } m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_493.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is: AB-a-NZ.",
|
|
"gt_answers": "A B = 2 a = \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_494.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(W_7^2 + W_8^2 = W_9^2 + W_{10}^2\\)\n\nThis formula represents the relationship between the squares of the weights of the first nine and the last nine elements of a sequence. The weights are represented by the letters W, and the elements are numbered from 1 to 10. The formula states that the squares of the weights of the first nine elements must equal the squares of the weights of the last nine elements.",
|
|
"gt_answers": "W > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_495.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\sim \\Delta E A C \\sim \\Delta E C B\n",
|
|
"image_path": "./data/HME100K/test_images/test_496.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x _ { 2 } = - 2 - \\sqrt { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_497.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x^2 + 3x - 4\\)",
|
|
"gt_answers": "y = 3 x - 5 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_498.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(6x^2 + 6y^2 = 36\\)\n\nThis formula can be written in LaTeX as:\n\n\\(6x^2 + 6y^2 = 36\\)",
|
|
"gt_answers": "x _ { 2 } = \\frac { - b + 6 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_499.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(AH_2-21 = 92 - 21 = 71\\)",
|
|
"gt_answers": "\\frac { 4 ( a - 2 ) } { a ( a - 2 ) } > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_501.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(CO_2 + 2H_2O \\rightarrow 2CO_2 + H_2 + O_2\\)",
|
|
"gt_answers": "C O _ { 2 } + C a ( O H ) _ { 2 } = C a C O _ { 3 } \\downarrow + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_503.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(AB + AD + EF + GH + IJ + KL + MN + OO + PQ + RS + TU + VW + XY + ZZ = 100\\)",
|
|
"gt_answers": "A B ^ { 2 } - B E ^ { 2 } = A D ^ { 2 } - E O ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_505.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "( 3 ) ( ( 3 k - 7 ) = 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_506.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mathematical formula using the Greek letter pi (\u03c0) and the letter \"i\" (i). The formula is written in a script-like font, which adds a unique and artistic touch to the equation.",
|
|
"gt_answers": "1 \\geq - \\frac { 1 } { 2 } x \\geq - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_508.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: LABcBd = 800*ODLcBd + 100*ODLbBd + 108*ODLdBd.",
|
|
"gt_answers": "\\angle A O C + \\angle B O D = \\frac { 1 } { 2 } \\angle B O D + \\angle B O D = 1 0 8 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_510.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: y = 2x^2 - 2x + 1.",
|
|
"gt_answers": "y _ { 1 } = - 1 y _ { 2 } = - 2 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_511.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3.4314 x 1.4 = 5.1996.",
|
|
"gt_answers": "3 1 . 4 \\times 3 1 . 4 = 9 8 5 . 9 6 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_513.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 120 - 20 = 100.",
|
|
"gt_answers": "1 \\div 2 0 = \\frac { 2 0 } { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_514.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2 + d^2\\)",
|
|
"gt_answers": "\\frac { a ^ { 2 } } { 4 5 a ^ { 2 } } + \\frac { 4 a ^ { 2 } } { 4 5 b ^ { 2 } } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_516.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nS(x) = 3x^2 - 2x + 1\n\nThe formula is written in LaTeX format using the `LaTeX` package.",
|
|
"gt_answers": "S : \\pi \\times ( \\frac { 3 a } { 2 } ) ^ { 2 } = \\frac { 9 \\pi a ^ { 2 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_517.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(I_{gl} = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\vert g \\vert a _ { n + 1 } \\vert - \\vert g \\vert a _ { n } \\vert = \\vert g \\frac { \\vert a _ { n + 1 } \\vert } { \\vert a _ { n } \\vert . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_519.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36 \\cdot 36 + 36",
|
|
"gt_answers": "3 0 \\div 3 6 = \\frac { 3 6 } { 3 0 } = \\frac { 6 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_520.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a2 + b2 = c2.",
|
|
"gt_answers": "x _ { 2 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_521.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3\\cdot 36 = 3\\cdot 12 + 3\\cdot 24\\)",
|
|
"gt_answers": "3 6 \\div 1 2 = 3 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_523.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3 = 5.",
|
|
"gt_answers": "0 < \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_524.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\nP = E * D / (2 * R)\n\nwhere P is the pressure, E is the Young's modulus, D is the diameter, and R is the radius.",
|
|
"gt_answers": "P = \\frac { F } { S } = \\frac { 1 2 0 0 0 N } { 0 . 1 2 m ^ { 2 } } = 1 \\times 1 0 ^ { 5 } P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_526.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a few numbers and letters, which can be represented in LaTeX using the following code:\n\n\\begin{code}\n\\documentclass{article}\n\\usepackage{amsmath}\n\\begin{document}\n\\begin{equation}\n\\begin{aligned}\na + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s + t + u + v + w + x + y + z = 100\n\\end{aligned}\n\\end{equation}\n\\end{document}\n\\end{code}\n\nThis code creates a mathematical equation with the given formula and the variables a through z. The equation is aligned using the `aligned` environment and the equation is centered using the `center` environment.",
|
|
"gt_answers": "\\frac { 1 } { 3 0 } = \\frac { 1 } { 3 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_527.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)\n\nThis is a quadratic equation in the variable x, with the coefficients 2, 3, and 4. The equation has a solution of x = 2, which means that the square of 2 plus 3x plus 4 is equal to 10.",
|
|
"gt_answers": "x _ { 1 } = \\frac { \\sqrt { 6 } } { 2 } , x _ { 2 } = - \\frac { \\sqrt { 6 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_528.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(4\\cdot 0.3 \\cdot 0.5 \\cdot 0.7 \\cdot 0.9 \\cdot 1.1 \\cdot 1.3 \\cdot 1.5 \\cdot 1.7 \\cdot 1.9 \\cdot 2.1 \\cdot 2.3 \\cdot 2.5 \\cdot 2.7 \\cdot 2.9 \\cdot 3.1 \\cdot 3.3 \\cdot 3.5 \\cdot 3.7 \\cdot 3.9 \\cdot 4.1 \\cdot 4.3 \\cdot 4.5 \\cdot 4.7 \\cdot 4.9 \\cdot 5.1 \\cdot 5.3 \\cdot 5.5 \\cdot 5.7 \\cdot 5.9 \\cdot 6.1 \\cdot 6.3 \\cdot 6.5 \\cdot 6.7 \\cdot 6.9 \\cdot 7.1 \\cdot 7.3 \\cdot 7.5 \\cdot 7.7 \\cdot 7.9 \\cdot 8.1 \\cdot 8.3 \\cdot 8.5 \\cdot 8.7 \\cdot 8.9 \\cdot 9.1 \\cdot 9.3 \\cdot 9.5 \\cdot 9.7 \\cdot 9.9 \\cdot 10.1 \\cdot 10.3 \\cdot 10.5 \\cdot 10.7 \\cdot 10.9 \\cdot 11.1 \\cdot 11.3 \\cdot 11.5 \\cdot 11.7 \\cdot 11.9 \\cdot 12.1 \\cdot 12.3 \\cdot 12.5 \\cdot 12.7 \\cdot 12.9 \\cdot 13.1 \\cdot 13.3 \\cdot 13.5 \\cdot 13.7 \\cdot 13.9 \\cdot 14.1 \\cdot 14.3 \\cdot 14.5 \\cdot 14.7 \\cdot 14.9 \\cdot 15.1 \\cdot 15.3 \\cdot 15.5 \\cdot ",
|
|
"gt_answers": "( 3 ) S = 1 4 \\times 0 . 3 m ^ { 2 } = 4 . 2 m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_530.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten style using the Greek alphabet. The formula is written in a way that it can be easily read and understood by someone who is familiar with the Greek alphabet. However, it is not possible to provide a precise LaTeX representation of the formula without knowing the exact symbols used in the image.",
|
|
"gt_answers": "\\Delta B D C \\sim \\Delta A E C\n",
|
|
"image_path": "./data/HME100K/test_images/test_531.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "- \\sqrt { 3 } x + 4 \\sqrt { 3 } = ( \\sqrt { 3 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_532.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{a^2 + b^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a^2}{2} + \\frac{b^2 - a^2}{2} + \\frac{b^2 + a",
|
|
"gt_answers": "6 a b + 2 \\times \\frac { 3 \\sqrt { 3 } } { 2 } \\times 6 ^ { 2 } \\div 6 a b + 3 \\sqrt { 3 } b ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_533.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nP = 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "P = \\rho g h = 1 0 \\times 1 0 ^ { 3 } k g / m ^ { 3 } \\times 1 0 N / c g\n",
|
|
"image_path": "./data/HME100K/test_images/test_534.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 3x - 4 = 0\\)\n\nThis formula represents a quadratic equation, where x is the variable and the expression on the left side represents the equation's expression. The expression on the right side represents the equation's solution.",
|
|
"gt_answers": "( x ^ { 2 } + \\frac { 1 } { 3 } ) ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_535.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2^{25} - 2^{24} + 2^{23} - 2^{22} + 2^{21} - 2^{20} + 2^{19} - 2^{18} + 2^{17} - 2^{16} + 2^{15} - 2^{14} + 2^{13} - 2^{12} + 2^{11} - 2^{10} + 2^{9} - 2^{8} + 2^{7} - 2^{6} + 2^{5} - 2^{4} + 2^{3} - 2^{2} + 2^{1} - 2^{0} = 65536\\)",
|
|
"gt_answers": "5 : 4 = 2 5 : 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_537.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3.4x1x6x6x2.8.",
|
|
"gt_answers": "3 . 1 4 \\times 1 ^ { 2 } \\times 6 \\times \\frac { 1 } { 3 } = 6 . 2 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_539.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(AP_c + H_2O = CO_2 + H_2\\)",
|
|
"gt_answers": "A P = \\sqrt { ( 0 + 1 ) ^ { 2 } + ( 1 + 1 ) ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_540.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(A + B + C = D + E + F\\)\n\nThe formula is written using the mathematical symbols for addition, subtraction, multiplication, and division.",
|
|
"gt_answers": "\\frac { A D } { B C } = \\frac { D E } { B E } = \\frac { 1 6 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_541.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x^2 + 4x - 1\\)",
|
|
"gt_answers": "3 2 x - 1 1 2 \\cdot = 1 . 4 - 2 6 x + x ^ { 2 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_542.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "b = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_543.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(y = \\frac{x^2 + 2x + 1}{x^2 + 3x + 2} + 1\\)",
|
|
"gt_answers": "\\frac { x } { a + 2 } + \\frac { y } { b - 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_544.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle B = \\angle E C D \\angle E C D = \\angle O C B\n",
|
|
"image_path": "./data/HME100K/test_images/test_545.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 + c^2 = 3k^2\\)\n\nwhere a, b, and c are the lengths of the sides of a triangle, and k is the hypotenuse.",
|
|
"gt_answers": "D A = \\frac { 8 } { 3 } k\n",
|
|
"image_path": "./data/HME100K/test_images/test_546.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 2000 = 0\\)",
|
|
"gt_answers": "6 4 x - 8 0 x < - 2 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_547.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "y _ { 1 } = 7 , y _ { 2 } = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_548.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "A M g ( O H ) _ { 2 } + 2 H C\n",
|
|
"image_path": "./data/HME100K/test_images/test_550.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"sin(2BLC) = 13C/A3.\"",
|
|
"gt_answers": "\\sin \\angle B A C = \\frac { B C } { A B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_552.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2 + 2 = 4 + 4 = 8.\"",
|
|
"gt_answers": "+ 2 H C l = C a C l _ { 2 } + H _ { 2 } O + C O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_553.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: \"B-44 = 1/2(B-43)^2 + 1/2(B-42)^2 + 1/2(B-41)^2 + 1/2(B-40)^2 + 1/2(B-39)^2 + 1/2(B-38)^2 + 1/2(B-37)^2 + 1/2(B-36)^2 + 1/2(B-35)^2 + 1/2(B-34)^2 + 1/2(B-33)^2 + 1/2(B-32)^2 + 1/2(B-31)^2 + 1/2(B-30)^2 + 1/2(B-29)^2 + 1/2(B-28)^2 + 1/2(B-27)^2 + 1/2(B-26)^2 + 1/2(B-25)^2 + 1/2(B-24)^2 + 1/2(B-23)^2 + 1/2(B-22)^2 + 1/2(B-21)^2 + 1/2(B-20)^2 + 1/2(B-19)^2 + 1/2(B-18)^2 + 1/2(B-17)^2 + 1/2(B-16)^2 + 1/2(B-15)^2 + 1/2(B-14)^2 + 1/2(B-13)^2 + 1/2(B-12)^2 + 1/2(B-11)^2 + 1/2(B-10)^2 + 1/2(B-9)^2 + 1/2(B-8)^2 + 1/2(B-7)^2 + 1/2(B-6)^2 + 1/2(B-5)^2 + 1/2(B-4)^2 + 1/2(B-3)^2 + 1/2(B-2)^2 +",
|
|
"gt_answers": "B ( - \\frac { 1 } { 2 } , - 4 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_554.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x2 - 6.",
|
|
"gt_answers": "\\frac { 3 } { 7 } \\times 2 = \\frac { 6 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_556.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(AB = 15^{\\circ} + 30^{\\circ} - 45^{\\circ}\\)",
|
|
"gt_answers": "\\angle D O B = \\angle D B \\dot { E } + \\angle A E D = 7 5 ^ { \\circ } ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_558.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left",
|
|
"gt_answers": "\\frac { 2 } { x + y } + \\frac { 1 } { x - y } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_560.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 2y = 6 - 25.\"",
|
|
"gt_answers": ". \\frac { 3 } { 2 } y - \\frac { 1 } { 3 } y = b - 2 \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_561.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/3 = 0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
|
|
"gt_answers": "I = \\frac { Q } { t } = \\frac { 3 c } { 1 0 s } = 0 . 3 A\n",
|
|
"image_path": "./data/HME100K/test_images/test_562.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(CH4) + 3(CH3) + 4(CH2) + 6(CH) = 18(C) + 12(H) + 12(N) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + 6(C) + 6(H) + ",
|
|
"gt_answers": "r _ { c } = C H = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_563.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Y = 2x + 1.\"",
|
|
"gt_answers": "y = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_564.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a-k2-1.",
|
|
"gt_answers": "a - k ^ { 2 } - 1 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_565.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nCu2+ + H2O + 2OH- \u2192 Cu(OH)2 + H2",
|
|
"gt_answers": "C u O + H _ { 2 } S O _ { 4 } = C u S O _ { 4 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_568.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( 2 5 . 1 2 \\div 3 . 1 4 \\div 2 ) ^ { 2 } \\times 3 . 1 4 \\times 1 . 8 \\times 1 . 7 \\div 3 . 4 = 4 5 . 2 1 6 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_569.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as CusO4 + FeSO4 + CuSO4 + FeSO4 + CuSO4.",
|
|
"gt_answers": "C u S O _ { 4 } + F e = F e S O _ { 4 } + C u\n",
|
|
"image_path": "./data/HME100K/test_images/test_570.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\angle D F B + \\angle F B D = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_572.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(ml^2 = 2 \\cdot l \\cdot r\\)\n\nThis formula represents the area of a square with sides of length l and r.",
|
|
"gt_answers": "\\vert m \\vert - 2 = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_573.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BMtMo20-80.\"",
|
|
"gt_answers": "B M ^ { 2 } + M O ^ { 2 } = B D ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_576.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 5 0 \\div 2 0 0 0 0 \\times 1 0 0 \\% = 1 7 . 5 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_578.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "( - 2 \\frac { 1 } { 7 } ) \\times ( - 1 . 2 ) \\div ( - 1 \\frac { 2 } { 5 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_579.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(y = 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 . 7 \\approx 1 . 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_581.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, but it can be translated into LaTeX as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2",
|
|
"gt_answers": "y = \\frac { 1 } { 2 } x ^ { 2 } + 4 x - 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_582.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\n\\(a^2 + b^2 + c^2 = 3ab + 4ac + 5bc\\)",
|
|
"gt_answers": "a b + \\frac { \\sqrt { 3 } } { 4 } ( a ^ { 2 } + b ^ { 2 } ) x\n",
|
|
"image_path": "./data/HME100K/test_images/test_583.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 6(2x-3) + 20(x-10) = 100.",
|
|
"gt_answers": "\\frac { 6 } { 2 0 } = \\frac { 6 \\div 2 } { 2 0 \\div 2 } = \\frac { 3 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_584.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 8x^2 + 12x + 10\\)",
|
|
"gt_answers": "y = \\frac { 1 } { 4 x - 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_585.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 3(x + 1) - 4(x - 1) = 3x - 4x + 3 - 4 = 3x - 4.",
|
|
"gt_answers": "\\frac { 8 1 } { 8 1 + 1 7 5 } = ( \\frac { 3 } { 4 } ) ^ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_586.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(b^2 + a^2 = a^2 + b^2\\)",
|
|
"gt_answers": "( x + \\frac { b } { 2 a } ) ^ { 2 } = \\frac { b ^ { 2 } - 4 a c } { 4 a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_590.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 5x + 3\\)",
|
|
"gt_answers": "y = \\frac { 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_592.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 139 = 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 3 g = 1 3 \\div 1 0 0 0 0 = \\frac { 1 3 } { 1 0 0 0 } k g\n",
|
|
"image_path": "./data/HME100K/test_images/test_593.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 300x150 - 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 0 0 + 7 5 x = 3 0 0 + 7 5 \\times 6 = 7 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_594.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten format, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with the letters \"H\" and \"N\" in it, which could be a representation of the formula \"HN = 1/2.\"",
|
|
"gt_answers": "x + \\frac { n ( n + 1 ) } { x } = 2 n + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_595.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x + 5y = 10`.",
|
|
"gt_answers": "8 0 x = 2 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_596.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 6x^2 + 25x + 10\\)",
|
|
"gt_answers": "\\frac { 3 } { 2 } y - \\frac { 1 } { 3 } y = 6 - 2 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_597.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{a^2 + b^2}{c^2} = \\frac{a^2 + b^2}{c^2}\n\\end{equation}\n\nThis is a simple algebraic equation that demonstrates the commutative property of multiplication.",
|
|
"gt_answers": "\\frac { a } { 2 c } = \\frac { a ^ { 2 } + c ^ { 2 } - b ^ { 2 } } { 2 a c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_598.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: `2x^2 + 3x + 4 = 0`.",
|
|
"gt_answers": "f ( x ) = \\vert 2 x + m - 1 \\vert + \\vert 2 x - 3 \\vert\n",
|
|
"image_path": "./data/HME100K/test_images/test_599.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "> 1 8 3 0 > 1 8 0 3 > 1 3 8 0 > 1 3 0 8 > 1 0 8 3 > 1 0 3 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_600.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} +",
|
|
"gt_answers": "f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 1 2 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_601.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{a^2 + b^2}{a^2 - b^2} = \\frac{a^2 + b^2}{a^2 - b^2}\n\\end{equation}\n\nThis is a simple algebraic expression that can be easily solved using the distributive property of multiplication.",
|
|
"gt_answers": "c ^ { 4 } - a ^ { 2 } c ^ { 2 } = a ^ { 2 } c ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_603.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x + 2 y = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_605.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\n2x^2 + 3x - 4 = 0\n\\end{equation}\n\nThe equation is written in the form of an equation with two variables, x and y, and an expression involving the variables. The equation is also written in the form of an equation with an equal sign, which indicates that the two sides of the equation are equal.",
|
|
"gt_answers": "\\frac { 7 } { 8 } - \\frac { 4 } { 5 } + \\frac { 1 } { 2 } = \\frac { 3 5 } { 4 0 } - \\frac { 3 2 } { 4 0 } + \\frac { 2 0 } { 4 0 } = \\frac { 2 3 } { 4 0 } ( t )\n",
|
|
"image_path": "./data/HME100K/test_images/test_606.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{a^2}{b^2} + \\frac{c^2}{d^2} \\right) = \\frac{1}{2} \\left( \\frac{a^2}{b^2} + \\frac{c^2}{d^2} \\right)\n\\end{equation}\n\nThis equation is a simple algebraic expression that combines the squares of the four sides of a square, with the result being the square of the area of the square.",
|
|
"gt_answers": "\\Delta P _ { A } = \\frac { \\Delta G _ { n } } { S _ { A } - \\Delta _ { 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_607.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_608.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(b^2 + a^2 = 4ab\\)",
|
|
"gt_answers": "- \\frac { b } { 2 a } = + \\frac { b } { + 2 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_609.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{2x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{2x^2 + 3x + 4}{x^2 + 2x + 3}\n\\end{equation}\n\nThis is a simple algebraic expression that can be evaluated using the rules of algebra.",
|
|
"gt_answers": "\\frac { 1 } { 2 } : \\frac { 2 } { 3 } = \\frac { 3 } { 4 } : x\n",
|
|
"image_path": "./data/HME100K/test_images/test_610.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"h = 3/2b + 1/2a\".",
|
|
"gt_answers": "\\sqrt { 3 a } \\div \\sqrt { 6 a b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_611.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 1 } { 3 } \\times 3 . 1 4 \\times ( 2 \\div 2 ) ^ { 2 } \\times 0 . 6 = 0 . 6 2 8 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_613.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "( x - y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_614.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "1 0 c 1 + \\frac { 1 5 } { 2 } a \\% > - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_615.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, but it can be translated to English as \"100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { y _ { 1 } + \\frac { 1 } { 2 } } { x _ { 1 } - t } = x _ { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_616.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "D E = \\sqrt { C E ^ { 2 } - A D ^ { 2 } } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_617.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x + 1\\)",
|
|
"gt_answers": "y ^ { 2 } = \\frac { 4 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_618.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2 \\times x \\times e^{3 \\times t} = 2 \\times x \\times e^{3 \\times t} \\times e^{3 \\times t} = 2 \\times x \\times e^{6 \\times t} = 2 \\times x \\times e^{3 \\times t + 3 \\times t} = 2 \\times x \\times e^{6 \\times t + 3 \\times t} = 2 \\times x \\times e^{9 \\times t} = 2 \\times x \\times e^{3 \\times t + 3 \\times t + 3 \\times t} = 2 \\times x \\times e^{12 \\times t} = 2 \\times x \\times e^{3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t} = 2 \\times x \\times e^{18 \\times t} = 2 \\times x \\times e^{3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t} = 2 \\times x \\times e^{27 \\times t} = 2 \\times x \\times e^{3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + 3 \\times t + ",
|
|
"gt_answers": "2 ^ { 2 } x \\in ( \\frac { 3 \\pi } { 2 } , 2 \\pi )\n",
|
|
"image_path": "./data/HME100K/test_images/test_619.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(x + 1) - 3(x - 2) = 6x - 12.",
|
|
"gt_answers": "\\frac { 3 } { 4 } : \\frac { 2 } { 3 } = 9 : 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_621.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 - 3xy = 0\\)",
|
|
"gt_answers": "\\textcircled { 2 } x = 2 y = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_623.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = 1 + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_625.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(Cu^{2+} + C_{4}H_{6}O_{6}^{2-}\\rightarrow Cu^{2+}C_{4}H_{6}O_{6}\\).",
|
|
"gt_answers": "C _ { 1 } O + H _ { 2 } = C u + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_626.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x = \\frac { 4 0 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_627.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(P = \\frac{I_{max} \\cdot R_{a} \\cdot A}{V_{max}}\\)\n\nwhere:\n\n* P is the power (watts)\n* I_{max} is the maximum current (amps)\n* R_{a} is the resistance (ohms)\n* A is the area (square meters)\n* V_{max} is the maximum voltage (volts)\n\nThis formula can be used to calculate the power output of a solar panel given the maximum current, maximum voltage, and the area of the panel.",
|
|
"gt_answers": "P _ { 1 } M a x = U _ { 1 } \\cdot I _ { \\max } = I _ { 1 } ^ { 2 } \\max \\cdot R _ { 1 } = ( 2 A ) ^ { 2 } \\times 5 \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_628.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 . 8 k g \\div 1 0 k g = 0 . 2 8 k g\n",
|
|
"image_path": "./data/HME100K/test_images/test_629.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3\\sqrt{2} + 2\\sqrt{3} = 10\\sqrt{2} + 2\\sqrt{3} = 10\\sqrt{2} + 4\\sqrt{6} = 10\\sqrt{2} + 4\\sqrt{12} = 10\\sqrt{2} + 8\\sqrt{3} = 10\\sqrt{2} + 16\\sqrt{6} = 10\\sqrt{2} + 32\\sqrt{3} = 10\\sqrt{2} + 64\\sqrt{6} = 10\\sqrt{2} + 128\\sqrt{3} = 10\\sqrt{2} + 256\\sqrt{6} = 10\\sqrt{2} + 512\\sqrt{3} = 10\\sqrt{2} + 1024\\sqrt{6} = 10\\sqrt{2} + 2048\\sqrt{3} = 10\\sqrt{2} + 4096\\sqrt{6} = 10\\sqrt{2} + 8192\\sqrt{3} = 10\\sqrt{2} + 16384\\sqrt{6} = 10\\sqrt{2} + 32768\\sqrt{3} = 10\\sqrt{2} + 65536\\sqrt{6} = 10\\sqrt{2} + 131072\\sqrt{3} = 10\\sqrt{2} + 262144\\sqrt{6} = 10\\sqrt{2} + 524288\\sqrt{3} = 10\\sqrt{2} + 1048576\\sqrt{6} = 10\\sqrt{2} + 2097152\\sqrt{3} = 10\\sqrt{2} + 4194304\\sqrt{6} = 10\\sqrt{2} + 8388608\\sqrt{3",
|
|
"gt_answers": "2 2 6 \\times \\frac { 3 } { 5 } = \\frac { 6 7 8 } { 5 } c m \\approx 1 3 5 . 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_630.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": ". \\Delta A B C \\cong \\Delta A C N ( S A S )\n",
|
|
"image_path": "./data/HME100K/test_images/test_631.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(20 \\times 3.14 \\times 20 = 62.88\\)",
|
|
"gt_answers": "3 . 1 4 \\times 2 0 = 6 2 . 8 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_632.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "- 3 k + 2 - k + 1 = 0 , k = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_633.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\therefore \\frac { b } { a } = \\tan \\frac { \\pi } { 3 } = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_634.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\na^2 + b^2 + c^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca",
|
|
"gt_answers": "( \\frac { a - 2 } { a + 2 } + \\frac { 8 a } { . a ^ { 2 } - 4 } ) \\div \\frac { a + 2 . } { a ^ { 2 } - 2 a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_635.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\",
|
|
"gt_answers": "A E = E D , C E\n",
|
|
"image_path": "./data/HME100K/test_images/test_636.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"a^2 + b^2 = c^2.\"",
|
|
"gt_answers": "f ( x ) = x ^ { 2 } - 4 x + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_637.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"12:44\" using the LaTeX format.",
|
|
"gt_answers": "1 2 \\div 4 = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_638.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{4} \\right) = \\frac{1}{4}\n\\end{equation}\n\nThis equation can be read as \"half of the sum of one-half and one-fourth is equal to one-fourth.\"",
|
|
"gt_answers": ", x = \\frac { 2 9 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_639.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 2x + 3.",
|
|
"gt_answers": "y = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_640.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V_{o} = \\frac{E_{o}}{R_{o}} = \\frac{9}{10} \\times 10^{-9} = 9 \\times 10^{-10}\\)",
|
|
"gt_answers": "v _ { 0 } = \\frac { F } { 2 B } - \\frac { B d 9 } { m }\n",
|
|
"image_path": "./data/HME100K/test_images/test_641.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 1 } { 6 } ( 3 a ^ { 2 } - 3 b ^ { 2 } + 6 - 2 a ^ { 2 } + 4 b ^ { 2 } - 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_642.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2(30 + 20) = 60 + 40\".",
|
|
"gt_answers": "4 A l + 3 O _ { 2 } = 2 A l _ { 2 } O _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_643.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ho + H2O = H2 + O2.\"",
|
|
"gt_answers": "2 N a O H + C u C l _ { 2 } = C u ( O H ) _ { 2 } \\downarrow + 2 N a C l\n",
|
|
"image_path": "./data/HME100K/test_images/test_644.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, and the resultant value of their sum, 10.",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\cdot \\frac { 2 } { 3 } x + \\frac { 1 } { 2 } \\cdot \\frac { 4 } { 3 } = \\frac { 2 } { 5 } x - \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_645.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 100 - 1000 = 0.",
|
|
"gt_answers": "7 0 - 7 0 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_646.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 5 \\div 1 0 0 = 0 . 2 5 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_647.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "2 \\pi t + \\frac { \\pi } { 4 } = \\frac { 3 } { 2 } \\pi 2 \\pi t = \\frac { 5 } { 4 } \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_648.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Chinese.",
|
|
"gt_answers": "y = x ^ { 2 } - 6 x + 9 = ( x - 3 ) ^ { 2 . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_649.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible for me to accurately transcribe it using LaTeX. However, I can provide a rough translation of the formula:\n\n\"The sum of the squares of the first 100 natural numbers is equal to the sum of the squares of the first 100 even numbers.\"",
|
|
"gt_answers": "x _ { 3 } = \\frac { - 5 + \\sqrt { x - 1 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_650.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x^2 + 3x + 4 = 0.\"",
|
|
"gt_answers": "\\frac { 3 } { 2 x + y } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_652.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 1 = 0\\)",
|
|
"gt_answers": "5 \\times \\frac { 1 } { 3 0 } = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_653.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(x^2 + y^2 = 180^2\\)",
|
|
"gt_answers": "\\angle 2 = 1 8 0 ^ { \\circ } - \\angle 1 = 1 8 0 ^ { \\circ } - 4 0 ^ { \\circ } = 1 4 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_654.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "C D \\bot M B\n",
|
|
"image_path": "./data/HME100K/test_images/test_656.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z = 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 2",
|
|
"gt_answers": "A E ^ { 2 } - E B - E C , \\angle A E C = \\angle A E ^ { \\prime } C\n",
|
|
"image_path": "./data/HME100K/test_images/test_659.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"40-5y^34.\"",
|
|
"gt_answers": "4 0 - 5 y + 3 y\n",
|
|
"image_path": "./data/HME100K/test_images/test_660.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x + 2h = 2(x + h)",
|
|
"gt_answers": "\\varphi x _ { 2 } = \\frac { 2 _ { n } } { m + m }\n",
|
|
"image_path": "./data/HME100K/test_images/test_661.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x + y = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_662.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 100 - 70 = 30.",
|
|
"gt_answers": "\\frac { 7 } { 1 0 0 } = \\frac { 3 0 } { 3 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_663.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"W/F = 40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "W = F \\cdot S = 4 0 N \\cdot 1 0 m = 4 0 0 J\n",
|
|
"image_path": "./data/HME100K/test_images/test_664.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 2 = 0\\)",
|
|
"gt_answers": "( 2 a - 3 ) x = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_665.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\" in LaTeX format.",
|
|
"gt_answers": "x _ { 2 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_666.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 614 = 600.",
|
|
"gt_answers": "6 1 4 \\approx 6 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_667.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Eb(B-F) = 180\u00b0.\"",
|
|
"gt_answers": "E B C + \\angle D F B = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_668.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x3 + 6x2 - 2x + 1 = 0.\"",
|
|
"gt_answers": "S _ { \\Delta B O C } = O B \\cdot C E \\cdot \\frac { 1 } { 2 } = 4 \\times 3 \\times \\frac { 1 } { 2 } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_669.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "2 + 3 = - \\frac { 5 } { a } , 2 \\times 3 = \\frac { 1 } { a } ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_671.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 + c^2 = 3ab + 4ac + 5bc\\)",
|
|
"gt_answers": "\\frac { b + c } { a } = \\frac { a + c } { b } = \\frac { a + b } { c } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_672.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "3 x y ( x ^ { 2 } y - x y ^ { 2 } + x y ) - x y ^ { 2 } ( 2 x ^ { 2 } - 6 x y + 2 x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_673.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\",
|
|
"gt_answers": "\\frac { D E } { B C } = \\frac { 1 } { 3 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_674.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 4x + 1 = 0.\"",
|
|
"gt_answers": "\\therefore - 3 < x \\leq 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_675.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/5 + 3/5 + 5/5 + 8/5 = 18/5.",
|
|
"gt_answers": "\\frac { 1 } { 3 } + \\frac { 1 } { 5 } = \\frac { 8 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_676.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2} + 7^{2} + 8^{2} + 9^{2} + 10^{2} + 11^{2} + 12^{2} + 13^{2} + 14^{2} + 15^{2} + 16^{2} + 17^{2} + 18^{2} + 19^{2} + 20^{2} + 21^{2} + 22^{2} + 23^{2} + 24^{2} + 25^{2} + 26^{2} + 27^{2} + 28^{2} + 29^{2} + 30^{2} + 31^{2} + 32^{2} + 33^{2} + 34^{2} + 35^{2} + 36^{2} + 37^{2} + 38^{2} + 39^{2} + 40^{2} + 41^{2} + 42^{2} + 43^{2} + 44^{2} + 45^{2} + 46^{2} + 47^{2} + 48^{2} + 49^{2} + 50^{2} + 51^{2} + 52^{2} + 53^{2} + 54^{2} + 55^{2} + 56^{2} + 57^{2} + 58^{2} + 59^{2} + 60^{2} + 61^{2} + 62^{2} + 63^{2} + 64^{2} + 65^{2} + 66^{2} + 67^{2} + 68^{2} + 69^{2} + 70^{2} + 71^{2} + 72^{2} + 73^{2}",
|
|
"gt_answers": "2 \\cdot ( - \\frac { 1 } { 3 } ) \\cdot 3 6 + 9 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_678.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"f(x) = 1/x + 1/x^2 + 1/x^3 + 1/x^4 + 1/x^5 + 1/x^6 + 1/x^7 + 1/x^8 + 1/x^9 + 1/x^10 + 1/x^11 + 1/x^12 + 1/x^13 + 1/x^14 + 1/x^15 + 1/x^16 + 1/x^17 + 1/x^18 + 1/x^19 + 1/x^20 + 1/x^21 + 1/x^22 + 1/x^23 + 1/x^24 + 1/x^25 + 1/x^26 + 1/x^27 + 1/x^28 + 1/x^29 + 1/x^30 + 1/x^31 + 1/x^32 + 1/x^33 + 1/x^34 + 1/x^35 + 1/x^36 + 1/x^37 + 1/x^38 + 1/x^39 + 1/x^40 + 1/x^41 + 1/x^42 + 1/x^43 + 1/x^44 + 1/x^45 + 1/x^46 + 1/x^47 + 1/x^48 + 1/x^49 + 1/x^50 + 1/x^51 + 1/x^52 + 1/x^53 + 1/x^54 + 1/x^55 + 1/x^56 + 1/x^57 + 1/x^58 + 1/x^59 + 1/x^60 + 1/x^61 + 1/x^62 + 1/x^63 + 1/x",
|
|
"gt_answers": "= \\frac { - B H } { A H } = \\tan \\angle D A G\n",
|
|
"image_path": "./data/HME100K/test_images/test_679.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x2kz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xkz + 2xk",
|
|
"gt_answers": "2 x = 2 k \\pi ^ { 2 } \\pm \\frac { \\pi } { 6 } ( k \\in z )\n",
|
|
"image_path": "./data/HME100K/test_images/test_680.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{4567890}{1234567890}\n\\end{aligned}\n\\end{equation}\n\nThe formula is a fraction with the numerator being 4567890 and the denominator being 1234567890.",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_681.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x + 1 = 3\" in LaTeX format.",
|
|
"gt_answers": "x = \\frac { 1 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_682.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 400\\)",
|
|
"gt_answers": "\\angle B O D = \\angle C O D = \\frac { 1 } { 2 } \\angle B O C = \\frac { 1 } { 2 } \\times 1 2 0 ^ { \\circ } = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_683.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `2(a + b) + c = 2a + 2b + c`.",
|
|
"gt_answers": "\\angle A O C + \\angle C O D + \\angle D O E = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_684.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 2 = 0\\)",
|
|
"gt_answers": "x - \\frac { 1 } { 3 } x = \\frac { 2 } { 3 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_685.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3.244 + 7.333 + 3.333 = 14.807.",
|
|
"gt_answers": "3 \u3001 2 4 \\div 7 = 3 \\cdots 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_686.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(B_D + B_E + B_F + B_G + B_H + B_I + B_J + B_K + B_L + B_M + B_N + B_O + B_P + B_Q + B_R + B_S + B_T + B_U + B_V + B_W + B_X + B_Y + B_Z = 100\\)",
|
|
"gt_answers": "\\frac { B D } { D A } = \\frac { B E } { E M } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_687.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is the famous equation of energy conservation, which states that the total energy of an object is equal to the mass of the object multiplied by the square of its speed of light.",
|
|
"gt_answers": "\\frac { 1 } { x + y } = m\n",
|
|
"image_path": "./data/HME100K/test_images/test_688.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis equation represents the basic mathematical operation of multiplication, where the first term is multiplied by the second term, resulting in a fraction with a denominator of 4.",
|
|
"gt_answers": "2 N a O H + B a C O _ { 3 } \\downarrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_689.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"L2 + 4AoD - 65\u00b0\".",
|
|
"gt_answers": "\\angle 2 = \\frac { 1 } { 2 } \\angle A O D = 6 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_690.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(e^{x} = \\sum_{n=0}^{\\infty} \\frac{x^n}{n!} = \\lim_{n \\to \\infty} \\left(1 + \\frac{x}{n}\\right)^n\\)",
|
|
"gt_answers": "x = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_691.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\ny = 8x + 13\n\nThe formula is written in the form of an equation, where y is the dependent variable and x is the independent variable. The value of y is determined by multiplying x by 8 and adding 13.",
|
|
"gt_answers": "x = 1 8 , y = - 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_693.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(BP = \\frac{MP \\times 100}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { M P } { B P } = \\frac { P M } { P A } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_694.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 3(3-1) + 4(3-1) + 5(3-1) + 6(3-1) + 7(3-1) + 8(3-1) + 9(3-1) + 10(3-1) + 11(3-1) + 12(3-1) + 13(3-1) + 14(3-1) + 15(3-1) + 16(3-1) + 17(3-1) + 18(3-1) + 19(3-1) + 20(3-1) + 21(3-1) + 22(3-1) + 23(3-1) + 24(3-1) + 25(3-1) + 26(3-1) + 27(3-1) + 28(3-1) + 29(3-1) + 30(3-1) + 31(3-1) + 32(3-1) + 33(3-1) + 34(3-1) + 35(3-1) + 36(3-1) + 37(3-1) + 38(3-1) + 39(3-1) + 40(3-1) + 41(3-1) + 42(3-1) + 43(3-1) + 44(3-1) + 45(3-1) + 46(3-1) + 47(3-1) + 48(3-1) + 49(3-1) + 50(3-1) + 51(3-1) + 52(3-1) + 53(3-1) + 54(3-1) + 55(3-1) + 56(3-1) + 57(3-1) + 58(3-1) + 59(",
|
|
"gt_answers": "1 2 3 \\div 3 = 4 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_695.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "x = 0 . 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_696.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)\n\nThis is a quadratic equation in the variable x, with the coefficients 2, 3, and 4. The expression is written using the LaTeX equation editor, which allows for easy formatting and readability.",
|
|
"gt_answers": "\\frac { 7 } { 9 } = \\frac { 1 } { 9 } = \\frac { 6 } { 9 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_697.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3t^2 - 10t + 10 = 0.\"",
|
|
"gt_answers": "\\frac { 5 0 } { 3 } + b = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_698.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `2x^2 - 3x + 2 = 0`.",
|
|
"gt_answers": "- \\frac { 9 } { 5 } x - \\frac { 2 } { 3 } x \\leq 2 - 3 \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_699.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)\n\nThis is a quadratic equation in the variable x, with the coefficients 2, 3, and 4. The solution to this equation is x = 2.",
|
|
"gt_answers": "3 0 \\% + 2 0 \\% y = 1 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_700.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + y^2 = 1`.",
|
|
"gt_answers": "2 8 + 9 3 = 3 0 x - 5 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_701.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b^2(c^2+d^2) = (b^2)(c^2+d^2) = b^2c^2 + b^2d^2 + 2bcd\\)",
|
|
"gt_answers": "( b - c ) - ( a + d ) = b - c - a - d\n",
|
|
"image_path": "./data/HME100K/test_images/test_702.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 6 + 2\\sqrt{x - 6} + 3x - 10\\)",
|
|
"gt_answers": "y = \\frac { 6 } { k + 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_704.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"58.9567142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142",
|
|
"gt_answers": "5 8 . 0 9 < 5 8 . 1 7 < 5 8 . 5 2 < 5 9 . 0 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_707.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x2 - 2x + 1.",
|
|
"gt_answers": "\\frac { x - 1 } { 6 } - \\frac { 3 x - 1 } { 2 } > 2 - \\frac { x } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_708.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: `r^2 = 10^2 - 25^2`.",
|
|
"gt_answers": "r = d \\div 2 = 1 0 \\div 2 = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_709.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(57600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "5 7 6 + 3 0 + 2 7 0 = 8 7 6 \u3001 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_710.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 744 = 774.",
|
|
"gt_answers": "x = - \\frac { 2 } { 7 + 4 \\sqrt { 3 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_711.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x^2 + 4x + 5 = 10\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = \\frac { 2 } { 3 } \\times \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_712.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 2 } { x - 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_713.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 3x + 2 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_714.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BG/BC\" and is likely a formula for calculating the ratio of two numbers. The \"BG\" and \"BC\" represent the two numbers being compared, and the \"/\" symbol represents the division operation.",
|
|
"gt_answers": "O G / / B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_715.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 5x + 15}{x + 3} = 15\n\\end{equation}\n\nThis equation can be solved using the method of factoring. The first step is to factor out the common factor of (x + 3) from both the numerator and denominator. This gives us:\n\n\\begin{equation}\n\\frac{x^2 + 5x + 15}{x + 3} = \\frac{(x + 3)(x + 2)}{x + 3} = \\frac{x^2 + 2x + 3x + 2}{x + 3} = \\frac{x^2 + 5x + 6}{x + 3}\n\\end{equation}\n\nThe next step is to factor out the common factor of 6 from both the numerator and denominator. This gives us:\n\n\\begin{equation}\n\\frac{x^2 + 5x + 6}{x + 3} = \\frac{x^2 + 5x + 6}{x + 3} = \\frac{x^2 + 5x + 6}{x + 3} = \\frac{x^2 + 5x + 6}{x + 3}\n\\end{equation}\n\nThe final step is to factor out the common factor of 3 from both the numerator and denominator. This gives us:\n\n\\begin{equation}\n\\frac{x^2 + 5x + 6}{x + 3} = \\frac{x^2 + 5x + 6}{x + 3} = \\frac{x^2 + 5x + 6}{x + 3} = \\frac{x^2 + 5x + 6}{x + 3}\n\\end{equation}\n\nThe final expression of the formula is:\n\n\\begin{equation}\nx^2 + 5x + 6 = 3x^2 + 15x + 6\n\\end{equation}\n\nSolving for x, we get:\n\n\\begin{equation}\nx = \\frac{-6 \\pm \\sqrt{",
|
|
"gt_answers": "1 5 \\times \\frac { 2 x - 7 } { 3 } = 1 5 \\times \\frac { 3 - 2 x } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_716.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LB07-80^{\\circ}\\)",
|
|
"gt_answers": "\\angle B O D = 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_717.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(6x^2 + 4x^3 + 4x^4 + 4x^5 + 4x^6 + 4x^7 + 4x^8 + 4x^9 + 4x^{10} + 4x^{11} + 4x^{12} + 4x^{13} + 4x^{14} + 4x^{15} + 4x^{16} + 4x^{17} + 4x^{18} + 4x^{19} + 4x^{20} + 4x^{21} + 4x^{22} + 4x^{23} + 4x^{24} + 4x^{25} + 4x^{26} + 4x^{27} + 4x^{28} + 4x^{29} + 4x^{30} + 4x^{31} + 4x^{32} + 4x^{33} + 4x^{34} + 4x^{35} + 4x^{36} + 4x^{37} + 4x^{38} + 4x^{39} + 4x^{40} + 4x^{41} + 4x^{42} + 4x^{43} + 4x^{44} + 4x^{45} + 4x^{46} + 4x^{47} + 4x^{48} + 4x^{49} + 4x^{50} + 4x^{51} + 4x^{52} + 4x^{53} + 4x^{54} + 4x^{55} + 4x^{56} + 4x^{57} + 4x^{58} + 4x^{59} + 4x^{60} + 4x^{61} + 4x^{62} + 4x^{63} + 4x^{64} + 4x^{65}",
|
|
"gt_answers": "1 2 \\times 6 \\times 2 = 1 4 4 ( d m ^ { 3 } ) = 1 4 4 ( L )\n",
|
|
"image_path": "./data/HME100K/test_images/test_719.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "2 \\frac { 1 } { 2 } x - \\frac { 2 } { 3 } x = 5 + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_720.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "1 - \\frac { 1 } { 4 } \\sin ^ { 2 } \\alpha = 1 - \\frac { 1 } { 4 } ( 1 - \\cos ^ { 2 } \\alpha )\n",
|
|
"image_path": "./data/HME100K/test_images/test_721.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 36 = 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + ",
|
|
"gt_answers": "3 6 \\div 4 = \\boxed { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_722.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Japanese.",
|
|
"gt_answers": "a + 3 b\n",
|
|
"image_path": "./data/HME100K/test_images/test_723.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(0.08 \\times 100 + 0.2 \\times 25 = 20.8\\)",
|
|
"gt_answers": "0 . 0 8 = \\frac { 8 } { 1 0 0 } = \\frac { 2 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_724.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_725.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\nP = 2.54 x 10^(-10) x 12 x 2 x 0.02 x 0.005 x 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "P \\cdot Q : t = \\frac { \\lambda } { V } = \\frac { 1 . 2 m } { 2 0 / s } = 0 . 6 s\n",
|
|
"image_path": "./data/HME100K/test_images/test_726.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "x = k \\pi + \\frac { \\pi } { 2 } , k \\in z ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_727.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1600/1000 = 1.6\" using the LaTeX formula notation.",
|
|
"gt_answers": "1 6 0 0 \\div 1 0 0 0 = 1 . 6 ( d m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_728.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{",
|
|
"gt_answers": "f ( - \\frac { \\pi } { 4 } ) = f ( \\frac { 3 } { 4 } \\pi ) = \\frac { \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_730.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x = - \\frac { \\sqrt { 1 0 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_731.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x(8-2) = 16-4 = 12.\"",
|
|
"gt_answers": "x + 5 ( m - 8 ) = m + 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_732.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "f ( 5 ) = \\cos \\frac { 5 \\pi } { 3 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_733.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a number and a symbol, which could be a mathematical operator such as \"+\" or \"-\".",
|
|
"gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_734.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"f(x) = 2x^2 - 1\".",
|
|
"gt_answers": "\\{ x 1 - b \\leq x \\leq 3 \\}\n",
|
|
"image_path": "./data/HME100K/test_images/test_735.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis is a simple algebraic equation that can be solved by multiplying both sides by 2 and then dividing both sides by the denominator. The result is:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis is the same expression as the original equation.",
|
|
"gt_answers": "x = \\frac { 2 \\sqrt { 2 } + \\sqrt { 2 8 } } { 4 } = \\frac { \\sqrt { 2 } \\pm \\cdot \\sqrt { 7 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_736.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\angle 1 = \\angle 2 = \\angle 3 = \\angle D E C\n",
|
|
"image_path": "./data/HME100K/test_images/test_737.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 2n^2 = 4n^2 + 4x^2\\)",
|
|
"gt_answers": "a = \\frac { 2 \\ln x } { x ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_738.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"B = 2(v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2 + v^2/2",
|
|
"gt_answers": "B = \\frac { M o ( V _ { 0 } + V _ { 1 } ) } { 6 e V }\n",
|
|
"image_path": "./data/HME100K/test_images/test_739.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"40-2BC\".",
|
|
"gt_answers": "A O = \\frac { 1 } { 2 } B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_740.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 0 m = 1 0 0 0 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_741.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^3 - 3x + 5\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_742.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_{2}H_{5}O_{2} + 2CO_{2} \\rightarrow 2CO_{2} + 3H_{2}O\\)",
|
|
"gt_answers": "\\cos c = \\frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { 2 a b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_743.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) - 3(6a + 2b) = 6(3a + 2b) -",
|
|
"gt_answers": "6 ( \\frac { x } { 6 } - \\frac { 6 a - 1 } { 3 } ) = 6 ( x - \\frac { 5 a - 1 } { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_744.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nZn(OH)2 + H2O = Zn(OH)3 + H2",
|
|
"gt_answers": "Z n + 2 H C l = H _ { 2 } \\uparrow +\n",
|
|
"image_path": "./data/HME100K/test_images/test_746.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(n \\cdot (n + 1) \\cdot (n + 2) \\cdot (n + 3) \\cdot (n + 4) \\cdot (n + 5) \\cdot (n + 6) \\cdot (n + 7) \\cdot (n + 8) \\cdot (n + 9) \\cdot (n + 10) \\cdot (n + 11) \\cdot (n + 12) \\cdot (n + 13) \\cdot (n + 14) \\cdot (n + 15) \\cdot (n + 16) \\cdot (n + 17) \\cdot (n + 18) \\cdot (n + 19) \\cdot (n + 20) \\cdot (n + 21) \\cdot (n + 22) \\cdot (n + 23) \\cdot (n + 24) \\cdot (n + 25) \\cdot (n + 26) \\cdot (n + 27) \\cdot (n + 28) \\cdot (n + 29) \\cdot (n + 30) \\cdot (n + 31) \\cdot (n + 32) \\cdot (n + 33) \\cdot (n + 34) \\cdot (n + 35) \\cdot (n + 36) \\cdot (n + 37) \\cdot (n + 38) \\cdot (n + 39) \\cdot (n + 40) \\cdot (n + 41) \\cdot (n + 42) \\cdot (n + 43) \\cdot (n + 44) \\cdot (n + 45) \\cdot (n + 46) \\cdot (n + 47) \\cdot (n + 48) \\cdot (n + 49) \\cdot (n + 50) \\cdot (n + 51) \\cdot (n + 52) \\cdot (n + 53) \\cdot (n + 54) \\cdot (n + 55) \\cdot (n + 56) \\",
|
|
"gt_answers": "\\frac { 1 } { ( n + 1 ) ^ { 2 } } < \\frac { 1 } { n ( n + 1 ) } = \\frac { 1 } { n } - \\frac { 1 } { n + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_749.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\begin{equation}\n\\begin{aligned}\n\\mathrm{rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) + rad(AC) + rad(PC) + rad(AB) + rad(BC) +",
|
|
"gt_answers": "\u3001 A D \u3001 B C = A B \u3001 D C\n",
|
|
"image_path": "./data/HME100K/test_images/test_751.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(d_{1y} = 2d_{1x} - 2d_{2x} + d_{2y}\\)",
|
|
"gt_answers": "x - 2 y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_752.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n2n + 3h + 3s = 2(n + 1) + 3(h + 1) + 3(s + 1)\n\nThis formula represents the total number of electrons in a neutral atom of an element with atomic number n, atomic mass number A, and valence number Z. The formula can be used to calculate the number of electrons in an atom of any element, given the values of n, A, and Z.",
|
|
"gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_754.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `x^2 + 5x - 4 = 0`.",
|
|
"gt_answers": "( 6 + 1 5 ) x = 5 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_755.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "D O E = \\angle D B E + \\angle A E B = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_756.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(L = \\frac{BC}{2} \\cdot \\cos \\theta\\)",
|
|
"gt_answers": "\\cdot \\angle B C D = \\frac { 1 } { 2 } \\times 5 0 ^ { \\circ } = 2 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_758.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the multiplication of two fractions, each with a denominator of 2. The result is a fraction with a denominator of 4.",
|
|
"gt_answers": "A N = \\frac { 1 } { 2 } A _ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_759.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "D E = \\frac { 1 } { 2 } A C > E F = \\frac { 1 } { 2 } A B ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_760.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 12x4=48.",
|
|
"gt_answers": "1 2 \\times 4 = 4 8 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_761.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ue = LdVd.\"",
|
|
"gt_answers": "u _ { e } = \\alpha - \\alpha V\n",
|
|
"image_path": "./data/HME100K/test_images/test_763.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times 2 + 2\\times ",
|
|
"gt_answers": "2 n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_764.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"trend-jnd\".",
|
|
"gt_answers": "b _ { n + 1 } - b _ { n } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_765.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2.556 + 13.656 = 16.212 + 13.656 = 30.868\\)",
|
|
"gt_answers": "1 2 . 5 6 + 1 2 5 . 6 = 1 3 8 . 1 6 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_766.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(30-10) + 5(85-50) + 7(65-30) + 9(55-20) + 11(45-10) + 13(35-5) + 15(25-0) + 17(15-5) + 19(10-0) + 21(5-0) + 23(0-5) + 25(0-0) = 1000.",
|
|
"gt_answers": "2 7 + 3 0 = 5 7 6 3 - 5 = 5 8 3 7 + 6 = 4 3 1 9 + 5 = 2 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_767.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(AOC = \\frac{3 \\times 5 \\times 7 \\times 9 \\times 11 \\times 13 \\times 15 \\times 17 \\times 19 \\times 21 \\times 23 \\times 25 \\times 27 \\times 29 \\times 31 \\times 33 \\times 35 \\times 37 \\times 39 \\times 41 \\times 43 \\times 45 \\times 47 \\times 49 \\times 51 \\times 53 \\times 55 \\times 57 \\times 59 \\times 61 \\times 63 \\times 65 \\times 67 \\times 69 \\times 71 \\times 73 \\times 75 \\times 77 \\times 79 \\times 81 \\times 83 \\times 85 \\times 87 \\times 89 \\times 91 \\times 93 \\times 95 \\times 97 \\times 99 \\times 101 \\times 103 \\times 105 \\times 107 \\times 109 \\times 111 \\times 113 \\times 115 \\times 117 \\times 119 \\times 121 \\times 123 \\times 125 \\times 127 \\times 129 \\times 131 \\times 133 \\times 135 \\times 137 \\times 139 \\times 141 \\times 143 \\times 145 \\times 147 \\times 149 \\times 151 \\times 153 \\times 155 \\times 157 \\times 159 \\times 161 \\times 163 \\times 165 \\times 167 \\times 169 \\times 171 \\times 173 \\times 175 \\times 177 \\times 179 \\times 181 \\times 1",
|
|
"gt_answers": "\\angle A O C = 3 6 0 ^ { \\circ } - \\angle A O B - \\angle B O C = 3 6 0 ^ { \\circ } - 1 5 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_768.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: S = 60 - 15 + 45 - 3.",
|
|
"gt_answers": "S = 6 0 - 1 5 = 4 5 ( d m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_769.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: y = 2x^2 - 3.",
|
|
"gt_answers": "y = 2 x - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_770.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1+2=3\" using the LaTeX math notation.",
|
|
"gt_answers": "\\frac { 1 } { 1 2 } x = 7 + \\frac { 1 } { 6 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_771.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 2x - 4 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x \\div 1 . 2 = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_772.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"703 + 100 = 803.\"",
|
|
"gt_answers": "7 0 3 \\approx 7 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_773.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as AB-2NS.",
|
|
"gt_answers": "A B = 2 \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_774.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is: 2BaE FdAf-45.",
|
|
"gt_answers": "\\angle B A E + \\angle D A F = 4 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_776.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 5x - 3 = 0\\)",
|
|
"gt_answers": "x = - \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_777.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 - 3xy = 9\\)",
|
|
"gt_answers": "x _ { 2 } = 1 - \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_778.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `tan(x) = 7/14`.",
|
|
"gt_answers": "\\tan \\frac { \\frac { 1 4 } { 3 } \\pi } { - 2 \\cdot } = - \\frac { 7 } { 3 } \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_779.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `n^2 - 3n + 4 = 0`, where `n` is a variable.",
|
|
"gt_answers": "x = \\sqrt [ 3 ] { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_781.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "( x - a ) ^ { 2 } + ( y - 1 ) ^ { 2 } = a ^ { 2 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_782.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a few numbers and letters, which can be represented using LaTeX as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + y^2 + z^2 + 2xy + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + ",
|
|
"gt_answers": "a ^ { 2 } + a = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_783.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a few numbers and symbols, which could be a mathematical equation or a formula related to physics or chemistry.",
|
|
"gt_answers": "6 . m = \\pm 2 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_785.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x + 2y = 10\\)",
|
|
"gt_answers": "f ^ { \\prime } ( x ) - 9 x = 3 x ^ { 2 } + ( 2 b - 9 ) x + c = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_786.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\times 2 \\times 1 + 1 \\",
|
|
"gt_answers": ": \\frac { 1 } { 2 } B a \\times Q C = \\frac { 1 } { 2 } E P \\cdot P C + \\frac { 1 } { 2 } ( B a + E P ) Q P\n",
|
|
"image_path": "./data/HME100K/test_images/test_787.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(R_1 + R_2 = R_3 + R_4\\)",
|
|
"gt_answers": "R _ { 2 } = \\frac { U } { I _ { 2 } } = \\frac { 1 2 V } { 2 A } = 6 \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_788.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 2012 + 2013 + 2014 + 2015 + 2016 + 2017 + 2018 + 2019 + 2020 + 2021 + 2022 + 2023 + 2024 + 2025 + 2026 + 2027 + 2028 + 2029 + 2030 + 2031 + 2032 + 2033 + 2034 + 2035 + 2036 + 2037 + 2038 + 2039 + 2040 + 2041 + 2042 + 2043 + 2044 + 2045 + 2046 + 2047 + 2048 + 2049 + 2050 + 2051 + 2052 + 2053 + 2054 + 2055 + 2056 + 2057 + 2058 + 2059 + 2060 + 2061 + 2062 + 2063 + 2064 + 2065 + 2066 + 2067 + 2068 + 2069 + 2070 + 2071 + 2072 + 2073 + 2074 + 2075 + 2076 + 2077 + 2078 + 2079 + 2080 + 2081 + 2082 + 2083 + 2084 + 2085 + 2086 + 2087 + 2088 + 2089 + 2090 + 2091 + 2092 + 2093 +",
|
|
"gt_answers": "\\frac { 2 0 1 2 } { 2 0 1 3 } x = 2 0 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_790.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(2\\sqrt{b^2-2b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^2-b+1} = 2\\sqrt{b^",
|
|
"gt_answers": "\\frac { 6 0 . \\pi . 2 ^ { 2 } } { 3 6 0 } = \\frac { 2 \\pi } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_792.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible for me to accurately transcribe it into LaTeX format. However, I can provide a rough translation of the expression: \"The sum of the squares of the first 100 natural numbers.\"",
|
|
"gt_answers": "y _ { 2 } = \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_793.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"11-10 = 1\".",
|
|
"gt_answers": "+ \\frac { 1 } { 3 } = \\frac { 4 } { 1 0 } = \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_794.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x^2 + 3x + 2 = 0.",
|
|
"gt_answers": "3 x = \\frac { 3 } { 5 } \\times \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_796.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\nLCAB = 134\u00b0\n\nThe formula is written in LaTeX format, which is a standard mathematical notation used in scientific and technical documents.",
|
|
"gt_answers": "\\angle C A B = 1 3 4 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_797.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Greek, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a red circle around it, which indicates that it is likely a mathematical expression.",
|
|
"gt_answers": "O B = O A + O B\n",
|
|
"image_path": "./data/HME100K/test_images/test_799.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 0.055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555",
|
|
"gt_answers": "0 . 5 < 0 . 5 1 < 0 . 5 0 1 < 0 . 5 1 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_800.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x +",
|
|
"gt_answers": "( 1 - \\frac { 1 } { 1 2 } \\times 8 ) \\div ( 1 4 - 8 ) = \\frac { 1 } { 1 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_801.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"90x12360\" using LaTeX format.",
|
|
"gt_answers": "\\frac { 9 0 ^ { \\circ } \\times \\pi \\times x \\times 1 2 ^ { 2 } } { 3 6 0 ^ { \\circ } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_802.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nDH = \\frac{D}{D_0} \\cdot \\left( \\frac{A}{A_0} \\right)^2 \\cdot \\left( \\frac{B}{B_0} \\right)^2 \\cdot \\left( \\frac{C}{C_0} \\right)^2 \\cdot \\left( \\frac{D}{D_0} \\right)^2 \\cdot \\left( \\frac{E}{E_0} \\right)^2 \\cdot \\left( \\frac{F}{F_0} \\right)^2 \\cdot \\left( \\frac{G}{G_0} \\right)^2 \\cdot \\left( \\frac{H}{H_0} \\right)^2 \\cdot \\left( \\frac{I}{I_0} \\right)^2 \\cdot \\left( \\frac{J}{J_0} \\right)^2 \\cdot \\left( \\frac{K}{K_0} \\right)^2 \\cdot \\left( \\frac{L}{L_0} \\right)^2 \\cdot \\left( \\frac{M}{M_0} \\right)^2 \\cdot \\left( \\frac{N}{N_0} \\right)^2 \\cdot \\left( \\frac{O}{O_0} \\right)^2 \\cdot \\left( \\frac{P}{P_0} \\right)^2 \\cdot \\left( \\frac{Q}{Q_0} \\right)^2 \\cdot \\left( \\frac{R}{R_0} \\right)^2 \\cdot \\left( \\frac{S}{S_0} \\right)^2 \\cdot \\left( \\frac{T}{T_0} \\right)^2 \\cdot \\left( \\frac{U}{U_0} \\right)^2 \\cdot \\left( \\frac{V}{V_0} \\right)^2 \\cdot \\left( \\frac{W}{W_0} \\right)^2 \\cdot \\left( \\frac{X}{X_0} \\right)^2 \\cdot \\left( \\frac{Y}{Y_0} \\right)^2 \\cdot \\left( \\frac{Z}{Z_0} \\right)^2 \\cdot \\left",
|
|
"gt_answers": "D H = \\frac { 1 } { 2 } A D = \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_803.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 4x - 3 = 0\\)",
|
|
"gt_answers": "\\sqrt { 3 } - 1 - 2 \\sqrt { 3 } + 2 \\sqrt { 3 } - 4 = - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_804.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "x = 2 0 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_805.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(x^2 + 5x + 6 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = - \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_807.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{4} + \\frac{1}{9} \\right) = \\frac{1}{18}\n\\end{equation}\n\nThis equation can be simplified further by using the distributive property of multiplication over addition:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{4} + \\frac{1}{9} \\right) = \\frac{1}{2} \\left( \\frac{1}{4} \\cdot \\frac{1}{9} + \\frac{1}{9} \\cdot \\frac{1}{4} \\right) = \\frac{1}{2} \\left( \\frac{1}{16} + \\frac{1}{16} \\right) = \\frac{1}{16}\n\\end{equation}\n\nTherefore, the final expression of the formula is:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{4} + \\frac{1}{9} \\right) = \\frac{1}{16}\n\\end{equation}",
|
|
"gt_answers": "\\vert - \\frac { 1 } { 2 } - \\frac { 1 } { 4 } \\vert = \\frac { 9 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_808.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 4x + 2\\)",
|
|
"gt_answers": "\\frac { x _ { 2 } y _ { 1 } - x _ { 1 } y _ { 2 } } { y _ { 1 } - y _ { 2 } } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_809.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a black background, which could be written in LaTeX as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\text{Formula}\n\\end{aligned}\n\nThis equation is written in a standard mathematical notation, with the formula itself being the main content and the surrounding text being the title.",
|
|
"gt_answers": "3 x + 1 > 5 x - 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_810.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "P _ { 4 } ( - 1 + \\sqrt { 3 } , 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_811.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"bladladybebe=90%\".",
|
|
"gt_answers": "\\angle A D B = \\angle A D ^ { \\prime } B ^ { \\prime } = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_812.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae Ae",
|
|
"gt_answers": "\\frac { A E } { D E } = \\frac { A D } { D F } = \\frac { D E } { E F } ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_813.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBOF-a2\" using LaTeX format.",
|
|
"gt_answers": "\\angle B O F = \\frac { 1 } { 2 } a\n",
|
|
"image_path": "./data/HME100K/test_images/test_815.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(K_{eq} = \\frac{1}{2} \\left( \\frac{RT}{F} \\right) \\ln \\left( \\frac{P_1}{P_2} \\right) \\), where:\n\n* K_{eq} is the equilibrium constant\n* R is the universal gas constant\n* T is the temperature in Kelvin\n* F is the Faraday constant\n* P_{1} and P_{2} are the partial pressures of the reactants and products, respectively.",
|
|
"gt_answers": "k = - \\frac { 1 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_817.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 5\\)",
|
|
"gt_answers": "y =\n",
|
|
"image_path": "./data/HME100K/test_images/test_818.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 881267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-6271267-62712",
|
|
"gt_answers": "8 \\cdots 8 5 1 2 \\div 6 7 = 7 \\cdots 4 3 5 1 2 \\div 8 5 = 6 \\cdots 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_820.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\",
|
|
"gt_answers": "y = \\frac { 1 } { 2 } x ^ { 2 } - x - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_821.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 6x + 4 = 2(x^2 + 2x + 2)`.",
|
|
"gt_answers": "x ^ { 2 } - x - 6 + 4 = 2 x ^ { 2 } - 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_822.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 2x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "1 5 0 x = 8 0 \\times 1 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_823.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "y = \\sqrt { \\frac { 1 1 } { 9 } x ^ { 2 } - 4 x + 3 6 } ( 0 < x < 9 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_824.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nV = I/R\n\nThe formula represents the relationship between voltage (V) and current (I) in an electrical circuit, where R is the resistance of the circuit.",
|
|
"gt_answers": "V _ { c } = \\frac { 1 } { 2 } m / s\n",
|
|
"image_path": "./data/HME100K/test_images/test_825.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 2x^2 + 3x + 4.",
|
|
"gt_answers": "y _ { \\min } = 2 , y _ { m } G x = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_826.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4} \\).",
|
|
"gt_answers": ") = \\frac { 3 } { 6 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_827.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x = 3j + 4.\"",
|
|
"gt_answers": "x = - \\sqrt { 4 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_828.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten style, but it can be represented in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x 1 = 1 + \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_829.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(A + B + C = E + F + G\\)\n\nThe formula is written using the equation editor in LaTeX, which is a standard mathematical notation system for writing mathematical expressions.",
|
|
"gt_answers": "\\frac { A F } { C D } = \\frac { E F } { E D } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_830.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 49\\)",
|
|
"gt_answers": "3 . 1 4 \\times ( 5 ^ { 2 } - 4 ^ { 2 } ) = 2 8 . 2 6 ( c m ^ { 2 } ) 2 8 . 2 6 \\times 8 0 = 2 2 6 0 . 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_831.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the half of the half of a whole, which is equal to one fourth.",
|
|
"gt_answers": "O A \\cdot M P = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_832.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Pops 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "F = P S = 1 0 0 0 P a \\times 0 . 0 5 m ^ { 2 } = 5 0 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_833.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, where x is equal to 2 and y is equal to 3. The result of the equation is 10.",
|
|
"gt_answers": "\\frac { 9 2 } { 1 0 0 } = \\frac { 4 6 } { 3 0 } = \\frac { 2 3 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_834.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BDBIBC\" using the LaTeX formula notation.",
|
|
"gt_answers": ". B D \\bot B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_835.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(M = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "M = \\frac { 2 0 1 8 } { \\sqrt { 2 0 1 9 } - 1 } = \\sqrt { 2 0 1 9 } + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_836.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 3(2k + 1) + 2(k + 1) + 2k + 1.",
|
|
"gt_answers": "\\frac { 1 } { 3 } < k < 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_837.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5.\"",
|
|
"gt_answers": "x ^ { 2 } + \\frac { 1 } { x ^ { 2 } } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_838.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_839.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 2x + 3}{x^2 - 2x + 3}\n\\end{equation}\n\nThis formula can be simplified to:\n\n\\begin{equation}\n\\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} = \\frac{x^2 + 2x + 3}{x^2 - 2x + 3} =",
|
|
"gt_answers": "2 \\times \\frac { x + 1 } { 2 } = 2 \\times 1 - 2 \\times \\frac { 3 x - 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_840.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 16x^2 - 9x + 1 = 0.",
|
|
"gt_answers": "\\frac { 9 } { 1 6 } x = \\frac { 1 2 } { 1 6 } x + 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_841.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + y^2 + z^2 = 3xyz\n\\end{aligned}\n\\end{equation}\n\nThis formula represents the Pythagorean theorem, which states that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the hypotenuse.",
|
|
"gt_answers": "x _ { 1 } = \\frac { 3 } { 2 } , x _ { 2 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_842.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"OD = 4\" using LaTeX format.",
|
|
"gt_answers": "O D = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_843.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(CF = 3 + 2 \\cdot CF + CF \\cdot CF\\)",
|
|
"gt_answers": "C F = 3 \\sqrt { 2 } + \\frac { 3 } { 2 } \\sqrt { 2 } = \\frac { 9 } { 2 } \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_844.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `x^2 + y^2 = 1`.",
|
|
"gt_answers": "3 x - x + 6 = \\frac { 1 2 x } { 5 } - \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_845.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3(x + 1) = 13\\)\n\nThis formula can be represented using the following LaTeX code:\n\n\\(3x + 3 = 13\\)",
|
|
"gt_answers": "1 \\div 3 = \\frac { 1 } { 3 } ( k g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_846.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LARP 30.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle A B C = 3 0 ^ { \\circ } . O B =\n",
|
|
"image_path": "./data/HME100K/test_images/test_847.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 4x^2 + 6x + 4\\)",
|
|
"gt_answers": "C _ { 1 0 } ^ { 4 } x ^ { 6 } ( \\sqrt { 2 } y ) ^ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_848.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "O A = O C = O B , O\n",
|
|
"image_path": "./data/HME100K/test_images/test_849.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "y _ { 4 } = - \\frac { V } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_850.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "P = \\frac { F } { S }\n",
|
|
"image_path": "./data/HME100K/test_images/test_851.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis is the famous equation that describes the relationship between energy (E) and mass (m) of a body and its speed of movement (c).",
|
|
"gt_answers": "e ^ { 2 } > 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_852.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x < \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_853.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 10\\)",
|
|
"gt_answers": "x = - \\frac { - 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_854.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LDA + A = LDA + A\".",
|
|
"gt_answers": "\\angle D E A = 1 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_855.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"K = 1/2 (1/2 + 1/2) = 1/4.\"",
|
|
"gt_answers": "k = - \\frac { 1 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_856.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "\\frac { 1 } { x - y } : \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_857.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "\\sqrt { 2 5 } x ^ { 2 } = x - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_860.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2445-1956-3345-2023`.",
|
|
"gt_answers": "2 2 . 4 5 - 1 9 . 1 5 6 = 3 . 3 9 4 = 3 . 0 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_862.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)\n\nThis formula represents a quadratic equation, where x is the unknown variable and the other terms represent constants.",
|
|
"gt_answers": "\\frac { 8 } { 1 2 } x + \\frac { 9 } { 1 2 } x - \\frac { 1 0 } { 1 2 } x = \\frac { 4 } { 4 } + \\frac { 8 } { 4 } + \\frac { 9 } { 4 } - \\frac { 1 0 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_863.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "C _ { 3 } ^ { 0 } \\times ( \\frac { 1 } { 8 } ) ^ { 0 } \\times ( \\frac { 1 } { 8 } ) ^ { 3 } = \\frac { 3 4 3 } { 5 . 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_864.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\tan \\angle B C D = \\frac { B F } { C F } = \\frac { \\frac { 3 } { 2 } \\sqrt { 2 } } { \\frac { 9 } { 2 } \\sqrt { 2 } } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_865.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = mgh\\)\n\nwhere E is the energy, m is the mass of the object, g is the gravitational constant, and h is the height of the object above the ground.",
|
|
"gt_answers": "\\rho = \\frac { M } { V }\n",
|
|
"image_path": "./data/HME100K/test_images/test_866.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mathematical formula using the Greek letter \"pi\" (\u03c0) as the symbol for the constant. The formula is written in a way that it can be easily read and understood by a mathematician.",
|
|
"gt_answers": "3 = - \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_867.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a = a - b.",
|
|
"gt_answers": "a ^ { - 1 } = \\frac { 1 } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_870.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: sin(A) = sin(B) + sin(C) - sin(D).",
|
|
"gt_answers": "\\frac { b } { \\sin B } = \\frac { C } { \\sin C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_872.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"5.0 = 0.05 x 1000.\"",
|
|
"gt_answers": "- 0 . 5 = 1 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_873.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{b^2}{a^2} = \\frac{b^2}{a^2}\n\\end{equation}\n\nThis is a simple algebraic equation that demonstrates the commutative property of multiplication.",
|
|
"gt_answers": "= 6 \\times \\sqrt { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_875.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 400N = 400 kg * 9.81 m/s^2.",
|
|
"gt_answers": "G = m g = 5 0 k g \\times 9 . 8 N / k g = 4 9 0 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_876.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written in the form of a mathematical equation, with the letters \"ABCD\" representing the variables. The formula is likely an algebraic expression or a mathematical function.",
|
|
"gt_answers": "\\square A B C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_877.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "Y = 8 - 2x + 4cm",
|
|
"gt_answers": "r = 8 \\div 2 = 4 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_878.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 8x - 4 = 0\\)",
|
|
"gt_answers": "3 \\times ( - 8 ) + 8 = \\frac { 3 \\times ( - 8 ) } { 4 } + m\n",
|
|
"image_path": "./data/HME100K/test_images/test_879.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = z^2\\)",
|
|
"gt_answers": ". a _ { n } = 2 ^ { n } ( n \\in N ^ { \\ast } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_880.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"S = 2n + 1.\"",
|
|
"gt_answers": "S _ { n } = \\beta n ^ { 2 } + q n\n",
|
|
"image_path": "./data/HME100K/test_images/test_881.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"T = 2(2 + 3) - 4(6 + 7)\".",
|
|
"gt_answers": "\\pm \\sqrt { 2 x + y } = \\pm \\sqrt { 2 \\times 5 - 4 } = \\pm \\sqrt { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_883.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2NaO + 2000Na + 2000O = 2Na2O3.",
|
|
"gt_answers": "2 N a _ { 2 } O _ { 2 } + 2 C O _ { 2 } = 2 N a _ { 2 } C O _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_884.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 15 = 2x + 15.",
|
|
"gt_answers": "\\frac { 8 } { 1 5 } = \\frac { 8 \\times 3 } { 1 5 \\times 3 } = \\frac { 2 4 } { 4 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_886.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"5x + 3 = 15.\"",
|
|
"gt_answers": "1 5 \\div 5 \\times 1 = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_887.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{3}x^3 + \\frac{1}{4}x^4 + \\frac{1}{5}x^5 + \\frac{1}{6}x^6 + \\frac{1}{7}x^7 + \\frac{1}{8}x^8 + \\frac{1}{9}x^9 + \\frac{1}{10}x^{10} + \\frac{1}{11}x^{11} + \\frac{1}{12}x^{12} + \\frac{1}{13}x^{13} + \\frac{1}{14}x^{14} + \\frac{1}{15}x^{15} + \\frac{1}{16}x^{16} + \\frac{1}{17}x^{17} + \\frac{1}{18}x^{18} + \\frac{1}{19}x^{19} + \\frac{1}{20}x^{20} + \\frac{1}{21}x^{21} + \\frac{1}{22}x^{22} + \\frac{1}{23}x^{23} + \\frac{1}{24}x^{24} + \\frac{1}{25}x^{25} + \\frac{1}{26}x^{26} + \\frac{1}{27}x^{27} + \\frac{1}{28}x^{28} + \\frac{1}{29}x^{29} + \\frac{1}{30}x^{30} + \\frac{1}{31}x^{31} + \\frac{1}{32}x^{32} + \\frac{1}{33}x^{33} + \\frac{1}{34}x^{34} + \\frac{1}{35}x^{35} + \\frac{1}{36}x^{36} + \\frac{1}{37}x^{37} + \\frac{1}{38}x^{38",
|
|
"gt_answers": "y = ( x - 4 0 ) [ 5 0 0 - 1 0 ( x - 5 0 ) ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_888.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the formula is likely a mathematical expression involving addition, subtraction, multiplication, or division.",
|
|
"gt_answers": "\\frac { 1 } { 4 } + \\frac { 1 } { 5 } = \\frac { 9 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_889.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6} + \\frac{1}{7} + \\frac{1}{8} + \\frac{1}{9} + \\frac{1}{10} + \\frac{1}{11} + \\frac{1}{12} + \\frac{1}{13} + \\frac{1}{14} + \\frac{1}{15} + \\frac{1}{16} + \\frac{1}{17} + \\frac{1}{18} + \\frac{1}{19} + \\frac{1}{20} + \\frac{1}{21} + \\frac{1}{22} + \\frac{1}{23} + \\frac{1}{24} + \\frac{1}{25} + \\frac{1}{26} + \\frac{1}{27} + \\frac{1}{28} + \\frac{1}{29} + \\frac{1}{30} + \\frac{1}{31} + \\frac{1}{32} + \\frac{1}{33} + \\frac{1}{34} + \\frac{1}{35} + \\frac{1}{36} + \\frac{1}{37} + \\frac{1}{38} + \\frac{1}{39} + \\frac{1}{40} + \\frac{1}{41} + \\frac{1}{42} + \\frac{1}{43} + \\frac{1}{44} + \\frac{1}{45} + \\frac{1}{46} + \\frac{1}{47} + \\frac{1}{48} + \\frac{1}{49} + \\frac{1}{50} + \\frac{1}{51} + \\frac{1}{52} + \\frac{1}{53} + \\frac{1}{54} + \\frac{1}{55} + \\frac{1}{56} + \\frac{",
|
|
"gt_answers": "5 \\frac { 1 } { 2 } + \\frac { 1 } { 3 } x = \\frac { 3 } { 2 } x - 1 \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_891.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + 1\\)",
|
|
"gt_answers": "y - \\frac { 1 } { 6 } z = + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_892.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 41x + 41^2 = 0.\"",
|
|
"gt_answers": "x = \\frac { 3 2 0 } { 4 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_893.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `0.333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
|
|
"gt_answers": "t = \\frac { 1 } { 2 } \\times ( 0 . 3 s + 0 . 5 s ) = 0 . 4 s\n",
|
|
"image_path": "./data/HME100K/test_images/test_894.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 0 + 2 0 0 + 3 0 0 + 5 0 0 = 1 1 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_895.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{a^2 + b^2}{a^2 - b^2} = \\frac{a^2 + b^2}{a^2 - b^2}\n\\end{aligned}\n\\end{equation}\n\nThis is a simple algebraic expression that can be easily understood by anyone familiar with basic algebra.",
|
|
"gt_answers": "( a + 2 b ) ( 2 a - 4 b )\n",
|
|
"image_path": "./data/HME100K/test_images/test_899.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)",
|
|
"gt_answers": "x = 2 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_900.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few letters and numbers, which could be a representation of a mathematical expression in Korean.",
|
|
"gt_answers": "x _ { 1 } = \\frac { 5 } { 3 } \\times 2 = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_901.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2x + 3y = 10.",
|
|
"gt_answers": "\\sqrt [ 3 ] { 4 + \\frac { 1 7 } { 2 7 } } = \\frac { 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_902.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x4 - 7x5 = 13x9.",
|
|
"gt_answers": "\\frac { 2 x + 3 } { 4 9 } = \\frac { 4 x - 1 } { 7 } - \\frac { 5 } { 2 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_903.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as LCAP-CAP=45.",
|
|
"gt_answers": "\\angle C O D = \\angle C A P = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_904.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the image shows a mathematical formula with a negative sign in front of a number, which could be written as:\n\n-n",
|
|
"gt_answers": "\\frac { 4 } { 5 } : \\frac { 3 } { 4 } = 1 6 : 1 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_905.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "y ^ { 2 } = \\frac { 1 } { b ^ { 2 } + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_906.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "\\frac { x ^ { 2 } } { 4 } + \\frac { y ^ { 2 } } { 3 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_908.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"k = 1200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "k ^ { 2 } - 1 2 < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_909.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x = 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20 + 1/21 + 1/22 + 1/23 + 1/24 + 1/25 + 1/26 + 1/27 + 1/28 + 1/29 + 1/30 + 1/31 + 1/32 + 1/33 + 1/34 + 1/35 + 1/36 + 1/37 + 1/38 + 1/39 + 1/40 + 1/41 + 1/42 + 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48 + 1/49 + 1/50 + 1/51 + 1/52 + 1/53 + 1/54 + 1/55 + 1/56 + 1/57 + 1/58 + 1/59 + 1/60 + 1/61 + 1/62 + 1/63 + 1/64 + 1/65 + 1/66 + 1/67 + 1/68 + 1/69 + 1/70 + 1/71 + 1/72 + 1/73 + 1/74 + 1/75 + 1/76 + 1/77 + 1/78 + 1/79 + 1/80 + 1/81 + 1/82 + 1/83 + 1/84 + 1/85 + 1/86 + 1/",
|
|
"gt_answers": "x _ { 1 } = \\frac { \\sqrt { 3 a + 3 } } { a + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_910.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "\\frac { A E } { A C } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_911.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `y = x^2 + 2x + 1 km`.",
|
|
"gt_answers": ": t h e t i m e = ( x \\div y \\div 2 ) k m\n",
|
|
"image_path": "./data/HME100K/test_images/test_912.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 10\\)",
|
|
"gt_answers": "4 y ^ { 2 } + 1 2 y + 9 t y ^ { 2 } = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_913.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(f(x) = 3x^2 + 12x + 12\\)",
|
|
"gt_answers": "f ^ { \\prime } ( x ) = 3 x ^ { 2 } + 1 2 x + 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_914.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x-2 = 0\" in LaTeX format.",
|
|
"gt_answers": "x + y - 3 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_915.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(W = 40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "W = 4 0 0 ( x + 3 y )\n",
|
|
"image_path": "./data/HME100K/test_images/test_916.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { c } { a } = \\sqrt { \\frac { a ^ { 2 } + b ^ { 2 } } { a } } = \\sqrt { 1 + \\frac { b ^ { 2 } } { a ^ { 2 } } } > \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_917.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Korean.",
|
|
"gt_answers": "C _ { 3 } ^ { 2 } ( \\frac { 1 } { 2 } ) ^ { 3 } \\cdot \\frac { 1 } { 2 } = \\frac { 3 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_918.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as a2 + b2 = c2.",
|
|
"gt_answers": "a = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_919.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 0 m = 3 0 0 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_920.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x = 444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444",
|
|
"gt_answers": "1 3 + x = \\frac { 1 } { 2 } ( 4 7 + x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_921.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"mz-bz\" and is likely a mathematical formula. However, without more context or information about the formula, it is difficult to provide a precise LaTeX representation.",
|
|
"gt_answers": "m ^ { 2 } - 5 m - 6 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_925.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x + 2y = 12.\"",
|
|
"gt_answers": "\\frac { 9 } { 4 } + \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_926.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15",
|
|
"gt_answers": "\\frac { 1 } { 1 5 } + \\frac { 4 } { 1 5 } + \\frac { 7 } { 1 5 } = \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_927.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x = \\sqrt { 2 } + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_928.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "q = \\frac { 4 \\pi \\rho r ^ { 3 } g } { 3 E }\n",
|
|
"image_path": "./data/HME100K/test_images/test_930.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x^2 + 3x - 4 = 0.",
|
|
"gt_answers": "\\frac { x } { 3 } = \\frac { y } { 4 } = x : y = ( 3 ) : ( 4 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_933.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical equation with a plus sign and a minus sign, which could be a simple addition or subtraction problem.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x + 3 = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_934.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2n2s + 2n2o + 2n2h + 2n2s2 + 2n2o2 + 2n2h2 + 2n2s3 + 2n2o3 + 2n2h4 + 2n2s5 + 2n2o5 + 2n2h6 + 2n2o7 + 2n2h8 + 2n2o9 + 2n2h10 + 2n2o11 + 2n2h12 + 2n2o13 + 2n2h14 + 2n2o15 + 2n2h16 + 2n2o17 + 2n2h18 + 2n2o19 + 2n2h20 + 2n2o21 + 2n2h22 + 2n2o23 + 2n2h24 + 2n2o25 + 2n2h26 + 2n2o27 + 2n2h28 + 2n2o29 + 2n2h30 + 2n2o31 + 2n2h32 + 2n2o33 + 2n2h34 + 2n2o35 + 2n2h36 + 2n2o37 + 2n2h38 + 2n2o39 + 2n2h40 + 2n2o41 + 2n2h42 + 2n2o43 + 2n2h44 + 2n2o45 + 2n2h46 + 2n2o47 + 2n2h48 + 2n2o49 + 2n2h50 + 2n2o51 + 2n2h52 + 2n2o53 + 2n2h54 + 2n2o55 + 2n2h56 + 2n2o57 + 2n2h58 + 2n2o59 + ",
|
|
"gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_935.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x(5-x) = 15.",
|
|
"gt_answers": "\\frac { 3 } { 4 } \\times \\frac { 3 \\times 5 } { 5 4 \\times 5 } = \\frac { 1 5 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_936.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "\\frac { 1 } { 3 } ( \\frac { 3 } { 2 } x - 1 ) = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_937.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 24 - 6 + 4.",
|
|
"gt_answers": "\\frac { 2 4 } { 6 } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_938.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2^{2} + 2^{3} + 2^{4} + 2^{5} + 2^{6} + 2^{7} + 2^{8} + 2^{9} + 2^{10} + 2^{11} + 2^{12} + 2^{13} + 2^{14} + 2^{15} + 2^{16} + 2^{17} + 2^{18} + 2^{19} + 2^{20} + 2^{21} + 2^{22} + 2^{23} + 2^{24} + 2^{25} + 2^{26} + 2^{27} + 2^{28} + 2^{29} + 2^{30} + 2^{31} + 2^{32} + 2^{33} + 2^{34} + 2^{35} + 2^{36} + 2^{37} + 2^{38} + 2^{39} + 2^{40} + 2^{41} + 2^{42} + 2^{43} + 2^{44} + 2^{45} + 2^{46} + 2^{47} + 2^{48} + 2^{49} + 2^{50} + 2^{51} + 2^{52} + 2^{53} + 2^{54} + 2^{55} + 2^{56} + 2^{57} + 2^{58} + 2^{59} + 2^{60} + 2^{61} + 2^{62} + 2^{63} + 2^{64} + 2^{65} + 2^{66} + 2^{67} + 2^{68} + 2^{69} + 2^{70} + 2^{71} + 2^{72} + 2^{73}",
|
|
"gt_answers": "\\frac { 1 } { 7 } [ \\frac { 1 } { 5 } ( \\frac { x + 2 } { 3 } + 4 ) + 6 ] + 8 = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_939.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(a + b = c\\)\n\nThis is a basic algebraic equation that represents the addition of two numbers, a and b, to equal a third number, c.",
|
|
"gt_answers": "a d = b c = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_940.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 3x + 4 = 0.\"",
|
|
"gt_answers": "x = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_941.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula is written in the form of an equation, where a, b, and c are variables and represent the squares of the corresponding numbers.",
|
|
"gt_answers": "\\frac { 1 } { 2 } + \\frac { 3 - a } { 3 } = \\frac { a } { b } - 3 \\times \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_942.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as C44+.",
|
|
"gt_answers": "c = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_943.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 - 2x + 1 = 0.\"",
|
|
"gt_answers": "x = - 2 \\pm \\sqrt { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_945.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis is a quadratic equation, where a, b, and c are the coefficients of the variables x, y, and z, respectively.",
|
|
"gt_answers": "\\cdot a ^ { 2 } - 4 a + 5 + a ^ { 2 } - 2 a + 1 0 = 1 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_946.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "a _ { n + 1 } = \\frac { n + 1 } { 2 } a _ { n + 1 } + a _ { n } - \\frac { n } { 2 } a _ { n } - a _ { n } - \\dot { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_948.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Laid-off = 45 + (25 * 180 / 360).\"",
|
|
"gt_answers": "\\angle A + \\angle A C D = 4 5 ^ { \\circ } + 1 3 5 ^ { \\circ } = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_949.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"M + L + G = 300.\"",
|
|
"gt_answers": "M G B + \\angle B G H + \\angle E G M = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_950.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(x^2 + y^2 = 19\\)",
|
|
"gt_answers": "\\frac { 1 } { a _ { n } } = \\frac { 1 } { a _ { 1 . } } + ( n - 1 ) \\times 3 = 3 n - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_951.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 15x + 10 = 0.\"",
|
|
"gt_answers": "x = \\frac { 1 5 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_952.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3x + 2y = 10\\)\n\nThis is a simple algebraic equation that can be solved using the addition and subtraction operations.",
|
|
"gt_answers": "\\sqrt { 3 } + \\sqrt { 3 } = \\sqrt { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_953.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: `3(1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100+101+102+103+104+105+106+107+108+109+110+111+112+113+114+115+116+117+118+119+120+121+122+123+124+125+126+127+128+129+130+131+132+133+134+135+136+137+138+139+140+141+142+143+144+145+146+147+148+149+150+151",
|
|
"gt_answers": "r = 1 8 . 8 4 \\div 3 . 1 4 \\div 2 = 3 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_954.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2 + d^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the hypotenuse.",
|
|
"gt_answers": "\\frac { a b } { 2 } = S _ { \\Delta } a b c = 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_955.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x _ { 2 } , y _ { 2 } \\in z ( x _ { i } - x _ { i } - 1 ) + ( y _ { i } - y _ { 2 - 1 } ) = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_956.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: BG + BH = AH + AF.",
|
|
"gt_answers": "\\frac { B G } { A G } = \\frac { B H } { A F }\n",
|
|
"image_path": "./data/HME100K/test_images/test_957.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(k = \\frac{1}{2}mv^2\\)\n\nThis formula relates the kinetic energy of an object to its mass (m) and its velocity squared (v^2).",
|
|
"gt_answers": "k - 3 > 0 \\Rightarrow k > 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_958.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, which are not supported by LaTeX. However, I can provide a rough translation of the formula into English:\n\n\"8x8 = 64\"",
|
|
"gt_answers": "- x . - 8 = \\frac { 1 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_959.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x = \\frac { \\pi } { 6 } o r \\frac { 2 \\pi } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_960.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "f ^ { \\prime } ( x ) = 3 x ^ { 2 } + 2 b x + 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_961.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{4} \\cdot \\frac{1}{8} \\cdot \\frac{1}{16} \\cdot \\frac{1}{32} \\cdot \\frac{1}{64} \\cdot \\frac{1}{128} \\cdot \\frac{1}{256} \\cdot \\frac{1}{512} \\cdot \\frac{1}{1024} \\cdot \\frac{1}{2048} \\cdot \\frac{1}{4096} \\cdot \\frac{1}{8192} \\cdot \\frac{1}{16384} \\cdot \\frac{1}{32768} \\cdot \\frac{1}{65536} \\cdot \\frac{1}{131072} \\cdot \\frac{1}{262144} \\cdot \\frac{1}{524288} \\cdot \\frac{1}{1048576} \\cdot \\frac{1}{2097152} \\cdot \\frac{1}{4194304} \\cdot \\frac{1}{8388608} \\cdot \\frac{1}{16777216} \\cdot \\frac{1}{33554432} \\cdot \\frac{1}{67108864} \\cdot \\frac{1}{134217728} \\cdot \\frac{1}{268435456} \\cdot \\frac{1}{536870912} \\cdot \\frac{1}{1073741824} \\cdot \\frac{1}{2147483648} \\cdot \\frac{1}{4294967296} \\cdot \\frac{1}{8589934592} \\cdot \\frac{1}{17179869184} \\cdot \\frac{1}{343793836816} \\cdot \\",
|
|
"gt_answers": "\\frac { 1 } { 3 } : \\frac { 1 } { 6 } = \\frac { 1 } { 2 } : \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_963.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\frac { a } { a - 1 } = a - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_964.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"GY = 6 + 12 + 18 + 24 + 30 + 36 + 42 + 48 + 54 + 60 + 66 + 72 + 78 + 84 + 90 + 96 + 102 + 108 + 114 + 120 + 126 + 132 + 138 + 144 + 150 + 156 + 162 + 168 + 174 + 180 + 186 + 192 + 198 + 204 + 210 + 216 + 222 + 228 + 234 + 240 + 246 + 252 + 258 + 264 + 270 + 276 + 282 + 288 + 294 + 300 + 306 + 312 + 318 + 324 + 330 + 336 + 342 + 348 + 354 + 360 + 366 + 372 + 378 + 384 + 390 + 396 + 402 + 408 + 414 + 420 + 426 + 432 + 438 + 444 + 450 + 456 + 462 + 468 + 474 + 480 + 486 + 492 + 498 + 504 + 510 + 516 + 522 + 528 + 534 + 540 + 546 + 552 + 558 + 564 + 570 + 576 + 582 + 588 + 594 + 600 + 606 + 612 + 618 + ",
|
|
"gt_answers": "9 x - 4 x = 6 + 3 + 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_967.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nZn2Cl2 + 2H2O \u2192 Zn(OH)2 + 2Cl2 + H2",
|
|
"gt_answers": "Z n + 2 H C l = Z n C l _ { 2 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_968.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "z _ { 1 } + z _ { 2 } = - \\frac { b } { - a } = 2 p\n",
|
|
"image_path": "./data/HME100K/test_images/test_969.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + y^2 + z^2 + 2xy + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz +",
|
|
"gt_answers": "\\vert 2 x + m - 1 \\vert + 3 - 2 x \\leq 6 - 2 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_970.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "( 1 ) 4 ( 2 x - 1 ) < 3 ( 4 x + 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_971.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(m = \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left(",
|
|
"gt_answers": ": \\frac { m ( m + 1 ) } { ( m - 1 ) ^ { 2 } } \\cdot \\frac { m - 1 } { m } = \\frac { m + 1 } { m - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_973.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(AB + AD + BC + CD = 2(AB + BC) + AD + BC\\)\n\nThis formula can be rearranged to obtain the following equation:\n\n\\(AB + BC + CD + AD = 2(AB + BC) + CD\\)\n\nThis equation can be simplified further to obtain the following expression:\n\n\\(AB + BC + CD = 2(AB + BC) + CD\\)\n\nThis is the formula for the sum of the four sides of a quadrilateral.",
|
|
"gt_answers": "\\frac { D G } { B A } = \\frac { A D } { A B } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_974.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{6 \\times 10^{5} \\times 10^{6} \\times 10^{7}}{6 \\times 10^{5} \\times 10^{6} \\times 10^{7}} = 1 \\times 10^{18} \\)",
|
|
"gt_answers": "S _ { 1 } = \\frac { V } { h } = 2 . 5 \\times 1 0 ^ { - 2 } m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_975.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x _ { 2 } = - \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_976.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "x _ { 1 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_978.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\ce{NaOH + H2SO4 -> Na2SO4 + H2O}\n\\end{equation}\n\nThis formula represents the chemical reaction between sodium hydroxide (NaOH) and sulfuric acid (H2SO4) to produce sodium sulfate (Na2SO4) and water (H2O).",
|
|
"gt_answers": "C a ( O H ) _ { 2 } + N a _ { 2 } C O _ { 3 } = C a C O _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_979.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"P(A or B) = P(A) + P(B) - P(A and B).\"",
|
|
"gt_answers": "P ( A ) P ( B ) = \\frac { 1 } { 5 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_980.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nb + 3 = 5\n\nThe formula is written in the form of an equation, where the variable \"b\" is on the left side of the equal sign, and the variable \"3\" is on the right side. The result of the equation is \"5,\" which is the solution to the equation.",
|
|
"gt_answers": "b = 3 - \\sqrt { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_981.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten format, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a negative sign in front of the expression, which can be represented in LaTeX as follows:\n\n\\(x^2 - 2x + 1\\)",
|
|
"gt_answers": "5 \\div 8 = \\frac { 5 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_982.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"50 ab-2 + 20 ab-1 + 10 ab + 5 ab-4 + 2 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1 ab-3 + 1 ab-2 + 1 ab-1 + 1 ab + 1 ab-4 + 1",
|
|
"gt_answers": "S _ { \\Delta } a b c = \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_983.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Delpn\" using LaTeX format.",
|
|
"gt_answers": "A E \\bot P N\n",
|
|
"image_path": "./data/HME100K/test_images/test_984.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/2(x + 1) - 1/2(x - 1) = 1/4(x^2 - 1).",
|
|
"gt_answers": "1 8 0 ^ { \\circ } - 4 0 ^ { \\circ } - 9 0 ^ { \\circ } = 5 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_985.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5.\"",
|
|
"gt_answers": "x = 6 \\div \\frac { 2 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_986.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{3}x^3 + \\frac{1}{4}x^4 + \\frac{1}{5}x^5 + \\frac{1}{6}x^6 + \\frac{1}{7}x^7 + \\frac{1}{8}x^8 + \\frac{1}{9}x^9 + \\frac{1}{10}x^{10} + \\frac{1}{11}x^{11} + \\frac{1}{12}x^{12} + \\frac{1}{13}x^{13} + \\frac{1}{14}x^{14} + \\frac{1}{15}x^{15} + \\frac{1}{16}x^{16} + \\frac{1}{17}x^{17} + \\frac{1}{18}x^{18} + \\frac{1}{19}x^{19} + \\frac{1}{20}x^{20} + \\frac{1}{21}x^{21} + \\frac{1}{22}x^{22} + \\frac{1}{23}x^{23} + \\frac{1}{24}x^{24} + \\frac{1}{25}x^{25} + \\frac{1}{26}x^{26} + \\frac{1}{27}x^{27} + \\frac{1}{28}x^{28} + \\frac{1}{29}x^{29} + \\frac{1}{30}x^{30} + \\frac{1}{31}x^{31} + \\frac{1}{32}x^{32} + \\frac{1}{33}x^{33} + \\frac{1}{34}x^{34} + \\frac{1}{35}x^{35} + \\frac{1}{36}x^{36} + \\frac{1}{37}x^{37} + \\frac{1}{38}x",
|
|
"gt_answers": "\\sqrt [ 3 ] { ( \\sqrt { 2 a - 1 } ) } = 3 \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_987.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\therefore \\frac { 1 } { 2 } = \\frac { 3 ^ { 2 } - 2 b c - ( \\sqrt { 3 } ) ^ { 2 } } { 2 b c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_988.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{x^2}{2} + \\frac{y^2}{2} + \\frac{z^2}{2} = \\frac{1}{2} \\left(x^2 + y^2 + z^2\\right) \\)",
|
|
"gt_answers": "f ( x ) = \\frac { e ^ { 2 } x } { x } < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_989.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(sin(A + B) = sin(A)cos(B) + cos(A)sin(B)\\)",
|
|
"gt_answers": "S _ { \\Delta A B C } = \\frac { 1 } { 2 } b c \\sin A = \\frac { 1 } { 2 } b c \\cdot \\frac { 5 } { 1 3 } = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_990.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(16^2 + 16^2 - 16^2 - 16^2 = 0\\)",
|
|
"gt_answers": "= 1 6 a ^ { 4 } - 8 1 b\n",
|
|
"image_path": "./data/HME100K/test_images/test_992.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(K_{T} = \\frac{1}{2} \\left( \\frac{1}{R_{1}} + \\frac{1}{R_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1}{T_{1}} + \\frac{1}{T_{2}} \\right) \\left( \\frac{1",
|
|
"gt_answers": "x = k \\pi - \\frac { \\pi } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_993.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2H2O + CO2 = 2H2CO3 + O2.",
|
|
"gt_answers": "2 L i O H + C O _ { 2 } = L i _ { 2 } C O _ { 3 } + H _ { 2 } O .\n",
|
|
"image_path": "./data/HME100K/test_images/test_994.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 12\\)",
|
|
"gt_answers": "6 2 8 + ( 3 1 . 4 \\div 3 . 1 4 \\div 2 ) ^ { 2 } \\times 2 \\times 3 . 1 4 = 7 8 5 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_995.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 61+70=131.",
|
|
"gt_answers": "6 + 1 = 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_996.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3(2 - 1) + 2(1 - 2) = 6 - 3.",
|
|
"gt_answers": "\\frac { 1 } { 3 } + \\frac { 1 } { 3 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_997.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(n^2 + 2n + 1 = 3n^2 + 2n + 1\\)",
|
|
"gt_answers": "\\sqrt { a ^ { 2 } + 1 } = \\sqrt { ( 1 + a ) ^ { 2 } + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_998.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mathematical formula using the Greek letter \"pi\" (\u03c0) as the symbol for the ratio of the circumference of a circle to its diameter. The formula is written in the form of a fraction, with the numerator being the circumference and the denominator being the diameter. The formula is written in a way that the Greek letter \"pi\" is used as the symbol for the ratio, rather than the letter \"p\" or \"C\" for circumference and \"d\" for diameter.",
|
|
"gt_answers": "C E = B E = 2 5 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_999.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\rightarrow d _ { A } \\rightarrow B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1000.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"960 = 36 x 27\".",
|
|
"gt_answers": "9 6 \\div 6 0 = 1 \\cdots 3 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1001.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\begin{equation}\n\\frac{A}{B} = \\frac{AC}{BC}\n\\end{equation}\n\nThis formula states that the ratio of two numbers, A and B, is equal to the ratio of their corresponding products, AC and BC.",
|
|
"gt_answers": "\\frac { B E } { A B } = \\frac { A E } { A C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1002.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: `m-0.5*6720 + 0.5*6720 = 6720`.",
|
|
"gt_answers": "m - 2 0 + 2 0 = 6 + 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1004.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "f ( - x ) = \\frac { 1 } { 2 ^ { x } } + 2 ^ { x } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1006.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{1 + \\left( \\frac{1}{100} \\right)^2} = \\frac{1}{1 + \\left( \\frac{1}{1000} \\right)^2} = \\frac{1}{1 + \\left( \\frac{1}{10000} \\right)^2} = \\frac{1}{1 + \\left( \\frac{1}{100000} \\right)^2} = \\frac{1}{1 + \\left( \\frac{1}{1000000} \\right)^2} = \\frac{1}{1 + \\left( \\frac{1}{100000000} \\right)^2} = \\frac{1}{1 + \\left( \\frac{1}{10000000000} \\right)^2} = \\frac{1}{1 + \\left( \\frac{1}{10000000000000} \\right)^2} = \\frac{1}{1 + \\left( \\frac{1}{10000000000000000} \\right)^2} = \\frac{1}{1 + \\left( \\frac{1}{100000000000000000000} \\right)^2} = \\frac{1}{1 + \\left( \\frac{1}{10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "7 . 5 2 - 7 . 0 1 = 0 . 5 1 7 6 . 8 0 - 7 1 . 6 8 = 5 . 1 2 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1007.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 1 } { k } < \\frac { 1 } { 2 ^ { x 1 } 2 ^ { x 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1008.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Major(A) + Major(B) = Major(A + B)\".",
|
|
"gt_answers": "N a _ { 2 } S O _ { 4 } + B a C l _ { 2 } = B a C l _ { 2 } \\downarrow + 2 N a C l\n",
|
|
"image_path": "./data/HME100K/test_images/test_1009.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Adal = 12cm.\"",
|
|
"gt_answers": "A D = \\frac { 1 } { 2 } A C = 1 2 c m .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1010.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Bd = AB + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD + BC + CD + AD",
|
|
"gt_answers": "\\frac { B D } { A B } = \\frac { A B } { B C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1014.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as y = 200x.",
|
|
"gt_answers": "y = \\sqrt { 2 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1015.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"28.6673333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
|
|
"gt_answers": "2 8 . 2 6 \\div 3 = 9 . 4 2 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1016.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/2(x^2 + 1/2(x^2 - 1)) + 1/2(x^2 - 1/2(x^2 + 1)).",
|
|
"gt_answers": "5 6 + 4 0 = 9 6 9 5 - 4 0 =\n",
|
|
"image_path": "./data/HME100K/test_images/test_1017.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x10^11x14-30x10^7x300x10^3x10^2x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0x10^1x10^0",
|
|
"gt_answers": "2 5 \\times 1 0 \\times 1 4 = 3 5 0 0 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1018.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
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|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
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|
"answer": "The expression in the image is written in Korean, and it is not possible for me to accurately transcribe it using LaTeX. However, I can provide a rough translation of the formula:\n\n\"The sum of the squares of the first 100 natural numbers.\"",
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|
"gt_answers": "\\cdot \\frac { x } { 3 } \\leq \\theta \\leq \\frac { 2 } { 3 } \\pi\n",
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"image_path": "./data/HME100K/test_images/test_1019.jpg",
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"model_name": "mPLUG"
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},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"cos(x) = sin(x) / (1 + cos(x))\".",
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"gt_answers": "\\cos C = \\frac { \\sqrt { 3 } } { 2 }\n",
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"image_path": "./data/HME100K/test_images/test_1021.jpg",
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"model_name": "mPLUG"
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|
},
|
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{
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|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"R-V = 0\" using LaTeX format.",
|
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"gt_answers": "R = \\frac { U } { I }\n",
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"image_path": "./data/HME100K/test_images/test_1023.jpg",
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"model_name": "mPLUG"
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|
},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)\n\nThis is a quadratic equation in the variable x.",
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"gt_answers": "4 a + c = ( 4 a + c ) ( \\frac { 1 } { a } + \\frac { 1 } { c } ) = 5 x + \\frac { c } { a } + \\frac { 4 a } { 4 c } \\geq 5 + \\sqrt [ 2 ] { \\frac { c } { a } \\cdot \\frac { 4 a } { c } } = 9 .\n",
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"image_path": "./data/HME100K/test_images/test_1024.jpg",
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"model_name": "mPLUG"
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},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + 2x - 3a = 0\n\\end{aligned}\n\\end{equation}\n\nThis equation represents a quadratic equation in the variable x, with the coefficients 2x and -3a. The solution to this equation is given by the quadratic formula:\n\n\\begin{equation}\nx = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\n\\end{equation}\n\nIn this case, the quadratic formula simplifies to:\n\n\\begin{equation}\nx = \\frac{-b \\pm \\sqrt{b^2 - 4(2x - 3a)(2x - 3a)}}{2(2x - 3a)}\n\\end{equation}\n\nSolving for x, we obtain:\n\n\\begin{equation}\nx = \\frac{-b \\pm \\sqrt{b^2 - 16(2x - 3a)(2x - 3a)}}{4(2x - 3a)}\n\\end{equation}\n\nThe solution to this equation is x = -b \u00b1 2\\sqrt{b^2 - 16(2x - 3a)(2x - 3a)}/4(2x - 3a).",
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"gt_answers": "\\frac { 2 x ( - 1 ) - a } { 3 } - \\frac { - 1 - a } { 2 } = - 1 = - 1\n",
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"image_path": "./data/HME100K/test_images/test_1025.jpg",
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"model_name": "mPLUG"
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|
},
|
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{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(K_s = \\frac{1}{4\\pi\\epsilon_0 \\epsilon_r \\mu_0} \\int_0^\\infty \\frac{1}{r^2} \\int_0^\\pi \\frac{1}{r^2 \\sin^2 \\theta} \\int_0^{2\\pi} \\frac{1}{r^2 \\sin^2 \\theta \\cos^2 \\phi} dr d\\theta d\\phi\\)",
|
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"gt_answers": "k = \\frac { 1 } { 2 }\n",
|
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"image_path": "./data/HME100K/test_images/test_1026.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so I cannot provide a direct translation. However, I can provide the LaTeX code for the expression:\n\n\\begin{equation}\n2x^2 + 2x + 2 = 5x^2 + 5x + 2\n\\end{equation}\n\nThis is a quadratic equation in the variable x, with the coefficients 2x^2, 2x, and 2. The solution to this equation is x = 2, which means that the square of the x-coordinate is 4, and the x-coordinate itself is 2.",
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"gt_answers": "2 \\alpha + \\frac { 2 } { 3 } \\pi = 2 k \\pi + \\frac { 2 } { 3 } \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_1027.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x5 = 20.\"",
|
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"gt_answers": "\\frac { 4 } { 7 } \\times 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1028.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: `27000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
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"gt_answers": "3 0 \\times 3 0 \\times 3 0 = 2 7 0 0 0 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1029.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 4 0 0 0 } { x } - \\frac { 4 0 0 0 + 8 0 } { ( 1 + 2 0 \\% ) x } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1030.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical equation with the letters \"x\" and \"y\" in it, which can be represented in LaTeX as follows:\n\n\\begin{equation}\nx + y = z\n\\end{equation}\n\nThis equation represents the addition of two numbers, x and y, to produce the result z.",
|
|
"gt_answers": "\\frac { 4 } { 2 4 } x = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1031.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "( - \\frac { 1 } { n } ) ( - 2 ) = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1032.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = a + bx + c\\sin(x) + d\\cos(x)\\)\n\nThe formula is a polynomial equation with four terms, where a, b, c, and d are constants.",
|
|
"gt_answers": "\\angle F D E = \\angle B A D + \\angle A B D , \\angle B A D = \\angle C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1033.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A + B + C = D + E + F.\"",
|
|
"gt_answers": "\\frac { A D } { A E } = k\n",
|
|
"image_path": "./data/HME100K/test_images/test_1034.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"B = 47.2 + 2.5 * A * 0.75 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.2",
|
|
"gt_answers": "B a C l _ { 2 } + N a _ { 2 } C O _ { 3 } = B a C O _ { 3 } t + 2 N a C l\n",
|
|
"image_path": "./data/HME100K/test_images/test_1035.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(sin(x) + sin(y) = 2sin(x/2)cos(y/2)\\)",
|
|
"gt_answers": "\\sin a = - \\sqrt { 1 - \\cos ^ { 2 } a } = - \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1036.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"22.5 - 5 = 17.5.\"",
|
|
"gt_answers": "\\angle B A M = 2 2 . 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1038.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1/2(5dm)3.",
|
|
"gt_answers": "6 c m = \\frac { 3 } { 5 } d m\n",
|
|
"image_path": "./data/HME100K/test_images/test_1039.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 5x - 15 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 1 2 } \\div \\frac { 5 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1040.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x2 + 2x2 = 5000.",
|
|
"gt_answers": "S _ { x } = 2 s = 2 \\times 2 5 0 c m = 5 0 0 c m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1041.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(e^x = \\sum_{n=0}^\\infty \\frac{x^n}{n!} \\tag{1}\\label{eq:e_series}\\)`",
|
|
"gt_answers": "\\rho = \\frac { m } { V }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1042.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{CD}{AB} = \\frac{CD}{AB} \\cdot \\frac{AB}{CD}\n\\end{equation}\n\nThis formula can be used to calculate the ratio of two sides of a triangle, given the lengths of the sides CD and AB.",
|
|
"gt_answers": "C D = \\frac { C A \\cdot B C } { A B \\cdot } = \\frac { 1 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1043.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": ": a + ( b ) = a + ( a ) = a + ( a + 1 ) = a ^ { 2 } + a , a ( - E 1 , 0 ) .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1045.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 18x = 36m.",
|
|
"gt_answers": "1 8 \\times 2 = 3 6 m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1046.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as BaCO3 + H2O = Ba(OH)2 + CO2.",
|
|
"gt_answers": "B a C O _ { 3 } + H N O _ { 3 } = B a N O _ { 3 } + C O _ { 2 } \\uparrow + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1047.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( 1 ) \\because A ( - 1 , 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1048.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{a^2 + b^2 - 3ab}{a^2 - 4ab + b^2}\n\\end{equation}\n\nThe equation is a quadratic equation in the variable \"a\" and \"b\".",
|
|
"gt_answers": "9 - 2 x + 6 = x - 3 - 6 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1050.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a Chinese character in the middle, which could be a symbol or a word.",
|
|
"gt_answers": "3 x = \\frac { m } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1051.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6} + \\frac{1}{7} + \\frac{1}{8} + \\frac{1}{9} + \\frac{1}{10} + \\frac{1}{11} + \\frac{1}{12} + \\frac{1}{13} + \\frac{1}{14} + \\frac{1}{15} + \\frac{1}{16} + \\frac{1}{17} + \\frac{1}{18} + \\frac{1}{19} + \\frac{1}{20} + \\frac{1}{21} + \\frac{1}{22} + \\frac{1}{23} + \\frac{1}{24} + \\frac{1}{25} + \\frac{1}{26} + \\frac{1}{27} + \\frac{1}{28} + \\frac{1}{29} + \\frac{1}{30} + \\frac{1}{31} + \\frac{1}{32} + \\frac{1}{33} + \\frac{1}{34} + \\frac{1}{35} + \\frac{1}{36} + \\frac{1}{37} + \\frac{1}{38} + \\frac{1}{39} + \\frac{1}{40} + \\frac{1}{41} + \\frac{1}{42} + \\frac{1}{43} + \\frac{1}{44} + \\frac{1}{45} + \\frac{1}{46} + \\frac{1}{47} + \\frac{1}{48} + \\frac{1}{49} + \\frac{1}{50} + \\frac{1}{51} + \\frac{1}{52} + \\frac{1}{53} + \\frac{1}{54} + \\frac{1}{55} + \\frac",
|
|
"gt_answers": "3 b + \\frac { 5 } { 3 } \\times 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1052.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3 = 7.",
|
|
"gt_answers": "x = - \\frac { 3 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1053.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AB + AC + BC + CA = 100.\"",
|
|
"gt_answers": "\\frac { B D } { C E } = \\frac { A B } { A C } = k\n",
|
|
"image_path": "./data/HME100K/test_images/test_1054.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_o = \\frac{180^{\\circ} - 90^{\\circ}}{2} + 90^{\\circ} = 100^{\\circ}\\)",
|
|
"gt_answers": "\\angle C O E = 1 8 0 ^ { \\circ } - \\angle E O D = 1 8 0 ^ { \\circ } - 5 5 ^ { \\circ } = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1055.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x + 4 = 16.\"",
|
|
"gt_answers": "( 1 ) y = - \\frac { 4 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1056.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x \\times 3y \\times 3z = 18 \\times 16 \\times 12 = 18^3\\)",
|
|
"gt_answers": "3 \\times 3 \\times 1 8 = 1 6 2 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1057.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 14 - 6(b - 2) = 44.",
|
|
"gt_answers": "- \\frac { 1 5 } { 4 } < - ( 6 - 2 ) ^ { 2 } + 4 \\leq 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1058.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 65-3213.",
|
|
"gt_answers": "\\frac { 6 5 } { 3 } = 2 1 \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1059.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x - 2 = 0\\)",
|
|
"gt_answers": "x = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1061.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(17500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "S = - 2 5 0 \\times \\frac { 3 0 0 } { 1 7 } + 5 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1062.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { x ( x + 1 ) } { 2 } = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1063.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nAP = 40 + 30(x) + 3(x^2) + 2(x^3) + 1(x^4) + 0.5(x^5) + 0.25(x^6) + 0.125(x^7) + 0.0625(x^8) + 0.03125(x^9) + 0.015625(x^{10}) + 0.0078125(x^{11}) + 0.00390625(x^{12}) + 0.001953125(x^{13}) + 0.0009765625(x^{14}) + 0.00048828125(x^{15}) + 0.000244140625(x^{16}) + 0.0001220703125(x^{17}) + 0.00006103515625(x^{18}) + 0.000030517578125(x^{19}) + 0.00001528890625(x^{20}) + 0.00000764453125(x^{21}) + 0.000003822265625(x^{22}) + 0.00000191113125(x^{23}) + 0.000000905565625(x^{24}) + 0.00000045278125(x^{25}) + 0.00000022639375(x^{26}) + 0.000000113196875(x^{27})",
|
|
"gt_answers": "A P = 4 0 + 3 0 ( \\sqrt { 3 } - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1064.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"log(x) = log(a) + log(b) + log(c),\" where x is the unknown variable, a, b, and c are known constants, and log is the natural logarithm function.",
|
|
"gt_answers": "\\angle O C F = \\frac { 1 } { 2 } \\angle A C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_1065.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2^{5} \\cdot 3^{2} \\cdot 5^{3} \\cdot 7^{4} \\cdot 11^{5} \\cdot 13^{6} \\cdot 17^{7} \\cdot 19^{8} \\cdot 23^{9} \\cdot 29^{10} \\cdot 31^{11} \\cdot 37^{12} \\cdot 41^{13} \\cdot 43^{14} \\cdot 47^{15} \\cdot 53^{16} \\cdot 59^{17} \\cdot 65^{18} \\cdot 71^{19} \\cdot 77^{20} \\cdot 83^{21} \\cdot 89^{22} \\cdot 95^{23} \\cdot 101^{24} \\cdot 107^{25} \\cdot 113^{26} \\cdot 119^{27} \\cdot 125^{28} \\cdot 131^{29} \\cdot 137^{30} \\cdot 143^{31} \\cdot 149^{32} \\cdot 155^{33} \\cdot 161^{34} \\cdot 167^{35} \\cdot 173^{36} \\cdot 179^{37} \\cdot 185^{38} \\cdot 191^{39} \\cdot 197^{40} \\cdot 203^{41} \\cdot 209^{42} \\cdot 215^{43} \\cdot 221^{44} \\cdot 227^{45} \\cdot 233^{46} \\cdot 239^{47} \\cdot 245^{48} \\cdot 251^{49} \\cdot 257^{50} \\cdot 263^{51} \\cdot 269^{52} \\cdot 275^{53} \\cdot ",
|
|
"gt_answers": "- 6 . 5 5 ) ] = 4 9 \\frac { 7 } { 1 0 } - [ - 2 3 \\frac { 3 } { 4 } + ( - 6 \\frac { 1 1 } { 2 0 } ) ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_1066.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as Fe(OH)2(SO4)3.",
|
|
"gt_answers": "F e + H _ { 2 } S O 4 = H _ { 2 } \\uparrow + F e S O 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1067.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 3 = 0\\)",
|
|
"gt_answers": "x = \\frac { 3 } { 4 } + \\frac { 1 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1068.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(10x^2 + 20y^2 = 250\\)",
|
|
"gt_answers": "1 0 \\times 2 = 2 0 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1070.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is known as the equation of motion for a particle with mass m and energy E. It states that the total energy of a particle is equal to its mass multiplied by the square of its speed of light, c.",
|
|
"gt_answers": "m c = 1 2 \\times 0 . 1 = 1 . 2 g\n",
|
|
"image_path": "./data/HME100K/test_images/test_1071.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 2 = 4.\"",
|
|
"gt_answers": "\\frac { x } { x + 1 } = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1072.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(90^\\circ = 180^\\circ - 90^\\circ\\)",
|
|
"gt_answers": "\\angle E C D = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1073.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 1 } { 2 } x ^ { 2 } + x y + \\frac { 1 } { 2 } y ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1074.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 1 = 2x + 1\\)",
|
|
"gt_answers": "( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } ) ( 1 + 4 + 9 ) \\geqslant ( x + 2 y + 3 z ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1075.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2}",
|
|
"gt_answers": "D C D \\bot A D , D A \\bot A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_1076.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: `f(x) = 1x^2 + 3x + 4`.",
|
|
"gt_answers": "f ( x ) = \\vert x - a \\vert + 3 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1077.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "\\frac { 5 } { 6 } \\textcircled { < } \\frac { 5 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1078.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: HfO2 + ZnO = HfO4 + ZnO2.",
|
|
"gt_answers": "Z n + H _ { 2 } S O _ { 4 } = H _ { 2 } \\uparrow + Z n S O _ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1079.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\nn(n-1) - 3 = 0\n\nThis is a quadratic equation in the variable n, which can be solved using the quadratic formula.",
|
|
"gt_answers": "n = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1080.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2mg/ml = 3g/30ml.",
|
|
"gt_answers": "V _ { a b } = V = \\frac { 2 m g \\cdot R } { 3 B ^ { 2 } l ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1081.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 4x + 5 = 0.\"",
|
|
"gt_answers": ". x = 6 + 4 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1082.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x2000x1000x",
|
|
"gt_answers": "8 0 0 0 \\times \\frac { 1 } { 4 0 0 0 } = 2 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_1083.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": ". x ^ { 2 } + \\sqrt { 3 } t x + t ^ { 2 } - 1 = 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1084.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: sin(a) = a/2r.",
|
|
"gt_answers": "\\sin A = \\frac { a } { 2 R }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1086.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "k ^ { 2 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1087.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `X = 2.20 + 0.05T`.",
|
|
"gt_answers": "x = \\frac { 2 2 0 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1089.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 144 + 2(12) - 3(3) = 120.",
|
|
"gt_answers": "1 4 4 \\div 2 = 7 2 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1090.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(b^2 - x^2 = 4bx\\)\n\nThis formula is written in LaTeX format, with the variables in bold and the equal sign between them.",
|
|
"gt_answers": "\\overrightarrow { P A } = ( - 6 - x _ { 1 } - \\sqrt { 2 0 ( 1 - \\frac { x ^ { 2 } } { 3 6 } ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1091.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"a = b + c\" using LaTeX format.",
|
|
"gt_answers": "a c = b c\n",
|
|
"image_path": "./data/HME100K/test_images/test_1092.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(8 \\times 2 + 2 \\times 3 + 3 \\times 4 + 4 \\times 5 + 5 \\times 6 + 6 \\times 7 + 7 \\times 8 = 108 + 36 + 45 + 60 + 75 + 90 + 105 + 120 = 555\\)",
|
|
"gt_answers": "6 = \\frac { 8 } { 2 } h\n",
|
|
"image_path": "./data/HME100K/test_images/test_1093.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(n \\cdot (n + 1) \\cdot (n + 2) \\cdot (n + 3) \\cdot (n + 4) \\cdot (n + 5) \\cdot (n + 6) \\cdot (n + 7) \\cdot (n + 8) \\cdot (n + 9) \\cdot (n + 10) \\cdot (n + 11) \\cdot (n + 12) \\cdot (n + 13) \\cdot (n + 14) \\cdot (n + 15) \\cdot (n + 16) \\cdot (n + 17) \\cdot (n + 18) \\cdot (n + 19) \\cdot (n + 20) \\cdot (n + 21) \\cdot (n + 22) \\cdot (n + 23) \\cdot (n + 24) \\cdot (n + 25) \\cdot (n + 26) \\cdot (n + 27) \\cdot (n + 28) \\cdot (n + 29) \\cdot (n + 30) \\cdot (n + 31) \\cdot (n + 32) \\cdot (n + 33) \\cdot (n + 34) \\cdot (n + 35) \\cdot (n + 36) \\cdot (n + 37) \\cdot (n + 38) \\cdot (n + 39) \\cdot (n + 40) \\cdot (n + 41) \\cdot (n + 42) \\cdot (n + 43) \\cdot (n + 44) \\cdot (n + 45) \\cdot (n + 46) \\cdot (n + 47) \\cdot (n + 48) \\cdot (n + 49) \\cdot (n + 50) \\cdot (n + 51) \\cdot (n + 52) \\cdot (n + 53) \\cdot (n + 54) \\cdot (n + 55) \\cdot (n + 5",
|
|
"gt_answers": "d _ { n } = \\frac { a _ { n } } { n ( n + 1 ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1094.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "\\Delta A B E \\cong \\Delta D B E\n",
|
|
"image_path": "./data/HME100K/test_images/test_1095.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 0 : 2 \\theta = 2 \\cos ^ { 2 } \\theta - 1 = - \\frac { 7 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1096.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{x^2}{2} + 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 \\div 1 0 0 = 0 . 0 1 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1097.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = \\frac{2\\pi r^2}{G} \\cdot \\rho\\)\n\nwhere:\n\n* `m` is the mass of the object\n* `r` is the radius of the object\n* `G` is the gravitational constant\n* `\u03c1` is the density of the object.",
|
|
"gt_answers": "2 m - 3 + 5 - m = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1098.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2^{24} - 2^{23} + 2^{22} - 2^{21} + 2^{20} - 2^{19} + 2^{18} - 2^{17} + 2^{16} - 2^{15} + 2^{14} - 2^{13} + 2^{12} - 2^{11} + 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{24} - 2^{23} + 2^{22} - 2^{21} + 2^{20} - 2^{19} + 2^{18} - 2^{17} + 2^{16} - 2^{15} + 2^{14} - 2^{13} + 2^{12} - 2^{11} + 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{24} - 2^{23} + 2^{22} - 2^{21} + 2^{20} - 2^{19} + 2^{18} - 2^{17} + 2^{16} - 2^{15} + 2^{14} - 2^{13} + 2^{12} - 2^{11} + 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} =",
|
|
"gt_answers": "( 1 2 - 4 y ) ( 1 2 - 3 y ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1099.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + 8x + 3 = 0\n\\end{aligned}\n\\end{equation}\n\nThis is a quadratic equation in the variable x, which can be solved using the quadratic formula.",
|
|
"gt_answers": "2 \\times 1 8 = 3 6 . 1 2 \\times 3 = 3 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1100.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 + 30\\cdot 30 +",
|
|
"gt_answers": "M N = 3 0 \\sqrt { 3 } - 3 0 \\approx = 3 0 ( \\sqrt { 3 } - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1102.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{15}{25} + \\frac{25}{15} + \\frac{1",
|
|
"gt_answers": "a + 1 5 - 1 5 = 2 5 - 1 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1103.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the multiplication of two fractions, each with a denominator of 2. The result is a fraction with a denominator of 4.",
|
|
"gt_answers": "A H \\bot B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1104.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 30/750 = 0.04.",
|
|
"gt_answers": "3 1 0 \\div 5 0 = 6 \\cdots 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1105.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\therefore \\widehat { B D } = \\overline { C D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1107.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3-4m + 50.",
|
|
"gt_answers": "\\frac { 3 - 4 m } { 4 } \\leq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1108.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "h _ { 1 } = t _ { 1 } \\cdot V = 5 S . 0 . 3 m / s = 1 . 5 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_1109.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis equation is a simple algebraic identity, which can be easily verified by substituting the values of x and y for any real numbers.",
|
|
"gt_answers": "x ^ { 2 } - 5 x + 6 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1111.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 444 x 444 + 44",
|
|
"gt_answers": "[ ( 5 6 + 4 4 ) \\div 2 ] \\times ( 5 6 - 4 4 ) = 6 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1112.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as CB(1/100) = 1/100.",
|
|
"gt_answers": "\\overrightarrow { C B } = 1 1 , 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1113.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 14\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\n2x^2 + 3x + 4 = 14\n\\end{equation}\n\nThe equation is written using the `\\( \\)` and `\\)` symbols to indicate the beginning and end of the equation, respectively. The `x` variable is written using the `\\(x\\)` symbol, and the `+` and `=` signs are written using the `\\(+ \\)` and `\\(= \\)` symbols, respectively.",
|
|
"gt_answers": "( \\sqrt { 5 } + 1 ) x \\cdot 2 x \\times \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1114.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( \\frac { 3 } { 2 } a + b ) ^ { 2 } _ { ; } \\geq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1115.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(442244 - 442244 = 0\\)",
|
|
"gt_answers": "4 - 4 ( 2 k - 4 ) > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1116.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 1 = 5.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x - 1 = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1117.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 2n + 2m = 2(n + m)",
|
|
"gt_answers": "2 ^ { n } b _ { n } = 2 ^ { C m } - a ^ { a n - 1 } = 2 ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1119.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A + B = C\\)",
|
|
"gt_answers": "A E = 3 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1121.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x^2 - 3x + 4 = 0.",
|
|
"gt_answers": "- \\frac { 1 } { 2 } x - 3 x = 6 - 8 + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1122.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x + 1\\)",
|
|
"gt_answers": "y = \\frac { 7 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1123.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 4x(3-1/5) = 12.",
|
|
"gt_answers": "\\frac { G D } { A D } = \\frac { 3 x } { 3 - 2 x } = \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1124.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x + 3y = 10\\)",
|
|
"gt_answers": "\\frac { 4 } { 6 } < \\frac { 5 } { 6 } < 1 < \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1126.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 4x + 8 = 16\\)\n\nThis formula can be written using LaTeX as follows:\n\n\\(x^2 + 4x + 8 = 16\\)",
|
|
"gt_answers": "\\frac { x - 4 } { 3 } - 8 = - \\frac { x + 2 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1127.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given by:\n\nW = 400 - (x^2 + y^2) + 400x + 400y + 400xy\n\nThis formula can be written in LaTeX as follows:\n\nW = 400 - (x^2 + y^2) + 400x + 400y + 400xy",
|
|
"gt_answers": "W = - x ^ { 2 } + 7 x + 4 8 = - ( x - 3 . 5 ) ^ { 2 } + 6 0 . 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1128.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(T_{0} = 293.15 K\\)\n\nThis formula represents the temperature of the Earth's surface at the top of the atmosphere (TOA) in Kelvin (K) units.",
|
|
"gt_answers": "t = 0 . 5 s = 1 \\frac { 1 } { 4 } T\n",
|
|
"image_path": "./data/HME100K/test_images/test_1129.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x3 + 2x400cm = 1200cm^2\".",
|
|
"gt_answers": "8 0 0 \\times 3 = 2 4 0 0 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1130.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{x^2}{2} + 3x + 5\\)",
|
|
"gt_answers": "\\tan \\frac { \\theta } { 2 } = \\frac { \\sqrt { \\xi } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1131.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Be = ice.\"",
|
|
"gt_answers": "B E = \\frac { 1 } { 2 } C E\n",
|
|
"image_path": "./data/HME100K/test_images/test_1132.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(n^2 + n + 1 = 2n^2 + 2n + 1\\)\n\nThis formula can be rearranged to obtain the following equation:\n\n\\(n^2 + n + 1 = 2(n^2 + n) + 1\\)\n\nThis equation can be further simplified to obtain the following expression:\n\n\\(n^2 + n + 1 = 2n^2 + 2n + 1 - 2n^2 - 2n = 2n^2 + 2n + 1 - 2n^2 - 2n + 1 - 2n^2 - 2n = 0\\)\n\nThis equation has two solutions:\n\n1. n = 0, which gives the value of n as 0.\n2. n = 1, which gives the value of n as 1.",
|
|
"gt_answers": "b _ { n } = \\frac { 1 + 2 n a _ { n } } { a _ { n } } = \\frac { 1 } { a _ { n } } + 2 n = \\frac { 1 } { 2 ^ { n - 1 } } + 2 n\n",
|
|
"image_path": "./data/HME100K/test_images/test_1133.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 5 = 10\\)",
|
|
"gt_answers": "x = \\frac { 5 } { 3 } + k\n",
|
|
"image_path": "./data/HME100K/test_images/test_1135.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4x^2 + 2x - 3 = 0\\)",
|
|
"gt_answers": "4 \\times 8 \\times 2 = 6 4 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1136.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CE = BE + 4\" and is written in LaTeX format.",
|
|
"gt_answers": "\\tan 6 3 . 4 ^ { \\circ } = \\frac { C E } { B E }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1137.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(T = \\frac{1}{2} \\left(J + \\frac{1}{2} \\left(J \\cdot B \\right) \\right)\\)\n\nThe formula represents the total torque on a rigid body due to the applied force and the moment of inertia of the body. The force is represented by the variable J, and the moment of inertia is represented by the variable B. The total torque is calculated by multiplying the force by the distance from the center of mass to the point of application of the force, and then dividing by two. The result is then further divided by half of the product of the force and the moment of inertia.",
|
|
"gt_answers": "\\vert \\overrightarrow { a } + \\overrightarrow { b } \\vert = \\sqrt { 1 3 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1138.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nBa(OH)2 + NaCl = BaCl2 + 2H2O",
|
|
"gt_answers": "B a C l _ { 2 } + N a _ { 2 } C O _ { 3 } = B a C O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1139.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LQP = LBQ + 90\u00b0\".",
|
|
"gt_answers": "\\angle C P Q = \\angle B = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1140.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x _ { 4 } = - \\sqrt { 6 0 } - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1142.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(n = \\frac{m^2}{2m + 1}\\)",
|
|
"gt_answers": "( m - n ) ^ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1144.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(LA = 45^{\\circ} + 2\\times LAB\\)",
|
|
"gt_answers": "\\angle A B C = \\angle A = 4 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1145.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with the number 4 written in Japanese characters.",
|
|
"gt_answers": "x = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1146.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "x _ { 1 } + x _ { 2 } = \\frac { 1 2 k ^ { 2 } } { 3 k ^ { 2 } + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1147.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as B(TKX) = B(TK) + B(TX) + B(KX).",
|
|
"gt_answers": "B = B _ { 0 } + k x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1148.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"b^2 - 3b + 2 = 0.\"",
|
|
"gt_answers": "b = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1150.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "y _ { 2 } = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1151.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{3}x^3 + \\frac{1}{4}x^4 + \\frac{1}{5}x^5 + \\frac{1}{6}x^6 + \\frac{1}{7}x^7 + \\frac{1}{8}x^8 + \\frac{1}{9}x^9 + \\frac{1}{10}x^{10} + \\frac{1}{11}x^{11} + \\frac{1}{12}x^{12} + \\frac{1}{13}x^{13} + \\frac{1}{14}x^{14} + \\frac{1}{15}x^{15} + \\frac{1}{16}x^{16} + \\frac{1}{17}x^{17} + \\frac{1}{18}x^{18} + \\frac{1}{19}x^{19} + \\frac{1}{20}x^{20} + \\frac{1}{21}x^{21} + \\frac{1}{22}x^{22} + \\frac{1}{23}x^{23} + \\frac{1}{24}x^{24} + \\frac{1}{25}x^{25} + \\frac{1}{26}x^{26} + \\frac{1}{27}x^{27} + \\frac{1}{28}x^{28} + \\frac{1}{29}x^{29} + \\frac{1}{30}x^{30} + \\frac{1}{31}x^{31} + \\frac{1}{32}x^{32} + \\frac{1}{33}x^{33} + \\frac{1}{34}x^{34} + \\frac{1}{35}x^{35} + \\frac{1}{36}x^{36} + \\frac{1}{37}x^{37} + \\frac{1}{38}x",
|
|
"gt_answers": "f ^ { \\prime } ( x ) = - \\frac { 1 } { x ^ { 2 } } - 1 + \\frac { a } { x } = \\frac { a x - x ^ { 2 } - 1 } { x ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1152.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 10.5 = 10.5x + 2.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = 1 0 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1153.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(F_{i,j} = \\frac{1}{2} \\left(F_{i-1,j} + F_{i,j-1} - F_{i-1,j-1}\\right)\\)\n\nThis formula is used to calculate the force acting on a particle at position (i, j) in a two-dimensional array of particles. The force is calculated as the average of the forces acting on the particle from the left, right, and bottom sides, with the weighting factor of 1/2.",
|
|
"gt_answers": "F _ { 1 } L _ { 1 } = F _ { 2 } L 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1154.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left(",
|
|
"gt_answers": "c d = 1 , m ^ { 2 } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1156.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 600x6 + 1000 = 1600.",
|
|
"gt_answers": "6 0 k g \\times \\frac { 1 } { 6 } = 1 0 k g\n",
|
|
"image_path": "./data/HME100K/test_images/test_1157.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "3 . 1 4 \\times 2 \\times 1 . 8 \\div 3 \\times 1 . 8 = 1 3 . 5 6 4 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_1158.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6 > 0\" using LaTeX format.",
|
|
"gt_answers": "6 > \\square\n",
|
|
"image_path": "./data/HME100K/test_images/test_1159.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 27x + 14 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 2 4 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1160.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x ^ { 2 } - a x - 3 x + 3 = x ^ { 2 } - x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1163.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A(B+C) + D(E+F) = G(H+I) + J(K+L)\".",
|
|
"gt_answers": "\\angle A O C = 3 6 0 ^ { \\circ } - \\angle A O B - \\angle B O C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1165.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 10 = 100.\"",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1166.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{2x^2 + 3x + 4}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^",
|
|
"gt_answers": "y - \\frac { 2 } { y } - 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1168.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "x _ { 1 } = a , x _ { 2 } = \\frac { a + 1 } { a - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1169.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 15kJ/8 = 1.875kWh.",
|
|
"gt_answers": "1 5 ) k = - 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_1170.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\nd(x) = 2x - 3\n\nThe formula is written in LaTeX format, which is a standard mathematical notation used for writing mathematical expressions.",
|
|
"gt_answers": "d = \\frac { \\vert - a b \\vert } { c } = \\frac { \\sqrt { 3 } } { 4 } c\n",
|
|
"image_path": "./data/HME100K/test_images/test_1171.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "P \\cdot 1 \\frac { 1 } { 2 } ( - 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1172.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x + 4 = 16.\"",
|
|
"gt_answers": "\\frac { 4 } { 3 } x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1173.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Co-Citrus - Ag-59.\"",
|
|
"gt_answers": "a _ { 0 } - a _ { 1 } + a _ { 2 } \\cdots - a _ { 9 } = 5 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_1174.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y",
|
|
"gt_answers": "x ^ { 2 } + 2 x - 6 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1175.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "S _ { \\Delta A O F } = \\frac { 3 } { 2 } S _ { \\Delta B O F } = \\frac { 9 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1176.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { I _ { 1 } } { I _ { 2 } } = \\frac { R _ { 2 } } { R _ { 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1177.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6 + 9 = 15 - 9 = 6.\"",
|
|
"gt_answers": "\\boxed { 1 1 } + 6 < \\frac { 9 + 9 } { 1 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1178.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\na + b = 3\n\nThe formula is written in the form of an equation, with the variables a and b on the left side and the equal sign (=) in the middle. The result of the equation is 3, which is the value of the expression.",
|
|
"gt_answers": "a = \\frac { 2 } { 3 } \\cdot b = - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1179.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LBCD-90'\\)",
|
|
"gt_answers": "\\angle B C D = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1180.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "S = \\frac { 1 } { 2 } a b \\sin C = \\frac { 1 } { 2 } \\times 6 \\times \\frac { \\sqrt { 3 } } { 2 } = \\frac { 3 \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1181.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { b } { 3 a } + \\frac { a } { 2 b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1182.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n2(2x + 4) = 4(2x + 4)\n\nThis is a simple algebraic equation that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "2 \\sqrt { 4 2 } > 2 \\sqrt { 4 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1184.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(5x^2 + 12x + 42 = 5x^2 + 12x + 42 \\cdot 5 = 5x^2 + 60x + 210\\)\n\nThe formula is a quadratic equation, where the variable x is squared and added to 12x and 42. The result is then multiplied by 5.",
|
|
"gt_answers": "5 5 \\times ( 1 5 \\div 2 ) = 4 1 2 . 5 ( L )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1186.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 10\\)",
|
|
"gt_answers": "x y ( x + y ) = 8 8 0 , x y + ( x + y ) = 7 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1187.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 0\\)",
|
|
"gt_answers": "x _ { 1 } = 1 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1188.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1",
|
|
"gt_answers": "A B : y = \\pm \\frac { \\sqrt { 1 1 } } { 1 1 } ( x + \\sqrt { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1189.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + y^2 + 2xy + 2xz + 2yz + 2xw + 2yw + 2z^2 + 2yw^2 + 2z^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 + 2yw^2 + 2xw^2 + 2yw^2 + 2xz^2 +",
|
|
"gt_answers": "x ^ { 2 } + 2 x y + y ^ { 2 } - 2 x y - 2 5 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1190.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Bd = B + D + C + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + 2C + 2D + 2B + ",
|
|
"gt_answers": "B D ^ { 2 } = B C ^ { 2 } + D C ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1191.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LFNQ = LONF + LONQ.\"",
|
|
"gt_answers": "\\angle F N Q = \\frac { 1 } { 2 } \\angle D N F\n",
|
|
"image_path": "./data/HME100K/test_images/test_1192.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 2x^2 + 4x + 2 = 10.",
|
|
"gt_answers": "2 4 \\times \\frac { 5 x } { 2 4 } = 2 4 \\times \\frac { 3 x - 4 } { 8 } - 2 4 \\times 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1193.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few letters and numbers, which could be a representation of a mathematical expression in Korean.",
|
|
"gt_answers": "0 H = \\frac { 1 } { 2 } O C .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1194.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: a^2 + b^2 = c^2.",
|
|
"gt_answers": "a = 4 c = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1195.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 100.\"",
|
|
"gt_answers": "a x + b y = 7 \\textcircled { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1196.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "a c = 3 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1197.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mathematical formula using the Greek letter \"pi\" (\u03c0) as the symbol for the constant. The formula is written in a way that it can be easily read and understood by a mathematician or someone familiar with the subject.",
|
|
"gt_answers": "3 . 1 4 \\times ( \\frac { 8 } { 2 } ) ^ { 2 } x - 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1198.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "C D = B D = A D = \\frac { 1 } { 2 } A B ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1200.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/",
|
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"gt_answers": "1 \\div 8 1 = \\frac { 1 } { 8 1 }\n",
|
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"image_path": "./data/HME100K/test_images/test_1201.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + y^2}{2} = \\sqrt{x^2 + y^2}\n\\end{equation}\n\nThis formula states that the square root of the sum of the squares of two variables is equal to the square root of the sum of the variables themselves.",
|
|
"gt_answers": "y = \\pm 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1202.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(k = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "y = 1 - \\sqrt { 3 } k + \\frac { t } { 2 } , k + \\frac { \\sqrt { 3 } } { 2 } t )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1203.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{C_S}{C_A} = \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C_S}{C_A} \\cdot \\frac{C",
|
|
"gt_answers": "\\cos A = \\cos 3 0 ^ { . } = \\frac { A D } { A C } = \\frac { \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1204.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2006-06-06 to 2006-06-09 = 3 days.\"",
|
|
"gt_answers": "C O = 6 0 - 2 0 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1205.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2371.",
|
|
"gt_answers": "\\frac { 2 3 } { 2 0 } > 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1206.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the half of the square of one-half, which is equal to one-fourth.",
|
|
"gt_answers": "\\because \\angle C = \\angle C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1207.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n2.22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222",
|
|
"gt_answers": "\\textcircled { 3 } : 2 . 2 5 \\times 1 5 = 3 4 . 7 5 ( d m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1208.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(A = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "\\angle A = 8 0 ^ { \\circ } \\angle C = 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1209.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"F = ma,\" where \"F\" represents the force, \"m\" represents the mass, and \"a\" represents the acceleration.",
|
|
"gt_answers": "F = \\frac { w } { s }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1210.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is the equation of energy conservation, which states that the total energy of an object is constant, regardless of its motion or state of motion. The symbol \"E\" represents energy, \"m\" represents mass, and \"c\" represents the speed of light in a vacuum.",
|
|
"gt_answers": "\\frac { 2 \\pi } { w } = \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_1211.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x _ { 8 } = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1213.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(BG = \\frac{B}{G} = \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4} \\left( 1 + 1 \\right) = 1\\)\n\nThis formula is a simple algebraic expression that calculates the ratio of the base (B) to the height (G) of a right triangle. The formula is derived by dividing the base by the height and then taking the square root of the result. The final result is 1, which is the ratio of the base to the height of a right triangle.",
|
|
"gt_answers": "B G = B D = \\frac { 5 } { 2 } <\n",
|
|
"image_path": "./data/HME100K/test_images/test_1215.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LBAD = \\frac{1}{2} \\left( \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2}",
|
|
"gt_answers": "\\angle A E C = \\angle A C E = \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } - \\angle B A D )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1217.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 1/2(C2O3) + 1/2(H2O) = 1/2(CO2) + 1/2(H2O) + 1/2(O2).",
|
|
"gt_answers": "\\frac { 1 } { C _ { 1 0 } ^ { 2 } } = \\frac { 1 } { 4 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1219.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{18} \\cdot \\frac{1}{2} \\cdot \\frac{1}{3} \\cdot \\frac{1}{4} \\cdot \\frac{1}{5} \\cdot \\frac{1}{6} \\cdot \\frac{1}{7} \\cdot \\frac{1}{8} \\cdot \\frac{1}{9} \\cdot \\frac{1}{10} \\cdot \\frac{1}{11} \\cdot \\frac{1}{12} \\cdot \\frac{1}{13} \\cdot \\frac{1}{14} \\cdot \\frac{1}{15} \\cdot \\frac{1}{16} \\cdot \\frac{1}{17} \\cdot \\frac{1}{18}\n\\end{equation}\n\nThis expression represents the sum of the reciprocals of the first 18 integers, starting from 1.",
|
|
"gt_answers": "D ( - 5 , \\frac { 1 8 } { 2 5 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1220.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "y = a ( x - x ) ( x + x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1221.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(3x^2 + 6x - 12 = 0\\)",
|
|
"gt_answers": "3 x + 2 x - 2 = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1222.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LHC = ELB * 100\u00b0\".",
|
|
"gt_answers": "\\angle A C F = \\angle E C B = 1 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1224.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 26 = 30.",
|
|
"gt_answers": "\\frac { 1 3 } { 2 0 } x = 2 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1225.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{4} \\left( y_1^2 + y_2^2 + y_3^2 + y_4^2 \\right) + \\frac{1}{4} \\left( y_1^2 + y_2^2 + y_3^2 + y_4^2 \\right) + \\frac{1}{4} \\left( y_1^2 + y_2^2 + y_3^2 + y_4^2 \\right) + \\frac{1}{4} \\left( y_1^2 + y_2^2 + y_3^2 + y_4^2 \\right) = 1\n\\end{aligned}\n\\end{equation}\n\nThis formula is a quadratic equation in four variables, and it can be solved using the quadratic formula.",
|
|
"gt_answers": "x = - 2 , y = 4 , x = 4 , y = - 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1226.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x = J48.\"",
|
|
"gt_answers": "x = 5 \\sqrt { 4 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1228.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the multiplication of two fractions, each with a denominator of 2. The result is a fraction with a denominator of 4.",
|
|
"gt_answers": "1 - a ^ { 2 } \\geq 0 \\therefore - 1 \\leq a \\leq 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1229.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "\\vert y - \\sqrt { x } \\vert = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1230.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 30/16 = 1.875.",
|
|
"gt_answers": "\\frac { 3 0 } { 1 6 } = 1 \\frac { 1 4 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1233.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"fixi = 3x^2 + 4y^2 - 5xy - 6x - 7y - 8.\"",
|
|
"gt_answers": "f ^ { \\prime } ( x ) = 3 x ^ { 2 } - 6 a x + 2 b\n",
|
|
"image_path": "./data/HME100K/test_images/test_1235.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 8x^2 - 8x + 10\\)",
|
|
"gt_answers": "x ^ { 2 } + m ^ { 2 } - 2 m x + x ^ { 2 } - 8 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1236.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 16x + 4 = 0\\)",
|
|
"gt_answers": "x = \\frac { - 6 6 - 3 \\sqrt { 6 } } { 4 } = - \\sqrt { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1238.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2} \\left(x^2 + 2x + 1\\right)\\)",
|
|
"gt_answers": "y = \\frac { 1 } { 5 } a\n",
|
|
"image_path": "./data/HME100K/test_images/test_1239.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "Z n + C u ( N O ) = C u + Z n ( N O )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1240.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and symbols, which could be a representation of a mathematical expression in Japanese.",
|
|
"gt_answers": "\\frac { 3 } { 4 } x = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1243.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 100 - (20 - 5) = 70.",
|
|
"gt_answers": "\\frac { 5 5 } { 1 1 0 } = \\frac { 1 } { 2 } \\frac { 6 0 } { 1 2 0 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1244.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "= \\frac { 3 } { 5 } = \\frac { B D } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1246.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(H_{2}O + Fe^{2+} + 2NaOH \\rightarrow Fe^{3+} + 2NaOH + 2H_{2}O\\)",
|
|
"gt_answers": "H _ { 2 } S O _ { 4 } + F e = F e S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_1248.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 4x + 4 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = 6 \\div \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1249.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "x ^ { 2 } - 2 6 x + 1 6 9 = 1 6 ( 3 x + 6 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1250.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "e ^ { x _ { 0 } } - x _ { 0 } \\cdot e ^ { x _ { 0 } / h x _ { 0 } } = e\n",
|
|
"image_path": "./data/HME100K/test_images/test_1251.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( 3 x ^ { 2 } y ^ { 3 } ) \\cdot ( - 4 x ^ { m } y ^ { 4 } ) \\cdot ( 5 x y ^ { n } ) = - 6 0 x ^ { 5 } y ^ { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1252.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n(x + 1) / (x - 1) = 2",
|
|
"gt_answers": "( x + 7 ) .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1253.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x^2 + 2x + 9 = 9x^2 + 3x + 9\\)\n\nThis formula can be simplified by factoring out the common factor of 9 from both sides of the equation. The result is:\n\n\\(3x^2 + 2x + 9 = 9(x^2 + x + 3)\\)\n\nThis simplified equation can be further simplified by distributing the 9 on both sides of the equation. The result is:\n\n\\(3x^2 + 2x + 9 = 9(x^2 + x + 3) = 9(x^2 + x) + 9(3) = 9(x^2 + x) + 27\\)\n\nFinally, the simplified equation can be written as:\n\n\\(3x^2 + 2x + 9 = 9(x^2 + x) + 27\\)\n\nThis is the expression of the formula in LaTeX format.",
|
|
"gt_answers": "3 x - 2 = 9 + x + 3 - 6 \\sqrt { x + 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1254.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(x + y) - 3(x - y) = 0.",
|
|
"gt_answers": "\\frac { A E } { E B } = \\frac { \\dot { A } P } { B G }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1255.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 240/250 = 0.96.",
|
|
"gt_answers": "1 6 0 + 8 0 = 2 4 0 > 2 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1256.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)",
|
|
"gt_answers": "x _ { 2 } = - \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1257.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 16x7 + 17x6 + 18x5 + 19x4 + 20x3 + 21x2 + 22x1 + 23x0 = 167x0.",
|
|
"gt_answers": "1 6 7 \\times 2 + 1 6 7 \\times 3 + 1 6 7 \\times 5 = 1 6 7 \\times \\boxed { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1259.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3x^2 - 2x + 1}{x^2 - 2x + 1} = \\frac{3",
|
|
"gt_answers": "\\frac { 3 } { 4 x - 3 } - 2 = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1261.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(mg = 10kg\\)\n\nThis formula represents the relationship between the mass (m) of an object and its weight (g). The mass of the object is equal to 10 kilograms, and its weight is equal to 10 kilograms.",
|
|
"gt_answers": "m = \\frac { G } { g } = 1 0 ( k g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1264.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: y = kx^4.",
|
|
"gt_answers": "\\cdot y - 1 = k ( x - 4 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1265.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Lfoc(60)\".",
|
|
"gt_answers": "\\angle F O C = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1266.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(K_i = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": ". y = \\frac { k _ { 1 } } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1267.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: X = 6.783 + 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "x = \\frac { 1 6 } { 7 5 } \\div \\frac { 8 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1268.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(S_n = \\frac{1}{2} \\left( \\left( \\frac{1}{2} \\right)^n + \\left( \\frac{1}{2} \\right)^{n+1} \\right)\\)\n\nThis formula represents the sum of the first n terms of the Fibonacci sequence, where n is a positive integer.",
|
|
"gt_answers": "S _ { n } = n ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1269.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as BH10-3.",
|
|
"gt_answers": "B H = \\frac { 1 0 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1272.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 12x4x24m.",
|
|
"gt_answers": "1 2 \\times 4 \\times 5 = 2 4 0 c m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1273.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "( x + 2 y ) ( x - 2 y ) = 4 \\textcircled { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1274.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(a^2 + b^2 - 2ab = (a + b)^2 - a^2 - b^2\\)",
|
|
"gt_answers": "\\frac { 1 } { a } = \\frac { 3 - a . } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1275.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A + C = B + N\\)\n\nThis formula represents the relationship between the variables A, B, C, and N. The variables A and B represent two quantities, while C and N represent two other quantities. The equation states that the sum of A and C is equal to the sum of B and N.",
|
|
"gt_answers": "A C = C D = 1 0 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1277.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a shorthand form, which can be represented using LaTeX as follows:\n\n\\(A + B + C = D\\)\n\nThis formula represents the addition of three numbers, A, B, and C, to produce the result D.",
|
|
"gt_answers": "\\frac { A F } { F B } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1278.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(7x + 10y = 180\\)\n\nThis formula represents the relationship between two variables, x and y, where the sum of their products is equal to 180.",
|
|
"gt_answers": "\\frac { 1 } { 1 8 } + \\frac { 1 } { 1 2 } - \\frac { 1 } { 1 0 } = \\frac { 7 } { 1 8 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1279.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\ce{CO2 + 2H2O -> CH3OH + H2O + O2}\n\\end{equation}\n\nThis equation represents the chemical reaction between carbon dioxide (CO2) and water (H2O) to produce methanol (CH3OH) and oxygen (O2).",
|
|
"gt_answers": "6 N a O H + F e _ { 2 } ( S O _ { 4 } ) _ { 3 } = 3 N a _ { 2 } S O _ { 4 } + 2 F e ( O H ) _ { 3 } \\downarrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_1280.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 3x + 4 = 0.\"",
|
|
"gt_answers": "x = \\frac { 3 } { 2 } \\times \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1281.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2LBC-2LBC-120\u00b0\".",
|
|
"gt_answers": "\\angle B O C = 2 \\angle B A C = 1 2 0 ^ { \\circ } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1282.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as `x^2 + 128`.",
|
|
"gt_answers": "x _ { 2 } = ^ { 4 } \\sqrt { 1 2 8 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1283.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"s^2 = a^2 + b^2 - 2ab\".",
|
|
"gt_answers": "x = \\frac { 5 a + 1 } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1284.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x} + \\frac{1}{x^2} + \\frac{1}{x^3} + \\frac{1}{x^4} + \\frac{1}{x^5} + \\frac{1}{x^6} + \\frac{1}{x^7} + \\frac{1}{x^8} + \\frac{1}{x^9} + \\frac{1}{x^{10}} + \\frac{1}{x^{11}} + \\frac{1}{x^{12}} + \\frac{1}{x^{13}} + \\frac{1}{x^{14}} + \\frac{1}{x^{15}} + \\frac{1}{x^{16}} + \\frac{1}{x^{17}} + \\frac{1}{x^{18}} + \\frac{1}{x^{19}} + \\frac{1}{x^{20}} + \\frac{1}{x^{21}} + \\frac{1}{x^{22}} + \\frac{1}{x^{23}} + \\frac{1}{x^{24}} + \\frac{1}{x^{25}} + \\frac{1}{x^{26}} + \\frac{1}{x^{27}} + \\frac{1}{x^{28}} + \\frac{1}{x^{29}} + \\frac{1}{x^{30}} + \\frac{1}{x^{31}} + \\frac{1}{x^{32}} + \\frac{1}{x^{33}} + \\frac{1}{x^{34}} + \\frac{1}{x^{35}} + \\frac{1}{x^{36}} + \\frac{1}{x^{37}} + \\frac{1}{x^{38}} + \\frac{1}{x^{39}} + \\frac{1}{x^{40}} + \\frac{1}{x^{41}} + \\frac{1}{x^{42}} + \\frac{1}{x^{43}} + \\frac{1}{x^{44}} + \\frac{1}{x^{45}} + \\frac{1}{x",
|
|
"gt_answers": "x = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1285.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{n} \\sum_{i=1}^n \\left( \\frac{1}{n} \\sum_{j=1}^n \\left( \\frac{1}{n} \\sum_{k=1}^n \\left( \\frac{1}{n} \\sum_{l=1}^n \\left( \\frac{1}{n} \\sum_{m=1}^n \\left( \\frac{1}{n} \\sum_{n=1}^n \\left( \\frac{1}{n} \\sum_{o=1}^n \\left( \\frac{1}{n} \\sum_{p=1}^n \\left( \\frac{1}{n} \\sum_{q=1}^n \\left( \\frac{1}{n} \\sum_{r=1}^n \\left( \\frac{1}{n} \\sum_{s=1}^n \\left( \\frac{1}{n} \\sum_{t=1}^n \\left( \\frac{1}{n} \\sum_{u=1}^n \\left( \\frac{1}{n} \\sum_{v=1}^n \\left( \\frac{1}{n} \\sum_{w=1}^n \\left( \\frac{1}{n} \\sum_{x=1}^n \\left( \\frac{1}{n} \\sum_{y=1}^n \\left( \\frac{1}{n} \\sum_{z=1}^n \\left( \\frac{1}{n} \\sum_{a=1}^n \\left( \\frac{1}{n} \\sum_{b=1}^n \\left( \\frac{1}{n} \\sum_{c=1}^n \\left( \\frac{1}{n} \\sum_{d=1}^n \\left( \\frac{1}{n} \\sum_{e=1}^n \\left( \\frac{1}{n} \\sum_{f=1}^n \\left( \\frac{1}{n} \\sum_{g=1}^n \\left( \\frac{1}{n} \\sum_{h=1}^n \\left( \\frac{1}{n} \\sum_{i=1}^n \\",
|
|
"gt_answers": "( 2 ) a _ { n } = 4 + ( - 1 ) ( n - 1 ) = 5 - n\n",
|
|
"image_path": "./data/HME100K/test_images/test_1286.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = r^2\\)\n\nThis formula represents the equation of a circle, where x and y are the coordinates of a point on the circle, and r is the radius of the circle.",
|
|
"gt_answers": "= \\frac { 1 } { 2 } \\cos \\alpha - \\frac { \\sqrt { 3 } } { 2 } \\sin \\alpha + \\frac { 1 } { 2 } \\cos x + \\frac { \\sqrt { 3 } } { 2 } \\sin \\alpha = \\cos \\alpha\n",
|
|
"image_path": "./data/HME100K/test_images/test_1287.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(T = \\frac{L \\times A \\times G \\times M}{13}\\)\n\nwhere T is the temperature in degrees Celsius, L is the length of the object in meters, A is the area of the object in square meters, G is the mass of the object in kilograms, and M is the mass of the object in grams.",
|
|
"gt_answers": "\\frac { A G } { A P } = \\frac { \\frac { 1 } { 1 3 } } { \\frac { 1 3 } { 5 } } = \\frac { 5 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1289.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis equation represents the formula for the half of a square, which is the area of a square with one side of length 1.",
|
|
"gt_answers": "\\frac { A P } { A D } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1290.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 360\u00b0 - 50\u00b0 = 310\u00b0.",
|
|
"gt_answers": "3 6 0 ^ { \\circ } \\cdot ( \\frac { 1 } { 1 0 } + \\frac { 1 } { 1 5 } ) = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1291.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 15\\)",
|
|
"gt_answers": "x = \\frac { 1 7 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1292.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.",
|
|
"gt_answers": "a ^ { 2 } - b ^ { 2 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1293.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 7 + 6 + 11 + 15 + 19 + 23 + 27 + 31 + 35 + 39 + 43 + 47 + 51 + 55 + 59 + 63 + 67 + 71 + 75 + 79 + 83 + 87 + 91 + 95 + 99 + 103 + 107 + 111 + 115 + 119 + 123 + 127 + 131 + 135 + 139 + 143 + 147 + 151 + 155 + 159 + 163 + 167 + 171 + 175 + 179 + 183 + 187 + 191 + 195 + 199 + 203 + 207 + 211 + 215 + 219 + 223 + 227 + 231 + 235 + 239 + 243 + 247 + 251 + 255 + 259 + 263 + 267 + 271 + 275 + 279 + 283 + 287 + 291 + 295 + 299 + 303 + 307 + 311 + 315 + 319 + 323 + 327 + 331 + 335 + 339 + 343 + 347 + 351 + 355 + 359 + 363 + 367 + 371 + 375 + 379 + 383 + 387 + 391 + 395 + 399 + 403 + 407 + 411 + 415 + 419 + 42",
|
|
"gt_answers": "\\overline { x } = \\frac { 6 + 8 + 6 + 9 + 5 + 8 } { 6 } = 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_1294.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(PQ = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "O P _ { 1 } = O P _ { 2 } = \\frac { P _ { 1 } Q _ { 1 } } { \\sin 3 0 ^ { \\circ } } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1295.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x} + \\frac{1}{y} = \\frac{1}{x+y}\n\\end{equation}\n\nThis is the formula for the sum of the reciprocals of two numbers.",
|
|
"gt_answers": "\\frac { 1 } { x - y } = v\n",
|
|
"image_path": "./data/HME100K/test_images/test_1296.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(L_{AB}B_{C}C_{D}D_{E}E_{F}F_{G}G_{H}H_{I}I_{J}J_{K}K_{L}L_{M}M_{N}N_{O}O_{P}P_{Q}Q_{R}R_{S}S_{T}T_{U}U_{V}V_{W}W_{X}X_{Y}Y_{Z}Z_{A}A_{B}B_{C}C_{D}D_{E}E_{F}F_{G}G_{H}H_{I}I_{J}J_{K}K_{L}L_{M}M_{N}N_{O}O_{P}P_{Q}Q_{R}R_{S}S_{T}T_{U}U_{V}V_{W}W_{X}X_{Y}Y_{Z}Z_{A}A_{B}B_{C}C_{D}D_{E}E_{F}F_{G}G_{H}H_{I}I_{J}J_{K}K_{L}L_{M}M_{N}N_{O}O_{P}P_{Q}Q_{R}R_{S}S_{T}T_{U}U_{V}V_{W}W_{X}X_{Y}Y_{Z}Z_{A}A_{B}B_{C}C_{D}D_{E}E_{F}F_{G}G_{H}H_{I}I_{J}J_{K}K_{L}L_{M}M_{N}N_{O}O_{P}P_{Q}Q_{R}R_{S}S_{T}T_{U}U_{V}V_{W}W_{X}X_{Y}Y_{Z}Z_{A}A_{B}B_{C}C_{D}D_{E}E_{F}F_{G}G_{H}H_{I}I_{J}J_{K}K_{L}L_{M}M_{N}N_{O}O_{P}P_{Q}Q_{R}R_{S}S_{T}T_{",
|
|
"gt_answers": "\\angle A E B = 4 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1297.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2^{10} + 2^{0} - 2^{10} = 2^{20} - 2",
|
|
"gt_answers": "0 + 2 0 2 5 0 = 3 6 0 0 0 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1298.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `SOAPB-OA-ARP-MN-LN-IN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-BN-B",
|
|
"gt_answers": "O A P B = O A \\cdot A P = \\vert m \\vert \\cdot \\vert n \\vert = \\vert k\n",
|
|
"image_path": "./data/HME100K/test_images/test_1299.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(3.645 \\times 10^{6} \\div 3.3645 \\times 10^{6} = 1.045\\)",
|
|
"gt_answers": "3 . 5 g < 3 . 6 g < 5 g\n",
|
|
"image_path": "./data/HME100K/test_images/test_1300.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(C_2 + C_3 = 2C_1\\)\n\nThis formula represents the relationship between the charges of three capacitors, where C1, C2, and C3 are the capacitances of the three capacitors, and C2 + C3 = 2C1.",
|
|
"gt_answers": "1 - \\frac { C _ { 9 } } { C _ { 1 0 } ^ { 4 } } = \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1301.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 5x + 3 = 10.",
|
|
"gt_answers": "x = \\frac { 1 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1302.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(B = \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{AC}{AB} + \\frac{BC}{AB} + \\frac{AB}{AC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB}{BC} + \\frac{BC}{AC} + \\frac{AC}{BC} + \\frac{AB",
|
|
"gt_answers": ". B M = A B = \\frac { 1 } { 2 } B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1304.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(sin(x) = \\frac{sin(2x)}{2}\\)",
|
|
"gt_answers": "\\sin 4 5 ^ { \\circ } = \\frac { \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1305.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x + 1} = \\frac{x^2 + 4x + 1}{x^2 - 4x +",
|
|
"gt_answers": "\\frac { x } { 6 } - 4 x = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_1306.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LEBT = 35\u00b0\".",
|
|
"gt_answers": "\\angle E D F = \\angle E B F = 3 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1307.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x _ { 1 } = - 3 x _ { 2 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1308.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 7x - 10 = 0\\)",
|
|
"gt_answers": "( 1 + 1 5 \\% ) x \\times 9 0 \\% = x = 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_1309.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(76 - 4) = 144.",
|
|
"gt_answers": "\\frac { 3 6 } { 9 } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1311.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "x = \\frac { 2 } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1312.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as (9x^2 + 7y^2) = 144.",
|
|
"gt_answers": "( 9 1 - 6 ) \\times 5 = 7 5 ( d m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1313.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 20/100 = 0.2.",
|
|
"gt_answers": "x = 1 - \\frac { 1 } { 2 ^ { 1 0 0 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1314.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(AQ + HC = 40 cm\\)\n\nThe formula uses the variables A, Q, and H to represent the lengths of three sides of a triangle. The length of side A is represented by A, the length of side Q is represented by Q, and the length of side H is represented by H. The formula states that the sum of the lengths of sides A, Q, and H is equal to 40 centimeters.",
|
|
"gt_answers": "A Q = \\frac { A B } { \\cos A } = \\frac { 2 0 } { \\frac { 1 } { 2 } } = 4 0 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1315.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 2 = 10.\"",
|
|
"gt_answers": "2 + \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1317.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\tan(x) = \\frac{y}{x}\n\\end{equation}\n\nThis formula represents the tangent of an angle x in terms of its sine and cosine values, which are represented by the variables y and x.",
|
|
"gt_answers": "\\tan A = \\frac { 3 } { 4 } = \\frac { a } { b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1318.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(LEPC = 120^\\circ\\)",
|
|
"gt_answers": "\\angle E F C = 1 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1319.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 10\\)",
|
|
"gt_answers": "l x ^ { 2 } + y ^ { 2 } = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1320.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(V = \\frac{1}{14} \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\cdot 1000 \\",
|
|
"gt_answers": "\\frac { \\alpha } { y + 1 } = V\n",
|
|
"image_path": "./data/HME100K/test_images/test_1321.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(S_{PN} = \\frac{P_N}{N} + \\frac{P_N}{N-1} + \\frac{P_N}{N-2} + \\cdots + \\frac{P_N}{N-N_1} + \\frac{P_N}{N-N_2} + \\cdots + \\frac{P_N}{N-N_k} + \\cdots + \\frac{P_N}{N-N_l} + \\cdots + \\frac{P_N}{N-N_m} + \\cdots + \\frac{P_N}{N-N_n} + \\cdots + \\frac{P_N}{N-N_o} + \\cdots + \\frac{P_N}{N-N_p} + \\cdots + \\frac{P_N}{N-N_q} + \\cdots + \\frac{P_N}{N-N_r} + \\cdots + \\frac{P_N}{N-N_s} + \\cdots + \\frac{P_N}{N-N_t} + \\cdots + \\frac{P_N}{N-N_u} + \\cdots + \\frac{P_N}{N-N_v} + \\cdots + \\frac{P_N}{N-N_w} + \\cdots + \\frac{P_N}{N-N_x} + \\cdots + \\frac{P_N}{N-N_y} + \\cdots + \\frac{P_N}{N-N_z} + \\cdots + \\frac{P_N}{N-N_a} + \\cdots + \\frac{P_N}{N-N_b} + \\cdots + \\frac{P_N}{N-N_c} + \\cdots + \\frac{P_N}{N-N_d} + \\cdots + \\frac{P_N}{N-N_e} + \\cdots + \\frac{P_N}{N-N_f} + \\cdots + \\frac{P_N}{N-N_g} + \\cdots + \\frac{P_N}{N-N_h} + \\cdots + \\frac{P_N}{N-N_i}",
|
|
"gt_answers": "S _ { \\Delta P C N } = \\frac { 1 } { 2 } \\times ( \\frac { 1 } { 2 } + b )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1322.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^3 + y^3 = z^3.\"",
|
|
"gt_answers": "x = - 3 , y =\n",
|
|
"image_path": "./data/HME100K/test_images/test_1323.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 5x + 10 = 0\\)\n\nThis formula represents a quadratic equation, where x is the unknown variable and the other terms represent constants.",
|
|
"gt_answers": "\\frac { 1 2 } { 5 } x = \\frac { 1 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1324.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x^2 - 8x + 7 = 0`.",
|
|
"gt_answers": "2 2 + x - 2 2 = 8 7 \\div 2 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1325.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "1 7 = y ^ { 2 } - 4 y + 5 + y ^ { 2 } - 2 y + 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1327.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `a^2 + b^2 = c^2`.",
|
|
"gt_answers": "\\cdot b ^ { 2 } = a ^ { 2 } + c ^ { 2 } - 2 a c \\cdot \\cos B\n",
|
|
"image_path": "./data/HME100K/test_images/test_1328.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(a + b) - 3(a - b) = 2a - 3b.",
|
|
"gt_answers": "\\frac { b } { A B } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1330.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\cos a < 0 , \\tan a < 0 \\cot a < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1331.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901",
|
|
"gt_answers": "\\alpha 1 \\sim 2 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1332.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1040 + 1040 = 2080.\"",
|
|
"gt_answers": "= 1 0 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1334.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\nP = 0.5 * (100 - 50) + 0.5 * (100 - 50) = 0.5 * (100 - 100) = 0.0",
|
|
"gt_answers": "P = \\frac { W } { t } = \\frac { 6 0 0 J } { 1 0 s } = 6 0 w\n",
|
|
"image_path": "./data/HME100K/test_images/test_1335.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Sn2\" using LaTeX format.",
|
|
"gt_answers": "s n = n 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1336.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V = \\frac{2\\pi R^2}{3} \\cdot \\rho \\cdot g \\cdot h\\)\n\nwhere:\n\n* V is the volume of the sphere in cubic meters (m^3)\n* R is the radius of the sphere in meters (m)\n* \u03c1 is the density of the sphere material in kg/m^3\n* g is the gravitational acceleration due to Earth's mass in m/s^2\n* h is the height of the sphere in meters.",
|
|
"gt_answers": "V ^ { \\prime } = \\frac { \\Delta x ^ { 2 } } { t } = \\frac { 0 . 0 6 } { 0 . 5 } = 0 . 1 2 . m / s\n",
|
|
"image_path": "./data/HME100K/test_images/test_1338.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "A C \\bot B D\n",
|
|
"image_path": "./data/HME100K/test_images/test_1339.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(1 + 2) + 3(1 + 2) + 4(1 + 2) + 5(1 + 2) + 6(1 + 2) + 7(1 + 2) + 8(1 + 2) + 9(1 + 2) + 10(1 + 2) + 11(1 + 2) + 12(1 + 2) + 13(1 + 2) + 14(1 + 2) + 15(1 + 2) + 16(1 + 2) + 17(1 + 2) + 18(1 + 2) + 19(1 + 2) + 20(1 + 2) + 21(1 + 2) + 22(1 + 2) + 23(1 + 2) + 24(1 + 2) + 25(1 + 2) + 26(1 + 2) + 27(1 + 2) + 28(1 + 2) + 29(1 + 2) + 30(1 + 2) + 31(1 + 2) + 32(1 + 2) + 33(1 + 2) + 34(1 + 2) + 35(1 + 2) + 36(1 + 2) + 37(1 + 2) + 38(1 + 2) + 39(1 + 2) + 40(1 + 2) + 41(1 + 2) + 42(1 + 2) + 43(1 + 2) + 44(1 + 2) + 45(1 + 2) + 46(1 + 2) + 47(1 + 2) + 48(1 + 2) + 49(1 + 2) + 50(1 + 2) + 51(1 + 2) + 52(1 + 2) +",
|
|
"gt_answers": "\\angle 1 = \\frac { 1 } { 2 } \\angle B P Q , \\angle 2 = \\frac { 1 } { 2 } \\angle C Q P\n",
|
|
"image_path": "./data/HME100K/test_images/test_1340.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mathematical formula using the Greek letter \"pi\" (\u03c0) as the symbol for the ratio of the circumference of a circle to its diameter. The formula is written in a black font on a white background, and the text is surrounded by a black border.",
|
|
"gt_answers": "\\Delta B D E \\sim \\Delta E D O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1341.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"9 = 11/2.\"",
|
|
"gt_answers": "\\frac { 9 } { \\vert q \\vert } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1343.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(F = \\frac{G \\cdot m \\cdot l}{r^2}\\)\n\nwhere F is the force, G is the gravitational constant, m is the mass of the object, l is the length of the object, and r is the distance between the object and the center of the gravitational force.",
|
|
"gt_answers": "F = \\frac { 1 } { 2 } G = \\frac { 1 } { 2 } \\cdot 2 0 0 N = 1 0 0 N .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1344.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"100 - 70 = 30\".",
|
|
"gt_answers": "b > - 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1345.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x2 - 2 = 4.",
|
|
"gt_answers": "4 x + 2 x - 2 = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1346.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 200x2-400km.",
|
|
"gt_answers": "2 0 0 \\times 2 = 4 0 0 k m\n",
|
|
"image_path": "./data/HME100K/test_images/test_1347.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as LMN = 60\u00b0.",
|
|
"gt_answers": "\\angle M C N = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1348.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(p(x) = \\frac{n_1}{n_1 + n_2 + n_3 + n_4} \\cdot \\frac{n_2}{n_1 + n_2 + n_3 + n_4} \\cdot \\frac{n_3}{n_1 + n_2 + n_3 + n_4} \\cdot \\frac{n_4}{n_1 + n_2 + n_3 + n_4} = \\frac{n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4}{n_1 + n_2 + n_3 + n_4} = \\frac{n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4}{n_1 + n_2 + n_3 + n_4 - n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4} = \\frac{n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4}{n_1 + n_2 + n_3 + n_4 - n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4 \\cdot n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4} = \\frac{n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4}{n_1 + n_2 + n_3 + n_4 - n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4 \\cdot n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4 \\cdot n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4} = \\frac{n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4}{n_1 + n_2 + n_3 + n_4 - n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4 \\cdot n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4 \\cdot n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4 \\cdot n_1 \\cdot n_2 \\cdot n_3 \\cdot n_4}",
|
|
"gt_answers": "P ( x ) = n P ( 1 - P ) = 3 \\times \\frac { 1 } { 4 } \\times ( 1 - \\frac { 1 } { 4 } ) = \\frac { 9 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1349.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2^675 - 2^674 + 2^673 - 2^672 + 2^671 - 2^670 + 2^669 - 2^668 + 2^667 - 2^666 + 2^665 - 2^664 + 2^663 - 2^662 + 2^661 - 2^660 + 2^659 - 2^658 + 2^657 - 2^656 + 2^655 - 2^654 + 2^653 - 2^652 + 2^651 - 2^650 + 2^649 - 2^648 + 2^647 - 2^646 + 2^645 - 2^644 + 2^643 - 2^642 + 2^641 - 2^640 + 2^639 - 2^638 + 2^637 - 2^636 + 2^635 - 2^634 + 2^633 - 2^632 + 2^631 - 2^630 + 2^629 - 2^628 + 2^627 - 2^626 + 2^625 - 2^624 + 2^623 - 2^622 + 2^621 - 2^620 + 2^619 - 2^618 + 2^617 - 2^616 + 2^615 - 2^614 + 2^613 - 2^612 + 2^611 - 2^610 + 2^609 - 2^608 + 2^607 - 2^606 + 2^605 - 2^6",
|
|
"gt_answers": "6 7 . 2 0 5 = 6 7 \\times 1 + 0 . 1 \\times 2 + 0 . 0 0 1 \\times 2 + 5 \\times 0 . 0 0 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1350.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Lacb = 70\u00b0.\"",
|
|
"gt_answers": "\\angle A C B = 7 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1353.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a negative sign in front of a number, which could be a negative exponent or a negative power.",
|
|
"gt_answers": "x _ { 1 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1354.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x6 + 16 = 100.\"",
|
|
"gt_answers": "- \\frac { 3 } { 1 6 } x = 1 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1357.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2}{2} + \\frac{y^2}{2} + \\frac{z^2}{2} = 1\n\\end{equation}\n\nThis is a quadratic equation in three variables, where x, y, and z represent the coordinates of a point in three-dimensional space. The equation states that the sum of the squares of the distances from the origin to the point is equal to 1.",
|
|
"gt_answers": "x = \\frac { 2 1 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1358.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)\n\nThis formula represents a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 2 } { 3 } x - \\frac { 1 } { 4 } x = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1359.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a few numbers and letters, which can be represented in LaTeX using the following code:\n\n\\begin{equation}\n\\begin{aligned}\nx & = 2 + 3 \\\\\ny & = 4 - 5\n\\end{aligned}\n\\end{equation}\n\nThis equation represents the addition of two numbers and the subtraction of two other numbers.",
|
|
"gt_answers": "x = \\frac { - 4 \\pm 4 - \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1360.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 5 = 0\\)",
|
|
"gt_answers": "\\frac { 3 } { 5 } \\times \\frac { 5 } { 1 2 } x - \\frac { 3 } { 5 } \\times \\frac { 5 } { 6 } - \\frac { 3 } { 5 } \\times 5 + 4 = x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1361.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 40 - 9 = 31.",
|
|
"gt_answers": "x = \\frac { 4 0 . } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1363.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Sapo = So Podi 1/5.\"",
|
|
"gt_answers": "S _ { \\Delta } P C D = S _ { \\Delta } P O D = 1 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1364.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\alpha + \\beta \\in ( \\pi , 2 \\pi )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1367.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3 \\sqrt{2} - 2 \\sqrt{3} = 6 \\sqrt{2} - 2 \\sqrt{3} = 6 \\sqrt{2} - 2 \\sqrt{6} = 6 \\sqrt{2} - 2 \\sqrt{12} = 6 \\sqrt{2} - 2 \\sqrt{24} = 6 \\sqrt{2} - 2 \\sqrt{48} = 6 \\sqrt{2} - 2 \\sqrt{96} = 6 \\sqrt{2} - 2 \\sqrt{192} = 6 \\sqrt{2} - 2 \\sqrt{384} = 6 \\sqrt{2} - 2 \\sqrt{768} = 6 \\sqrt{2} - 2 \\sqrt{1536} = 6 \\sqrt{2} - 2 \\sqrt{3072} = 6 \\sqrt{2} - 2 \\sqrt{6144} = 6 \\sqrt{2} - 2 \\sqrt{12288} = 6 \\sqrt{2} - 2 \\sqrt{24576} = 6 \\sqrt{2} - 2 \\sqrt{49152} = 6 \\sqrt{2} - 2 \\sqrt{98304} = 6 \\sqrt{2} - 2 \\sqrt{196416} = 6 \\sqrt{2} - 2 \\sqrt{392832} = 6 \\sqrt{2} - 2 \\sqrt{785664} = 6 \\sqrt{2} - 2 \\sqrt{1572968} = 6 \\sqrt{2} - 2 \\sqrt{3145728} = 6 \\sqrt{2} - 2 \\sqrt{62914560} = 6 \\sqrt{2} - 2 \\sqrt{125829120} = 6 \\sqrt{2} - 2 \\sqrt{251658240} = 6 \\sqrt{2} - 2",
|
|
"gt_answers": "\\sqrt [ 3 ] { 6 \\frac { 6 } { 2 1 5 } } = 6 \\sqrt [ 3 ] { \\frac { 6 } { 2 1 5 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1368.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x _ { 2 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1369.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Box 1000: 8000 cm.\"",
|
|
"gt_answers": "8 0 \\times 1 0 0 = 8 0 0 0 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1371.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"abthtia = bc\".",
|
|
"gt_answers": "\\frac { a b + b c + c a } { a b c } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1372.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( 1 8 0 ^ { \\circ } - a ) - ( 1 0 ^ { \\circ } - a ) = ( 1 8 0 ^ { \\circ } - 2 B + 6 ^ { \\circ } ) - ( 6 0 ^ { \\circ } - \\frac { 1 } { 3 } B - 1 4 ^ { \\circ } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1373.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "x _ { 1 } = x x _ { 2 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1374.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A_1 + A_2 + A_3 + A_4 = 90\\)",
|
|
"gt_answers": "\\angle A D B = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1375.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nPCG(x) = 1 + 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8 + 10x^9 + 11x^10 + 12x^11 + 13x^12 + 14x^13 + 15x^14 + 16x^15 + 17x^16 + 18x^17 + 19x^18 + 20x^19 + 21x^20 + 22x^21 + 23x^22 + 24x^23 + 25x^24 + 26x^25 + 27x^26 + 28x^27 + 29x^28 + 30x^29 + 31x^30 + 32x^31 + 33x^32 + 34x^33 + 35x^34 + 36x^35 + 37x^36 + 38x^37 + 39x^38 + 40x^39 + 41x^40 + 42x^41 + 43x^42 + 44x^43 + 45x^44 + 46x^45 + 47x^46 + 48x^47 + 49x^48 + 50x^49 + 51x^50 + 52x^51 + 53x^52 + 54x^53 + 55x^54 + 56x^55 + 57x^56 + 58x^57 + 59x^58 + 60x^59 + 61x^60 + 62x^61 + 63x^62 + 64x^63 + 6",
|
|
"gt_answers": "P ( x = 1 ) = \\frac { 1 } { 3 } \\cdot C _ { 4 } ^ { 2 } \\cdot ( \\frac { 1 } { 3 } ) ^ { 2 } ( \\frac { 2 } { 3 } ) ^ { 2 } = \\frac { 8 } { 8 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1376.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 3x + 2 = 13\\)\n\nThis formula can be written using LaTeX as follows:\n\n\\(x^2 + 3x + 2 = 13\\)\n\nThe LaTeX code for the formula is:\n\n\\begin{equation}\nx^2 + 3x + 2 = 13\n\\end{equation}\n\nThe equation is written in the form of an equation with the variable \"x\" on the left side and the expression on the right side. The equation is also written in the form of an equation with the variable \"x\" on the left side and the expression on the right side, separated by the equal sign.",
|
|
"gt_answers": "x _ { 3 } = \\frac { 1 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1377.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "= 3 3 0 \\div 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1378.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(L = \\frac{AC}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC",
|
|
"gt_answers": "\\angle C M N = \\arccos \\frac { \\sqrt { 3 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1379.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 130x^2 - 60x + 100.",
|
|
"gt_answers": "\\frac { 1 3 0 x - 2 6 } { 6 } =\n",
|
|
"image_path": "./data/HME100K/test_images/test_1380.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 8x8 = 512.",
|
|
"gt_answers": "8 \\times 8 \\times 8 = 5 1 2 ( m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1381.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(sin(x) = \\frac{sin(2x)}{2} + \\frac{sin(3x)}{3} + \\frac{sin(4x)}{4} + \\frac{sin(5x)}{5} + \\frac{sin(6x)}{6} + \\frac{sin(7x)}{7} + \\frac{sin(8x)}{8} + \\frac{sin(9x)}{9} + \\frac{sin(10x)}{10} + \\frac{sin(11x)}{11} + \\frac{sin(12x)}{12} + \\frac{sin(13x)}{13} + \\frac{sin(14x)}{14} + \\frac{sin(15x)}{15} + \\frac{sin(16x)}{16} + \\frac{sin(17x)}{17} + \\frac{sin(18x)}{18} + \\frac{sin(19x)}{19} + \\frac{sin(20x)}{20} + \\frac{sin(21x)}{21} + \\frac{sin(22x)}{22} + \\frac{sin(23x)}{23} + \\frac{sin(24x)}{24} + \\frac{sin(25x)}{25} + \\frac{sin(26x)}{26} + \\frac{sin(27x)}{27} + \\frac{sin(28x)}{28} + \\frac{sin(29x)}{29} + \\frac{sin(30x)}{30} + \\frac{sin(31x)}{31} + \\frac{sin(32x)}{32} + \\frac{sin(33x)}{33} + \\frac{sin(34x)}{34} + \\frac{sin(35x)}{35} + \\frac{sin(36x)}{36} + \\frac{sin(37x)}{37} + \\frac{sin(38x)}{38} + \\frac{sin(39x)}{39} + \\frac{sin(40x)}{40} + \\",
|
|
"gt_answers": "y = \\sin 2 ( x - \\frac { \\pi } { 6 } ) = \\sin ( 2 x - \\frac { \\pi } { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1382.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is the equation of energy, also known as the mass-energy equivalence formula. It states that the energy (E) of an object is equal to its mass (m) multiplied by the speed of light squared (c^2).",
|
|
"gt_answers": "m = \\frac { \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1383.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{4(4+3)}{(4+3)(4+3)} = \\frac{4(4+3)}{12} = 16\n\\end{aligned}\n\\end{equation}\n\nThe formula is a simple algebraic expression that calculates the product of two numbers, in this case, 4 and 3. The result is 16.",
|
|
"gt_answers": "b ^ { 2 } - 4 a c = 4 ( k - 1 ) ^ { 2 } - 4 ( k ^ { 2 } - 1 ) = - 8 k + 8 \\geq 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1384.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a mathematical formula using LaTeX. The formula is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "a c ^ { 2 } = b c ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1385.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{3}x + \\frac{1}{4}\\)",
|
|
"gt_answers": "y = \\frac { 1 2 - 3 x } { 5 } = - \\frac { 3 } { 5 } x + \\frac { 1 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1388.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 3x + 2y = 5.",
|
|
"gt_answers": "3 x + \\frac { x } { 2 } - \\frac { 1 } { 2 } = 3 - \\frac { 2 } { 3 } x + \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1389.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3x + 4x + 5x = 12x.",
|
|
"gt_answers": "\u3001 \\frac { x } { 1 \\times 2 } + \\frac { x } { 2 \\times 3 } + \\frac { x } { 3 \\times 4 } +\n",
|
|
"image_path": "./data/HME100K/test_images/test_1390.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "V = \\frac { s } { t }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1393.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LAPC(30, 30) = 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle P = \\angle A C P = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1395.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "3 . 8 x \\div 3 . 8 x \\div 3 . 8 = 1 1 . 4 \\div 3 . 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_1396.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\sqrt [ 3 ] { 3 A - 2 B } = \\sqrt [ 3 ] { 3 \\times 2 - 2 \\times ( - 1 ) } = \\sqrt [ 3 ] { 8 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1397.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 3x + 2.",
|
|
"gt_answers": "y _ { 3 } = - \\frac { 1 } { 3 } , y _ { 4 } \\cdot 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1398.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4b-2z2 + 3bz + 2b2z + 2b3z + 3b4z + 4b5z + 5b6z + 6b7z + 7b8z + 8b9z + 9b10z + 10b11z + 11b12z + 12b13z + 13b14z + 14b15z + 15b16z + 16b17z + 17b18z + 18b19z + 19b20z + 20b21z + 21b22z + 22b23z + 23b24z + 24b25z + 25b26z + 26b27z + 27b28z + 28b29z + 29b30z + 30b31z + 31b32z + 32b33z + 33b34z + 34b35z + 35b36z + 36b37z + 37b38z + 38b39z + 39b40z + 40b41z + 41b42z + 42b43z + 43b44z + 44b45z + 45b46z + 46b47z + 47b48z + 48b49z + 49b50z + 50b51z + 51b52z + 52b53z + 53b54z + 54b55z + 55b56z + 56b57z + 57b58z + 58b59z + 59b60z + 60b61z + 61b62z + 62b63z + 63b64z + 64",
|
|
"gt_answers": "b ^ { 2 } + b - 2 = 0 \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_1399.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2H2O + CO2 + HBr --> 2H2O + 2CO + HBr\".",
|
|
"gt_answers": "+ H _ { 2 } O + B r _ { 2 } \\rightarrow H C O O H + 2 H B r\n",
|
|
"image_path": "./data/HME100K/test_images/test_1400.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(S_{oab} = \\frac{n(n-1)}{2}\\)\n\nwhere S_{oab} represents the number of possible outcomes of a two-person game, n represents the number of possible actions for each player, and the subscript oab indicates that the outcome is based on the order of the actions taken by the two players.",
|
|
"gt_answers": "\\cdot S _ { \\Delta O A B } = \\frac { 3 } { 2 } \\therefore n = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1401.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(N_{a} + N_{b} = N_{a} + N_{b} + N_{c} + N_{d} + N_{e} + N_{f} + N_{g} + N_{h} + N_{i} + N_{j} + N_{k} + N_{l} + N_{m} + N_{n} + N_{o} + N_{p} + N_{q} + N_{r} + N_{s} + N_{t} + N_{u} + N_{v} + N_{w} + N_{x} + N_{y} + N_{z} + N_{aa} + N_{bb} + N_{cc} + N_{dd} + N_{ee} + N_{ff} + N_{gg} + N_{hh} + N_{ii} + N_{jj} + N_{kk} + N_{ll} + N_{mm} + N_{nn} + N_{oo} + N_{pp} + N_{qq} + N_{rr} + N_{ss} + N_{tt} + N_{uu} + N_{vv} + N_{ww} + N_{xx} + N_{yy} + N_{zz} + N_{aaa} + N_{bbb} + N_{ccc} + N_{ddd} + N_{eee} + N_{fff} + N_{ggg} + N_{hhh} + N_{iii} + N_{jjj} + N_{kkk} + N_{lll} + N_{mmm} + N_{nnn} + N_{ooo} + N_{ppp} + N_{qqq} + N_{rrr} + N_{sss} + N_{ttt} + N_{uuu} + N_{vvv} + N_{www} + N_{xxx} + N_{yyy} + N_{zzz} + N_{aaaa} + N_{bbbb} + N_{cccg} + N_{dddd} + N_{eeee} + N_{fffg} + N_{gggg} + N_{hhhh} + N_{iiiq} + N_{jjjj} + N_{kkkk}",
|
|
"gt_answers": "N a _ { 2 } S O _ { 4 } + 2 K O H = 2 N a O H + k _ { 2 } S O _ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1402.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "( a \\times b ) \\times c = a \\times ( b \\times c )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1403.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(n(n+1)(2n+1) = 2n^3 + 3n^2 + 3n + 1\\)",
|
|
"gt_answers": "( n - 1 ) a _ { n + 1 } - ( n - 2 ) a _ { n } - 2 a _ { n - 1 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1407.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 5x + 6 = 10\\)",
|
|
"gt_answers": "1 + \\frac { 3 } { 5 } + \\frac { 1 } { 5 } = 1 \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1408.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 x \\cdot 2 0 0 0 + 1 6 0 0 x + 1 0 0 0 ( 1 0 0 - 3 x ) \\leq 1 7 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1409.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1x0 = 0\" using LaTeX format.",
|
|
"gt_answers": "1 \\frac { 1 } { 3 } x + \\frac { 1 } { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1410.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x^2 + 1} = \\frac{1}{x^2} + \\frac{1}{1 + x^2}\n\\end{equation}\n\nThis formula can be simplified further by rearranging the terms:\n\n\\begin{equation}\n\\frac{1}{x^2 + 1} = \\frac{1}{x^2} + \\frac{1}{x^2 + 1}\n\\end{equation}\n\nThis is the same as the original expression.",
|
|
"gt_answers": "\\frac { x + 1 } { 2 } = 1 - \\frac { 3 x - 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1411.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "k = - \\frac { \\sqrt { 3 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1412.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": ": x = \\sqrt { 2 } - 1 , y = \\sqrt { 2 } + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1413.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x + 4 = 15.",
|
|
"gt_answers": "2 x + 4 y - 2 8 - 2 x + 3 y - 2 z = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1414.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "b c = ( - 1 ) \\times ( - 1 ) = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1415.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 25000x10000 = 2500000000.",
|
|
"gt_answers": "2 5 0 0 \\times \\frac { 1 } { 1 0 0 0 } = 2 . 5 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1416.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x ^ { 2 } + x ^ { 2 } + x = 2 ( x + 1 ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1417.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 3x + 1.",
|
|
"gt_answers": "x + y = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1419.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x + y = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1420.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "\\sqrt { 2 x - 3 } = 3 - x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1421.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"d/m^2 * s/m^2 = 1/m^2\". This formula can be rewritten as \"d/m^2 = 1/m^2 * s/m^2\" or \"d/m^2 = 1/m^2 * s\".",
|
|
"gt_answers": "d = \\frac { m k } { \\sqrt { k ^ { 2 } + 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1422.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(y = 4x + 4 + 4x^2 + 4x^3 + 4x^4 + 4x^5 + 4x^6 + 4x^7 + 4x^8 + 4x^9 + 4x^{10} + 4x^{11} + 4x^{12} + 4x^{13} + 4x^{14} + 4x^{15} + 4x^{16} + 4x^{17} + 4x^{18} + 4x^{19} + 4x^{20} + 4x^{21} + 4x^{22} + 4x^{23} + 4x^{24} + 4x^{25} + 4x^{26} + 4x^{27} + 4x^{28} + 4x^{29} + 4x^{30} + 4x^{31} + 4x^{32} + 4x^{33} + 4x^{34} + 4x^{35} + 4x^{36} + 4x^{37} + 4x^{38} + 4x^{39} + 4x^{40} + 4x^{41} + 4x^{42} + 4x^{43} + 4x^{44} + 4x^{45} + 4x^{46} + 4x^{47} + 4x^{48} + 4x^{49} + 4x^{50} + 4x^{51} + 4x^{52} + 4x^{53} + 4x^{54} + 4x^{55} + 4x^{56} + 4x^{57} + 4x^{58} + 4x^{59} + 4x^{60} + 4x^{61} + 4x^{62} + 4x^{63} + 4x^{64} +",
|
|
"gt_answers": "y = - ( x - 1 ) ^ { 2 } + 4 = - x ^ { 2 } + 2 x + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1425.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3/6 = 1/2 - 1/6.",
|
|
"gt_answers": "\\frac { 3 } { 8 } = \\frac { 6 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1426.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 3x + 1.",
|
|
"gt_answers": "y _ { 3 } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1427.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 5/2 - 4/3 = 1/6.",
|
|
"gt_answers": "\\frac { 5 } { 6 } \\div \\frac { 5 } { 4 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1428.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(100 \\div 25 = 4\\)\n\nThis is a simple division problem where the divisor (25) is divided by the dividend (100). The result is 4.",
|
|
"gt_answers": "\\cos C = \\frac { 2 \\sqrt { 5 } } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1429.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(1.12 \\times 10^{2} + 1.2 \\times 10^{1} + 1.1 \\times 10^{0} + 1.2 \\times 10^{-1} + 1.1 \\times 10^{-2} + 1.2 \\times 10^{-3} + 1.1 \\times 10^{-4} + 1.2 \\times 10^{-5} + 1.1 \\times 10^{-6} + 1.2 \\times 10^{-7} + 1.1 \\times 10^{-8} + 1.2 \\times 10^{-9} + 1.1 \\times 10^{-10} + 1.2 \\times 10^{-11} + 1.1 \\times 10^{-12} + 1.2 \\times 10^{-13} + 1.1 \\times 10^{-14} + 1.2 \\times 10^{-15} + 1.1 \\times 10^{-16} + 1.2 \\times 10^{-17} + 1.1 \\times 10^{-18} + 1.2 \\times 10^{-19} + 1.1 \\times 10^{-20} + 1.2 \\times 10^{-21} + 1.1 \\times 10^{-22} + 1.2 \\times 10^{-23} + 1.1 \\times 10^{-24} + 1.2 \\times 10^{-25} + 1.1 \\times 10^{-26} + 1.2 \\times 10^{-27} + 1.1 \\times 10^{-28} + 1.2 \\times 10^{-29} + 1.1 \\times 10^{-30} + 1.2 \\times 10^{-31} + 1.1 \\times 10^{-32} + 1.2 \\times 10^{-33} + 1",
|
|
"gt_answers": "1 . 2 ( 1 1 0 y + 1 2 0 x ) = 9 7 2 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1430.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2n + 1 = 2n + 2,\" where n is an integer.",
|
|
"gt_answers": "2 N a O H + C O _ { 2 } = N a _ { 2 } C O _ { 3 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1431.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 8510685 + 5098732 + 3276589 + 2345678 + 1234567 + 8976543 + 6543210 + 5432109 + 4321098 + 3210987 + 2109876 + 1987654 + 1876543 + 1765432 + 1654321 + 1543210 + 1432109 + 1321098 + 1210987 + 1109876 + 1098765 + 1087654 + 1076543 + 1065432 + 1054321 + 1043210 + 1032109 + 1021098 + 1010987 + 1009876 + 9987654 + 9876543 + 9765432 + 9654321 + 9543210 + 9432109 + 9321098 + 9210987 + 9109876 + 9098765 + 8987654 + 8887653 + 8787652 + 8687651 + 8587650 + 8487649 + 8387648 + 8287647 + 8187646 + 8087645 + 7987644 + 7887643 + 7787642 + 7687641 + 7587640 + 74876",
|
|
"gt_answers": "8 5 + 1 0 > 5 8 + 3 0 > 3 3 + 3 0 > 5 8 + 1 7 3 3 + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1432.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000",
|
|
"gt_answers": "1 4 0 0 _ { m } = k 4 + k 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1433.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in the form of a formula, which is a mathematical equation. The formula is written in a black box, and the letters \"FUBADAM\" are written inside the box.",
|
|
"gt_answers": "F / / E B , \\Delta D A M \\cong \\Delta C B F\n",
|
|
"image_path": "./data/HME100K/test_images/test_1434.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Catch Heads Reefest 2021.\"",
|
|
"gt_answers": "C a C l _ { 2 } + F e _ { 2 } O _ { 3 } = 2 F e C l _ { 2 } +\n",
|
|
"image_path": "./data/HME100K/test_images/test_1435.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 360^2\\)",
|
|
"gt_answers": "^ { 2 } \\times 8 \\times \\frac { 1 } { 3 } = 7 5 . 3 6 ( d m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1437.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"m(x) = 2x^2 + 3x + 4.\"",
|
|
"gt_answers": "( m - 4 ) ( m + 1 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1438.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "a ^ { 2 } x ^ { 2 } = a -\n",
|
|
"image_path": "./data/HME100K/test_images/test_1439.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": ": 2 x ^ { 2 } + b x + 1 = 0 ( 2 , b , c \\in R )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1441.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3 = 5.",
|
|
"gt_answers": "\\frac { x } { x - 1 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1442.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2(2x + 3y) = 12.\"",
|
|
"gt_answers": "\\frac { 6 \\sqrt { 2 } } { A E } = \\frac { A E } { 2 \\sqrt { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1443.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"Sabin C = 1/2 (1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20 + 1/21 + 1/22 + 1/23 + 1/24 + 1/25 + 1/26 + 1/27 + 1/28 + 1/29 + 1/30 + 1/31 + 1/32 + 1/33 + 1/34 + 1/35 + 1/36 + 1/37 + 1/38 + 1/39 + 1/40 + 1/41 + 1/42 + 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48 + 1/49 + 1/50 + 1/51 + 1/52 + 1/53 + 1/54 + 1/55 + 1/56 + 1/57 + 1/58 + 1/59 + 1/60 + 1/61 + 1/62 + 1/63 + 1/64 + 1/65 + 1/66 + 1/67 + 1/68 + 1/69 + 1/70 + 1/71 + 1/72 + 1/73 + 1/74 + 1/75 + 1/76 + 1/77 + 1/78 + 1/79 + 1/80 + 1/81 + 1/82 + 1/83 + 1/84 +",
|
|
"gt_answers": "S _ { \\Delta A B C } = \\frac { 1 } { 2 } a b \\sin C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1444.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 2xy + y^2 = 8xy + 8x + 8y + 4xy^2 + 4x^2y + 4xy^3 + 4x^3y + 4x^4y + 4x^5y + 4x^6y + 4x^7y + 4x^8y + 4x^9y + 4x^10y + 4x^11y + 4x^12y + 4x^13y + 4x^14y + 4x^15y + 4x^16y + 4x^17y + 4x^18y + 4x^19y + 4x^20y + 4x^21y + 4x^22y + 4x^23y + 4x^24y + 4x^25y + 4x^26y + 4x^27y + 4x^28y + 4x^29y + 4x^30y + 4x^31y + 4x^32y + 4x^33y + 4x^34y + 4x^35y + 4x^36y + 4x^37y + 4x^38y + 4x^39y + 4x^40y + 4x^41y + 4x^42y + 4x^43y + 4x^44y + 4x^45y + 4x^46y + 4x^47y + 4x^48y + 4x^49y + 4x^50y + 4x^51y + 4x^52y + 4x^53y + 4x^54y + 4x^55y + 4x^56y + 4x^57y + 4x^58y + 4x^59y + ",
|
|
"gt_answers": "x ^ { 2 } - 4 + 2 ( x + 1 ) ( x + 2 ) = - 8 ( x + 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1445.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle B O D = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1446.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SAP = 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1",
|
|
"gt_answers": "S _ { \\Delta A O P } = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1447.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 1000 - 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 4 0 0 } { 1 0 0 0 } = \\frac { 4 } { 1 0 } = \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1449.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: `X^2 + 2X + 3 = 0`.",
|
|
"gt_answers": "\\frac { x + 1 0 0 } { 2 8 0 - 4 0 } - \\frac { x } { 2 8 0 } \\geqslant 0 . 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1450.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 11x + 23 = 0.\"",
|
|
"gt_answers": "x = - \\frac { 1 1 } { 3 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1451.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{2} + 3^{3} + 5^{5} + 7^{7} + 11^{11} + 13^{13} + 17^{17} + 19^{19} + 23^{23} + 29^{29} + 31^{31} + 37^{37} + 41^{41} + 43^{43} + 47^{47} + 53^{53} + 59^{59} + 65^{65} + 71^{71} + 77^{77} + 83^{83} + 89^{89} + 97^{97} + 103^{103} + 109^{109} + 115^{115} + 121^{121} + 127^{127} + 133^{133} + 139^{139} + 145^{145} + 151^{151} + 157^{157} + 163^{163} + 169^{169} + 175^{175} + 181^{181} + 187^{187} + 193^{193} + 199^{199} + 205^{205} + 211^{211} + 217^{217} + 223^{223} + 229^{229} + 235^{235} + 241^{241} + 247^{247} + 253^{253} + 259^{259} + 265^{265} + 271^{271} + 277^{277} + 283^{283} + 289^{289}",
|
|
"gt_answers": "2 ( x + 5 ) - 6 < 3 ( 3 x + 2 ) ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_1452.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 2x - 1 = 0\\)",
|
|
"gt_answers": "\\frac { 2 - 1 0 x } { 3 } - 1 = \\frac { 2 - 6 x } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1454.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\nFe^{2+}(aq) + 2H_{2}O(l) \\rightarrow Fe(OH)_{4}^{2+}(aq) + 2H_{2}O(l)\n\\end{equation}\n\nThis formula represents the chemical reaction between iron(II) ions (Fe^{2+}) and hydrogen peroxide (H_{2}O_{2}) in aqueous solution, resulting in the formation of iron(III) hydroxide (Fe(OH)_{4}^{2+}) and water.",
|
|
"gt_answers": "F e _ { 2 } O _ { 3 } + 3 H _ { 2 } S O _ { 4 } = F e _ { 2 } ( S O _ { 4 } ) _ { 3 } + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1455.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(A + B) - 3(C + D) = 40 + 30 + 50 - 30 - 30 = 40 + 30 + 50 - 60 = 100.",
|
|
"gt_answers": "A F = A E + E F = 4 0 + 3 0 \\sqrt { 3 } - 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1456.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 6x6 = 6b6.",
|
|
"gt_answers": "6 \\times 6 \\times 6 = 2 1 6 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1457.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left(",
|
|
"gt_answers": "\\angle 1 = \\angle H Q P = \\frac { 1 } { 2 } \\angle D Q P\n",
|
|
"image_path": "./data/HME100K/test_images/test_1458.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 1 = 5.\"",
|
|
"gt_answers": "\\sqrt { 3 } \\times \\frac { 1 } { \\sqrt { 3 } } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1459.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(1/2) - 1/3 = 1/6.",
|
|
"gt_answers": "P M = \\sqrt { 3 ^ { 2 } - 2 ^ { 2 } } = \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1461.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 5x + 6 = 0`.",
|
|
"gt_answers": "\\frac { 1 } { 3 } x + 1 6 + \\frac { 2 } { 5 } x = x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1462.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few symbols, including a circle, a square, and a triangle.",
|
|
"gt_answers": "3 - \\frac { 3 } { 2 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1463.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = z^2\\)",
|
|
"gt_answers": "\\frac { 1 } { x } - \\frac { 2 } { 3 x } + \\frac { x } { 3 x - 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1464.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 4x - 4 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = - \\frac { 7 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1465.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 4x(16-4) = 14.",
|
|
"gt_answers": "1 6 x - 4 = 1 4 x + \\frac { 1 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1466.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(7 \\times 2^{2} = 144\\)",
|
|
"gt_answers": "y = \\frac { 2 \\sqrt { 7 } } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1467.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "0 < x < \\frac { 2 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1469.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Chinese.",
|
|
"gt_answers": "1 1 x = \\frac { 2 2 } { 5 } \\times \\frac { 1 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1470.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A + B = C + D\\)\n\nThe formula is an algebraic equation that represents the addition of two numbers.",
|
|
"gt_answers": "A E = 3 0 \\sqrt { 3 } - 3 0 + 4 0 = 3 0 \\sqrt { 3 } + 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1472.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with the letters \"x\" and \"y\" in it, which can be represented in LaTeX as follows:\n\n\\begin{equation}\nx + y = 2\n\\end{equation}\n\nThis is a simple algebraic equation that represents the addition of two numbers, where \"x\" is the first number and \"y\" is the second number.",
|
|
"gt_answers": "\\frac { 1 } { 6 } x = \\frac { 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1474.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Q = 25 - 25/3 = 10\".",
|
|
"gt_answers": "P = - 5 + 2 6 Q = 3 + t\n",
|
|
"image_path": "./data/HME100K/test_images/test_1475.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a black background, which could be written in LaTeX as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\text{Formula}\n\\end{aligned}\n\nThis equation is written in a standard mathematical notation, with the formula itself being the main content and the surrounding text being the equation's title.",
|
|
"gt_answers": "7 2 0 \\div 2 = 3 6 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1477.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "a = \\pm 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1478.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LB-LFDG\" using LaTeX format.",
|
|
"gt_answers": "\\angle B = \\angle F D C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1479.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 5x - 2 = 0\\)",
|
|
"gt_answers": "x _ { 1 } = \\frac { 3 + \\sqrt { 5 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1480.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"C(n, k) = n choose k.\"",
|
|
"gt_answers": "C \\equiv c - c - c - c \\equiv c\n",
|
|
"image_path": "./data/HME100K/test_images/test_1481.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 9\\)\n\nThis formula represents the relationship between the variables x and y, where x and y are both real numbers and x^2 represents the square of x, while y^2 represents the square of y. The result of the formula is that the sum of the squares of x and y is equal to 9.",
|
|
"gt_answers": ": \\frac { 9 } { 2 0 } \\times \\frac { 5 } { 4 } = \\frac { 9 } { 1 0 } ( k g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1482.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
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"gt_answers": "\\frac { \\sqrt { 2 } } { y } = \\frac { \\sqrt { x ^ { 2 } - 2 x + 2 } } { 3 - x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1483.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "= 2 \\sqrt { 2 } \\cdot \\sqrt { 1 + 2 b } = 2 \\sqrt { 3 } \\cdot \\sqrt { 1 + 2 b } = 4 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1484.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 4x + 8 = 0\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(x^2 + 4x + 8 = 0\\)",
|
|
"gt_answers": "x = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1485.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: Zn(OH)4 + H2SO4 = ZnSO4 + H2O + 2OH.",
|
|
"gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_1486.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LEBCo = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\angle E B C = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1487.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(13x^2 + 4x + 1 = 0\\)",
|
|
"gt_answers": "1 3 + x = \\frac { 1 } { 2 } ( 4 7 + x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1488.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"DEG(x) = 360\u00b0 - x\".",
|
|
"gt_answers": "\\therefore D E = x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1490.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) \\cdot \\cos(2\\theta) = 2\\pi r^2 \\cdot \\cos^2(2\\theta) = 2\\pi r^2 \\cdot \\cos^2(2\\theta) \\cdot \\cos(2\\theta) = 2\\pi r^2 \\cdot \\cos^3(2\\theta) = 2\\pi r^2 \\cdot \\cos^3(2\\theta) \\cdot \\cos(2\\theta) = 2\\pi r^2 \\cdot \\cos^4(2\\theta) = 2\\pi r^2 \\cdot \\cos^4(2\\theta) \\cdot \\cos(2\\theta) = 2\\pi r^2 \\cdot \\cos^5(2\\theta) = 2\\pi r^2 \\cdot \\cos^5(2\\theta) \\cdot \\cos(2\\theta) = 2\\pi r^2 \\cdot \\cos^6(2\\theta) = 2\\pi r^2 \\cdot \\cos^6(2\\theta) \\cdot \\cos(2\\theta) = 2\\pi r^2 \\cdot \\cos^7(2\\theta) = 2\\pi r^2 \\cdot \\cos^7(2\\theta) \\cdot \\cos(2\\theta) = 2\\pi r^2 \\cdot \\cos^8(2\\theta) = 2\\pi r^2 \\cdot \\cos^8(2\\theta) \\cdot \\cos(2\\theta) = 2\\pi r^2 \\cdot \\cos^9(2\\theta) = 2\\pi r^2 \\cdot \\cos^9(2\\theta) \\cdot \\cos(2\\theta) = 2\\pi r^2 \\cdot \\cos^{10}(2\\theta) = 2\\pi r^2 \\cdot \\cos^{10}(2\\theta) \\cdot \\cos(2\\theta) = 2\\pi r^2 \\cdot \\cos^{11}(2\\theta) = 2\\pi r^2 \\cdot \\",
|
|
"gt_answers": "\\tan \\angle ( A + B ) = \\frac { 2 \\tan ( A + B ) ^ { 3 } } { 1 - \\tan ^ { 2 } ( A + B ) } = - \\frac { 7 } { 2 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1491.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LADC = 2 * BDC + 1750\".",
|
|
"gt_answers": "\\angle A D C = \\frac { 1 } { 2 } \\angle B D C = \\frac { 1 } { 2 } \\times 7 5 ^ { \\circ } = ( \\frac { 7 5 } { 2 } ) ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1492.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2aart - this.\"",
|
|
"gt_answers": "2 ( a _ { 0 } + a _ { 2 } + \\cdots + a _ { 1 0 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1493.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{13 - 3}{4 - 3} = \\frac{13 - 3}{4 - 3}\n\\end{aligned}\n\\end{equation}\n\nThis is a simple algebraic expression that involves subtracting 3 from 13 and then dividing the result by the difference between 4 and 3.",
|
|
"gt_answers": "\\frac { 1 3 } { 3 } + \\frac { 1 } { 3 } = \\frac { 1 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1494.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = \\frac{1}{2}mv^2\\)\n\nThis formula represents the energy of an object in motion, where E is the energy, m is the mass of the object, and v is its velocity.",
|
|
"gt_answers": "y = \\frac { W } { Q }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1495.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "m ^ { 2 } - ( 2 \\cos \\alpha + 6 3 i n \\alpha ) m + 6 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1496.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^3 + 3x^2 - 2x - 1 = 0.\"",
|
|
"gt_answers": "x ^ { 2 } + 2 x = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1497.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "- 6 0 x ^ { 3 + m } y ^ { 7 + n } = - 6 0 x ^ { 5 } y ^ { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1498.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"5 + 5 = 10\" using the LaTeX formula notation.",
|
|
"gt_answers": "\\frac { 5 } { 6 } < \\frac { 5 } { 7 } < \\frac { 5 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1499.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 1 } { a _ { 1 } - 1 } = 1 ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_1500.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(x - 4) = 0.",
|
|
"gt_answers": "m = - \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1502.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A + B = C,\" where A, B, and C are variables.",
|
|
"gt_answers": "\\frac { A D } { B D } = \\frac { B D } { D C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1503.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645664566456645",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1505.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "2 - \\sqrt { 3 } - ( \\sqrt { 5 } - \\sqrt { 3 } + 1 3 - \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1506.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2x^2 + 3x + 4 = 180.",
|
|
"gt_answers": "( 1 8 0 - x ) \\div 2 = 1 8 0 - 8 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1507.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "x = 1 . 3 5 \\times \\frac { 1 0 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1508.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4) + (4x4)",
|
|
"gt_answers": "( 4 + 2 ) \\times ( 4 - 1 ) \\neq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1509.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the half of the half of a whole, which is equal to one fourth.",
|
|
"gt_answers": "4 ( 2 ) . A H = P H\n",
|
|
"image_path": "./data/HME100K/test_images/test_1510.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 8/37 + 7/37 = 1.",
|
|
"gt_answers": "\\frac { 8 } { 1 3 } > \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1511.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(28 \\times 18 + 16 \\times 12 + 10 \\times 8 + 6 \\times 4 + 2 \\times 1 = 196 + 192 + 160 + 80 + 40 + 2 = 668\\)",
|
|
"gt_answers": "\\frac { 1 } { 1 8 } - \\frac { 7 } { 1 8 0 } = \\frac { 3 } { 1 8 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1512.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 2 } { 5 } x = \\frac { 1 } { 2 } \\times \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1514.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nF + 6H + 3Cl + 3OH = 3H2O",
|
|
"gt_answers": "F e _ { 2 } O _ { 3 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1515.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(n \\cdot (n-1) \\cdot (n-2) \\cdot (n-3) \\cdot (n-4) \\cdot (n-5) \\cdot (n-6) \\cdot (n-7) \\cdot (n-8) \\cdot (n-9) \\cdot (n-10) \\cdot (n-11) \\cdot (n-12) \\cdot (n-13) \\cdot (n-14) \\cdot (n-15) \\cdot (n-16) \\cdot (n-17) \\cdot (n-18) \\cdot (n-19) \\cdot (n-20) \\cdot (n-21) \\cdot (n-22) \\cdot (n-23) \\cdot (n-24) \\cdot (n-25) \\cdot (n-26) \\cdot (n-27) \\cdot (n-28) \\cdot (n-29) \\cdot (n-30) \\cdot (n-31) \\cdot (n-32) \\cdot (n-33) \\cdot (n-34) \\cdot (n-35) \\cdot (n-36) \\cdot (n-37) \\cdot (n-38) \\cdot (n-39) \\cdot (n-40) \\cdot (n-41) \\cdot (n-42) \\cdot (n-43) \\cdot (n-44) \\cdot (n-45) \\cdot (n-46) \\cdot (n-47) \\cdot (n-48) \\cdot (n-49) \\cdot (n-50) \\cdot (n-51) \\cdot (n-52) \\cdot (n-53) \\cdot (n-54) \\cdot (n-55) \\cdot (n-56) \\cdot (n-57) \\cdot (n-58) \\cdot (n-59) \\cdot (n-60) \\cdot (n-61) \\cdot (n-62) \\cdot (n-63",
|
|
"gt_answers": "a _ { n } = \\frac { n + 1 } { n }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1516.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 15/27.",
|
|
"gt_answers": "\\frac { 1 5 } { 7 } = 2 \\frac { 1 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1517.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a formula using LaTeX format. The formula is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.",
|
|
"gt_answers": "a = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1518.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(W = 2 \\cdot 3 \\cdot 4 \\cdot 5 \\cdot 6 \\cdot 7 \\cdot 8 \\cdot 9 \\cdot 10 \\cdot 11 \\cdot 12 \\cdot 13 \\cdot 14 \\cdot 15 \\cdot 16 \\cdot 17 \\cdot 18 \\cdot 19 \\cdot 20 \\cdot 21 \\cdot 22 \\cdot 23 \\cdot 24 \\cdot 25 \\cdot 26 \\cdot 27 \\cdot 28 \\cdot 29 \\cdot 30 \\cdot 31 \\cdot 32 \\cdot 33 \\cdot 34 \\cdot 35 \\cdot 36 \\cdot 37 \\cdot 38 \\cdot 39 \\cdot 40 \\cdot 41 \\cdot 42 \\cdot 43 \\cdot 44 \\cdot 45 \\cdot 46 \\cdot 47 \\cdot 48 \\cdot 49 \\cdot 50 \\cdot 51 \\cdot 52 \\cdot 53 \\cdot 54 \\cdot 55 \\cdot 56 \\cdot 57 \\cdot 58 \\cdot 59 \\cdot 60 \\cdot 61 \\cdot 62 \\cdot 63 \\cdot 64 \\cdot 65 \\cdot 66 \\cdot 67 \\cdot 68 \\cdot 69 \\cdot 70 \\cdot 71 \\cdot 72 \\cdot 73 \\cdot 74 \\cdot 75 \\cdot 76 \\cdot 77 \\cdot 78 \\cdot 79 \\cdot 80 \\cdot 81 \\cdot 82 \\cdot 83 \\cdot 84 \\cdot 85 \\cdot 86 \\cdot 87 \\cdot 88 \\cdot 89 \\cdot 90 \\cdot 91 \\cdot 92 \\cdot 93 \\cdot 94 \\cdot 95 \\cdot 96 \\cdot 97 \\cdot 98 \\cdot 99 \\cdot 100 \\cdot 101 \\cdot ",
|
|
"gt_answers": "l y _ { 2 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1519.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as BF = 1234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234567891234",
|
|
"gt_answers": "B F = y . = 1 2 \\sqrt { 2 } = E F\n",
|
|
"image_path": "./data/HME100K/test_images/test_1520.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 9000\\)",
|
|
"gt_answers": "5 9 0 0 c m ^ { 2 } = 5 9 0 0 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1523.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 546789 x 687654 x 456789 x 3456789 x 23456789 x 123456789.",
|
|
"gt_answers": "\\frac { 1 } { 5 \\times 6 \\times 7 } - \\frac { 1 } { 6 \\times 7 \\times 8 } = \\frac { 1 } { 6 \\times 7 \\times 8 } \\times A\n",
|
|
"image_path": "./data/HME100K/test_images/test_1524.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(200 \\times 4 + 100 \\times 100 + 1800 \\times 800 = 1680000\\)",
|
|
"gt_answers": "2 0 0 a + 1 8 0 ( 1 0 0 - a ) < 1 8 0 8 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1525.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Bb6\" using the LaTeX format.",
|
|
"gt_answers": "A B = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1526.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "2 x = \\frac { 1 } { 2 0 } \\times 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_1527.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{400} \\cdot \\frac{1}{4",
|
|
"gt_answers": "S _ { n + 1 } - S _ { n } = 4 a _ { n } - 4 a _ { n } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1528.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 5\\)",
|
|
"gt_answers": "\\frac { 2 } { 5 } x = \\frac { 3 } { 4 } \\times \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1529.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. In this case, the variable is x, and the equation states that the square of x plus the square of y equals 1.",
|
|
"gt_answers": "x = \\frac { 1 3 } { 1 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1530.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(m = \\frac{3 \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3} \\times 10^{-3}",
|
|
"gt_answers": "y = m - \\frac { m + 1 } { 3 } = \\frac { 2 m - 1 } { 3 } ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_1531.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1x25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 \\times 2 5 0 0 0 = 5 0 0 0 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_1533.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with the letters \"x\" and \"5\" in it, which could be a representation of a mathematical expression in Chinese.",
|
|
"gt_answers": "\\frac { 2 } { 5 } x = \\frac { 3 } { 4 } \\times \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1534.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(1000 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 500 \\times 5",
|
|
"gt_answers": "1 0 0 \\times 4 5 \\times 4 . 5 = 2 0 2 5 0 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1535.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} \\right) = \\frac{1}{2} \\left",
|
|
"gt_answers": "f ^ { \\prime } ( x ) = \\frac { 2 a x ^ { 2 } - 1 } { x } ( x > 0 ) .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1537.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{3}x^3 + \\frac{1}{4}x^4 + \\frac{1}{5}x^5 + \\frac{1}{6}x^6 + \\frac{1}{7}x^7 + \\frac{1}{8}x^8 + \\frac{1}{9}x^9 + \\frac{1}{10}x^{10} + \\frac{1}{11}x^{11} + \\frac{1}{12}x^{12} + \\frac{1}{13}x^{13} + \\frac{1}{14}x^{14} + \\frac{1}{15}x^{15} + \\frac{1}{16}x^{16} + \\frac{1}{17}x^{17} + \\frac{1}{18}x^{18} + \\frac{1}{19}x^{19} + \\frac{1}{20}x^{20} + \\frac{1}{21}x^{21} + \\frac{1}{22}x^{22} + \\frac{1}{23}x^{23} + \\frac{1}{24}x^{24} + \\frac{1}{25}x^{25} + \\frac{1}{26}x^{26} + \\frac{1}{27}x^{27} + \\frac{1}{28}x^{28} + \\frac{1}{29}x^{29} + \\frac{1}{30}x^{30} + \\frac{1}{31}x^{31} + \\frac{1}{32}x^{32} + \\frac{1}{33}x^{33} + \\frac{1}{34}x^{34} + \\frac{1}{35}x^{35} + \\frac{1}{36}x^{36} + \\frac{1}{37}x^{37} + \\frac{1}{38}x",
|
|
"gt_answers": "a _ { n + 1 } = t ( a _ { n } ) = \\frac { 3 a _ { n } ^ { 1 } } { 2 a _ { n } + 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1538.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Li = 0.09 mL/m^2 * 0.001 m^3/m^2 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^3 * 0.001 m^3/m^",
|
|
"gt_answers": "l _ { 1 } = 0 . 9 m + 0 . 6 m = 1 . 5 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_1539.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{256}{256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 256 + 25",
|
|
"gt_answers": "2 5 8 < 2 8 5 < 5 2 8 < 5 8 2 < 8 2 5 < 8 5 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1540.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: NaCl + H2O = NaOH + Cl2.",
|
|
"gt_answers": "C H _ { 3 } C O O H + N a O H = C H _ { 3 } C O O N a + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1542.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(m = \\frac{3x^2 + 3y^2 - 2xy}{2(x^2 + y^2)}\\)\n\nThe formula is written in LaTeX format, which is a standard mathematical notation used for writing mathematical expressions. The equation is written in the form of an equation with the variables x and y on the left side, and the constant m on the right side. The equation is also written in the form of a fraction, with the numerator containing the terms x^2 and y^2, and the denominator containing the terms x^2 + y^2.",
|
|
"gt_answers": "\\Rightarrow y = \\frac { m } { m ^ { 2 } - 1 } ( \\frac { 3 } { 2 } x - 1 ) .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1543.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AOB = CootR\".",
|
|
"gt_answers": "A O B C = ( A O + B\n",
|
|
"image_path": "./data/HME100K/test_images/test_1544.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(W = 3 \\times 10^5 \\times 10^2 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0 \\times 10^0",
|
|
"gt_answers": "( 1 ) W _ { 2 } = J / s \\times 3 0 0 0 S = 7 2 0 0 J\n",
|
|
"image_path": "./data/HME100K/test_images/test_1545.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 50x + 30 = 100x + 30\\)\n\nThis formula can be rearranged to solve for x:\n\n\\(x^2 + 50x + 30 = 100x + 30\\)\n\n\\(x^2 + 50x = 70\\)\n\n\\(x^2 + 50x - 70 = 0\\)\n\n\\(x = \\frac{-70 \\pm \\sqrt{70^2 - 400}}{2} = \\frac{-70 \\pm \\sqrt{490}}{2} = \\frac{-70 \\pm 24.5}{2} = \\frac{-70 \\pm 12.25}{2} = \\frac{-70 \\pm 6.125}{2} = \\frac{-70 \\pm 3.0625}{2} = \\frac{-70 \\pm 1.53125}{2} = \\frac{-70 \\pm 0.765625}{2} = \\frac{-70 \\pm 0.3828125}{2} = \\frac{-70 \\pm 0.19140625}{2} = \\frac{-70 \\pm 0.09565625}{2} = \\frac{-70 \\pm 0.0478125}{2} = \\frac{-70 \\pm 0.02390625}{2} = \\frac{-70 \\pm 0.011953125}{2} = \\frac{-70 \\pm 0.0059765625}{2} = \\frac{-70 \\pm 0.00298875}{2} = \\frac{-70 \\pm 0.00149375}{2} = \\frac{-70 \\pm 0.00074375}{2} = \\frac{-70 \\pm 0.000371875",
|
|
"gt_answers": "\\frac { 4 } { 5 } x + 1 5 0 = 3 0 + \\frac { 3 } { 1 0 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1546.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"OBIDC2OC\" using LaTeX format.",
|
|
"gt_answers": "O B = B D = C D = O C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1547.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(y = \\frac{3y^2 + 4b - b^2}{2b}\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(y = \\frac{3y^2 + 4b - b^2}{2b}\\)",
|
|
"gt_answers": "\\frac { 1 } { 3 y + 4 } = b\n",
|
|
"image_path": "./data/HME100K/test_images/test_1549.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LHLC-90%.\"",
|
|
"gt_answers": "\\angle H \\angle C = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1550.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "\\frac { x ^ { 2 } - 2 } { x + 3 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1551.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LCD = 66.8 BP + 30.0 BP.\"",
|
|
"gt_answers": "\\angle C B D = 6 0 ^ { \\circ } , \\angle B C D = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1552.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "( y - 1 ) ^ { 2 } + 2 y ^ { 2 } - 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1553.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(W - 16) + 16 = 2W.",
|
|
"gt_answers": "W = \\frac { 2 \\pi } { 1 6 } = \\frac { \\pi } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1554.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x",
|
|
"gt_answers": ": \\frac { ( 5 - \\sqrt { 2 } ) \\sin \\theta } { \\cos \\theta ^ { 2 } } + \\frac { ( \\sqrt { 2 } - 5 ) \\cos \\theta } { \\sin ^ { 2 } \\theta }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1555.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"3x + 2y = 10.\"",
|
|
"gt_answers": "a _ { n + 1 } = \\frac { 3 } { 2 } a w ( n \\in N ^ { \\ast } ) a _ { 1 } = 1 \\neq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1556.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\nE = 1/2mv^2\n\nwhere E is the energy, m is the mass, and v is the velocity.",
|
|
"gt_answers": "F _ { f } = \\frac { p } { V } = \\frac { 1 . 2 \\times 1 0 ^ { 3 } W } { 6 } = 2 0 0 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_1557.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 13x + 32 = 0\\)\n\nThis formula can be solved using the quadratic formula:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\)\n\nIn this case, the quadratic formula simplifies to:\n\n\\(x = \\frac{-13 \\pm \\sqrt{13^2 - 4(13)(32)}}{2(13)} = \\frac{-13 \\pm \\sqrt{449}}{2(13)} = \\frac{-13 \\pm 22}{2(13)} = \\frac{-13 \\pm 11}{2(13)} = \\frac{-13 \\pm 5}{2(13)} = \\frac{-13 \\pm 2}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} = \\frac{-13 \\pm 1}{2(13)} =",
|
|
"gt_answers": "\\frac { 9 0 } { x } = \\frac { 1 3 5 } { x + 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1558.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: `x^2 + y^2 = 400`.",
|
|
"gt_answers": "A O = 5 x . = 5 \\times 1 0 0 = 5 0 0 m ^ { A }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1559.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 1 } { 2 } A _ { n } = \\frac { 1 } { 2 } + \\frac { 1 } { 2 ^ { 2 } } + \\cdots + \\frac { 1 } { 2 ^ { n } } - \\frac { n } { 2 ^ { n + 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1560.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(AB + BC = AC + BC\\)\n\nThis formula represents the associative property of addition, which states that the order of the terms in a sum does not affect the result. In this case, the sum of the terms AB, BC, AC, and BC is equal to the sum of the terms AC and BC.",
|
|
"gt_answers": "A B ^ { 2 } + A C ^ { 2 } = B C ^ { 2 } \\cdot \\therefore \\angle A = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1561.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to write it out using LaTeX format. However, the image shows a mathematical formula with a number and a symbol, which can be represented in LaTeX as follows:\n\n\\begin{equation}\n\\text{Number} + \\text{Symbol}\n\\end{equation}\n\nThis equation can be used to represent any mathematical expression that combines a number and a symbol.",
|
|
"gt_answers": "x \\geq \\frac { 5 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1563.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{1}{1",
|
|
"gt_answers": "C u O + H _ { 2 } S O _ { 4 } = C u S O _ { 4 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1564.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 2y^2 - 3xy + 2y - 1 = 0\\)",
|
|
"gt_answers": "( a - 1 ) x \\vert a \\vert + 1 - 3 x + 2 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1565.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(x^2 + 2x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 2 } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1568.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
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"gt_answers": "y _ { 3 } = \\frac { 2 } { 3 }\n",
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"image_path": "./data/HME100K/test_images/test_1569.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 4x - 4 = 0\\)\n\nThis is a quadratic equation in the variable x.",
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"gt_answers": "x _ { 1 } = \\frac { - 2 + \\sqrt { 4 - 4 a } } { 2 }\n",
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"image_path": "./data/HME100K/test_images/test_1571.jpg",
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"model_name": "mPLUG"
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|
},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
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"gt_answers": "1 + 2 n - 3 = a n \\Rightarrow a n = 2 n - 2\n",
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"image_path": "./data/HME100K/test_images/test_1572.jpg",
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"model_name": "mPLUG"
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|
},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a + b = c\\)\n\nThis is a basic algebraic equation that represents the addition of two numbers, a and b, to equal a third number, c.",
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"gt_answers": "a = \\frac { L } { I } = \\frac { 2 } { 1 } = 2\n",
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"image_path": "./data/HME100K/test_images/test_1573.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression of the formula in the image is:\n\n\\(AP = \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} = \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} \\cdot \\frac{sin(30\\pi/3)}{sin(20\\pi/3)} = \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} \\cdot \\frac{sin(30\\pi/3)}{sin(20\\pi/3)} \\cdot \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} = \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} \\cdot \\frac{sin(30\\pi/3)}{sin(20\\pi/3)} \\cdot \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} = \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} \\cdot \\frac{sin(30\\pi/3)}{sin(20\\pi/3)} \\cdot \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} = \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} \\cdot \\frac{sin(30\\pi/3)}{sin(20\\pi/3)} \\cdot \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} = \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} \\cdot \\frac{sin(30\\pi/3)}{sin(20\\pi/3)} \\cdot \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} = \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} \\cdot \\frac{sin(30\\pi/3)}{sin(20\\pi/3)} \\cdot \\frac{sin(20\\pi/3)}{sin(30\\pi/3)} = \\frac{sin(20\\pi/3)}{sin(30\\pi/3",
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"gt_answers": "A P ^ { 2 } = \\frac { 2 0 } { 3 } - \\frac { 1 6 } { 3 } \\cdot \\sin ( 2 \\theta + \\frac { 5 } { 6 } \\pi )\n",
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"image_path": "./data/HME100K/test_images/test_1574.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4}\n\\end{equation}\n\nThis equation represents the sum of two halves, which is equal to one half.",
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"gt_answers": "x _ { 1 } = \\frac { 7 } { 2 } , x _ { 2 } = - 1\n",
|
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"image_path": "./data/HME100K/test_images/test_1575.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "\\log _ { x } ^ { y } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1577.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nx^2 + 4x + 3 = 0\n\nThis is a quadratic equation in the variable x.",
|
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"gt_answers": "- x = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1578.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"A + B = C.\"",
|
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"gt_answers": "\\alpha - \\pi = \u3002 \\alpha - \\pi = a v c \\sin \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1579.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(K_{c} = \\frac{1}{2} \\left( \\frac{1}{R_{1}} + \\frac{1}{R_{2}} \\right) \\left( \\frac{1}{R_{3}} + \\frac{1}{R_{4}} \\right) \\left( \\frac{1}{R_{5}} + \\frac{1}{R_{6}} \\right) \\left( \\frac{1}{R_{7}} + \\frac{1}{R_{8}} \\right) \\left( \\frac{1}{R_{9}} + \\frac{1}{R_{10}} \\right) \\left( \\frac{1}{R_{11}} + \\frac{1}{R_{12}} \\right) \\left( \\frac{1}{R_{13}} + \\frac{1}{R_{14}} \\right) \\left( \\frac{1}{R_{15}} + \\frac{1}{R_{16}} \\right) \\left( \\frac{1}{R_{17}} + \\frac{1}{R_{18}} \\right) \\left( \\frac{1}{R_{19}} + \\frac{1}{R_{20}} \\right) \\left( \\frac{1}{R_{21}} + \\frac{1}{R_{22}} \\right) \\left( \\frac{1}{R_{23}} + \\frac{1}{R_{24}} \\right) \\left( \\frac{1}{R_{25}} + \\frac{1}{R_{26}} \\right) \\left( \\frac{1}{R_{27}} + \\frac{1}{R_{28}} \\right) \\left( \\frac{1}{R_{29}} + \\frac{1}{R_{30}} \\right) \\left( \\frac{1}{R_{31}} + \\frac{1}{R_{32}} \\right) \\left( \\frac{1}{R_{33}} + \\frac{1}{R_{34}} \\right) \\left( \\frac{1}{R_{35}} + \\frac{1}{R_{36}} \\right) \\left( \\frac",
|
|
"gt_answers": "k = - \\frac { 1 } { 4 } \\cdot \\frac { 3 2 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1580.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `4x(n^2) + 2n`.",
|
|
"gt_answers": "( 2 x + n ) ^ { 2 } = 4 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1581.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ale tau = 1/2 pi.\"",
|
|
"gt_answers": "A C = \\sqrt { A O ^ { 2 } + C D ^ { 2 } } = \\sqrt { 2 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1582.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CBA-456\" using the LaTeX format.",
|
|
"gt_answers": "\\because \\angle C B A = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1583.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 4x + 1 = 0.\"",
|
|
"gt_answers": "4 \\div \\frac { 2 } { 1 1 } = 4 \\times \\frac { 1 1 } { 2 } = \\frac { 2 4 \\times 1 1 } { 2 1 } = 2 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1584.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Wade's formula for the number of ways to arrange n distinct objects into k groups.\"",
|
|
"gt_answers": "_ { 1 } D E ^ { 2 } = D O \\cdot D B\n",
|
|
"image_path": "./data/HME100K/test_images/test_1585.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 19x5 + 4x4 = 100.",
|
|
"gt_answers": "1 4 \\times 1 4 = 1 9 6 ( c m ^ { 2 } ) 5 6 \\times 4 2 = 2 3 5 2 ( c m ^ { 2 } ) .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1586.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 10\\)",
|
|
"gt_answers": "3 . 1 4 \\times 5 ^ { 2 } = 7 8 . 5 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1587.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x = \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1589.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x + 2 = 5.",
|
|
"gt_answers": "\\frac { 3 + 2 } { 3 } = \\frac { 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1591.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 2 = 10\\)",
|
|
"gt_answers": "x ^ { 2 } - 3 x + ( \\frac { 3 } { 2 } ) ^ { 2 } = - 2 + ( \\frac { 3 } { 2 } ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1592.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 28x + 29 = 0\\)\n\nThis formula can be solved using the quadratic formula, which is:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\)\n\nSubstituting the values for a, b, and c from the original equation, we get:\n\n\\(x = \\frac{-28 \\pm \\sqrt{28^2 - 4(28)(29)}}{2(28)} = \\frac{-28 \\pm \\sqrt{744}}{2(28)} = \\frac{-28 \\pm 37}{2(28)} = \\frac{-28 \\pm 19}{2(28)} = \\frac{-28 \\pm 9}{2(28)} = \\frac{-28 \\pm 4}{2(28)} = \\frac{-28 \\pm 2}{2(28)} = \\frac{-28 \\pm 1}{2(28)} = \\frac{-28 \\pm 0.5}{2(28)} = \\frac{-28 \\pm 1}{2(28)} = \\frac{-28 \\pm 0.5}{2(28)} = \\frac{-28 \\pm 0.25}{2(28)} = \\frac{-28 \\pm 0.125}{2(28)} = \\frac{-28 \\pm 0.0625}{2(28)} = \\frac{-28 \\pm 0.03125}{2(28)} = \\frac{-28 \\pm 0.015625}{2(28)} = \\frac{-28 \\pm 0.0078125}{2(28)} = \\frac{-28 \\pm 0.00390625}{2(28)} = \\frac{-28 \\pm 0.001953125}{2(28)} = \\frac{-28 \\pm 0.0009765625}{2(28)} =",
|
|
"gt_answers": "x = \\frac { 2 1 } { 2 8 } - \\frac { 8 } { 2 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1593.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "= \\frac { C D } { C B } = 0 . 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1594.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "l \\cdot \\frac { 2 } { 5 } x = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1595.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 4}{x^2 - 2x +",
|
|
"gt_answers": "x = \\frac { 3 - 2 y } { 3 } = 1 - \\frac { 2 } { 3 } y\n",
|
|
"image_path": "./data/HME100K/test_images/test_1596.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 5x2 + 3x3 - 2x4 - 4x5 + 5x6 - 6x7 + 7x8 - 8x9 + 9x10 - 10x11 + 11x12 - 12x13 + 13x14 - 14x15 + 15x16 - 16x17 + 17x18 - 18x19 + 19x20 - 20x21 + 21x22 - 22x23 + 23x24 - 24x25 + 25x26 - 26x27 + 27x28 - 28x29 + 29x30 - 30x31 + 31x32 - 32x33 + 33x34 - 34x35 + 35x36 - 36x37 + 37x38 - 38x39 + 39x40 - 40x41 + 41x42 - 42x43 + 43x44 - 44x45 + 45x46 - 46x47 + 47x48 - 48x49 + 49x50 - 50x51 + 51x52 - 52x53 + 53x54 - 54x55 + 55x56 - 56x57 + 57x58 - 58x59 + 59x60 - 60x61 + 61x62 - 62x63 + 63x64 - 64x65 + 65x66 - 66x67 + 67x68 - 68x69 + 69x70 - 70x71 + 71x72 - 72x73 + 73x74 - 74x75 + ",
|
|
"gt_answers": "S _ { \\Delta A B C } = \\frac { 1 } { 2 } A B \\cdot C O = \\frac { 1 } { 2 } \\times 6 \\times 3 = 9 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1597.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(1 + 3x - 2x^2 + 5x^3 - 6x^4 + 7x^5 - 8x^6 + 9x^7 - 10x^8 + 11x^9 - 12x^{10} = 13x^{11} - 14x^{12} + 15x^{13} - 16x^{14} + 17x^{15} - 18x^{16} + 19x^{17} - 20x^{18} + 21x^{19} - 22x^{20} + 23x^{21} - 24x^{22} + 25x^{23} - 26x^{24} + 27x^{25} - 28x^{26} + 29x^{27} - 30x^{28} + 31x^{29} - 32x^{30} + 33x^{31} - 34x^{32} + 35x^{33} - 36x^{34} + 37x^{35} - 38x^{36} + 39x^{37} - 40x^{38} + 41x^{39} - 42x^{40} + 43x^{41} - 44x^{42} + 45x^{43} - 46x^{44} + 47x^{45} - 48x^{46} + 49x^{47} - 50x^{48} + 51x^{49} - 52x^{50} + 53x^{51} - 54x^{52} + 55x^{53} - 56x^{54} + 57x^{55} - 58x^{56} + 59x^{57} - 60x^{5",
|
|
"gt_answers": "\\frac { 1 } { 3 } x - \\frac { 1 } { 3 } - \\frac { 1 } { 5 } x = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1598.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LABD+LABL=LABL+LABL\\)",
|
|
"gt_answers": "\\angle A B D + \\angle A B C = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1599.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"15/10 = 1.5.\"",
|
|
"gt_answers": "\\frac { - 1 } { 1 6 } > \\frac { 1 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1600.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 - 13x + 18 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x > - \\frac { 7 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1601.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"42 - 22h - 12h^2 + 12h^3 - 12h^4 + 12h^5 - 12h^6 + 12h^7 - 12h^8 + 12h^9 - 12h^{10} + 12h^{11} - 12h^{12} + 12h^{13} - 12h^{14} + 12h^{15} - 12h^{16} + 12h^{17} - 12h^{18} + 12h^{19} - 12h^{20} + 12h^{21} - 12h^{22} + 12h^{23} - 12h^{24} + 12h^{25} - 12h^{26} + 12h^{27} - 12h^{28} + 12h^{29} - 12h^{30} + 12h^{31} - 12h^{32} + 12h^{33} - 12h^{34} + 12h^{35} - 12h^{36} + 12h^{37} - 12h^{38} + 12h^{39} - 12h^{40} + 12h^{41} - 12h^{42} + 12h^{43} - 12h^{44} + 12h^{45} - 12h^{46} + 12h^{47} - 12h^{48} + 12h^{49} - 12h^{50} + 12h^{51} - 12h^{52} + 12h^{53} - 12h^{54} + 12h^{55} - 12h^{56} + 12h^{57} - 12h^{5",
|
|
"gt_answers": "O _ { 2 } + 4 e ^ { - } + 2 H _ { 2 } O = 4 O H ^ { - }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1602.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle B O C = 9 0 - 2 0 = 7 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1603.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 5x3 + 3x5 = 15x6.",
|
|
"gt_answers": "\\frac { 5 } { 6 } = \\frac { 5 \\times 3 } { 6 \\times 3 } = \\frac { 1 5 } { 1 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1605.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "S 2 x ^ { 2 } - y ^ { 2 } - 7 = 0 \\textcircled { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1606.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula language. The formula is written in the form of a mathematical equation, with the letters \"A\" and \"B\" representing variables. The letter \"E\" represents the symbol for education, and the letter \"D\" represents the symbol for death. The formula is written in a way that the letters \"A\" and \"B\" are connected by a line, indicating that they are related to each other. The formula is written in a way that the letters \"E\" and \"D\" are connected by a line, indicating that they are related to each other.",
|
|
"gt_answers": "\\Delta B D E \\sim \\Delta E D O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1607.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(Cu^{2+}(OH)_{2} + H_{2}O \\rightarrow Cu(OH)_{2} + H_{2}O\\)\n\nThis formula represents the chemical reaction between copper(II) hydroxide and water, which results in the formation of copper(II) hydroxide and water.",
|
|
"gt_answers": "C u ( O H ) _ { 2 } + 2 H C l = C u C l _ { 2 } + 2 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1608.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1000x1000 + 100x100 + 10x10 + 1x1 = 1000000.",
|
|
"gt_answers": "\\frac { 1 0 0 x + 2 0 0 } { 2 5 } + \\frac { 1 0 x } { 5 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1610.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\therefore \\tan \\alpha = - \\frac { 2 \\sqrt { 2 } } { 1 } = - 2 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1612.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\pi r^2 + 2\\pi r^2 + 2\\pi r^2 + 2\\pi r^2 = 8\\pi r^2\\)",
|
|
"gt_answers": "2 \\angle 3 + 2 \\angle 4 = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1614.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A = 2x + 3.\"",
|
|
"gt_answers": "A E = \\sqrt { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1615.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 3x + 4\\)",
|
|
"gt_answers": "y + 3 \\cdot \\frac { 1 } { y } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1616.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "c = \\sqrt { 6 } + \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1617.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(p_1 + p_2 + p_3 + p_4 = 1\\)",
|
|
"gt_answers": "\\frac { \\sqrt { 2 } } { 2 } \\rho \\sin \\theta + \\frac { \\sqrt { 2 } } { 2 } \\rho \\cos \\theta = \\frac { \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1618.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2}",
|
|
"gt_answers": "C _ { n } ^ { 0 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1619.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "B r _ { 2 } > C N _ { 2 } > I _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1620.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: (4x^2 + 2x)(2x^2 + 4x + 2) = 4x^4 + 8x^3 + 12x^2 + 8x + 2.",
|
|
"gt_answers": "\\frac { 4 - a ^ { 2 } } { a ^ { 2 } - 2 a } = \\frac { ( 2 + a ) \\times ( 2 - a ) } { a ( a - 2 ) } = - \\frac { 2 + a } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1621.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "7 \u3001 5 7 0 0 \\times 2 4 0 = 1 3 6 8 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1625.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 13/100 = 0.13.",
|
|
"gt_answers": ": \\frac { 1 2 } { 6 0 } = 2 0 9 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1626.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Pet O2 = Cut TSqp\".",
|
|
"gt_answers": "F e + C u S O _ { 4 } = C u + F e S O _ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1627.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 100\\)\n\nThis formula represents the relationship between the variables x and y, where x and y are real numbers and the result is an integer. The expression is written in the form of an equation, where the left side represents the x-coordinate and the right side represents the y-coordinate. The equal sign indicates that the two sides are equal to each other. The result of the equation is 100, which is an integer.",
|
|
"gt_answers": "\\dot { 1 } - \\frac { \\dot { 7 } } { 1 5 } - \\frac { 1 } { 5 } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1629.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 10 - 40 = 30.",
|
|
"gt_answers": "\\frac { 7 } { 1 0 } = \\frac { 2 8 } { 4 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1630.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 9\\)",
|
|
"gt_answers": "7 \u3001 \\sqrt { \\frac { 4 } { 9 } } = \\pm \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1631.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2}{2} + \\frac{y^2}{2} = 1\n\\end{equation}\n\nThis is a quadratic equation in two variables, where x and y represent the two variables. The equation states that the sum of the squares of the two variables is equal to 1.",
|
|
"gt_answers": "x = \\frac { 1 } { a - 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1632.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 0 0 0 \\times \\frac { 1 } { 5 0 0 0 } = 2 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1634.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A^2 + B^2 = C^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "O B = \\frac { 1 } { 2 } A C = A O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1635.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 0 0 0 \\times ( 3 \\times 4 . 2 5 ^ { \\circ } A )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1637.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible for me to accurately transcribe it using LaTeX. However, I can provide a rough translation of the formula:\n\n\"The sum of the squares of the first n natural numbers is equal to the sum of the squares of the first n odd numbers.\"",
|
|
"gt_answers": "x _ { 4 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1638.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 8x11=96cm.",
|
|
"gt_answers": "8 \\times 1 2 = 9 6 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1639.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(y = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "8 2 0 < 8 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1640.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LDA-LBLC-LPCACA\".",
|
|
"gt_answers": "\\angle D C A = \\angle 3 + \\angle 4 + \\angle P C A\n",
|
|
"image_path": "./data/HME100K/test_images/test_1641.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "x _ { 1 } + x _ { 2 } = - \\frac { 8 k ^ { 2 } } { 3 + 4 k ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1644.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x3-3dcm\".",
|
|
"gt_answers": "4 \\times 3 \\times 3 = 3 6 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1645.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a Chinese character in the middle, which could be a symbol or a character used in mathematics.",
|
|
"gt_answers": "y = - \\frac { \\sqrt { 1 0 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1646.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(x^2 + 2x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 2 5 } { 9 } x ^ { 2 } = 1 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1648.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 3x^2 + 5x + 1\\)",
|
|
"gt_answers": "y _ { 3 } = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1650.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "+ y ^ { 2 } + y ^ { 2 } - 6 y + 1 0 = 1 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1651.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Sodium + Sulfur + Oxygen = SO2 + H2O.\"",
|
|
"gt_answers": "S _ { \\Delta A O B } = \\vert S _ { \\Delta O A D } - S _ { \\Delta O B D } \\vert\n",
|
|
"image_path": "./data/HME100K/test_images/test_1653.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nS = (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2) * (d/2)",
|
|
"gt_answers": "S = 1 0 c m \\times 1 0 c m = 1 0 0 c m ^ { 2 } = 0 . 0 1 m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1654.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\because x ^ { 2 } - x + 2 = x ^ { 2 } - x + \\frac { 1 } { 4 } + \\frac { 7 } { 4 } = ( x - \\frac { 1 } { 2 } ) ^ { 2 } + \\frac { 7 } { 4 } > 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1655.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2}",
|
|
"gt_answers": "1 - x + \\vert 1 2 x + m \\vert \\leq 3 - 2 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1656.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the formula is likely a mathematical equation or a chemical formula.",
|
|
"gt_answers": "( 6 k \\pi - \\frac { 3 \\pi } { 4 } , 6 k \\pi + \\frac { 3 \\pi } { 4 } ) ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_1657.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(0.05\\times 10^{-1} + 0.01\\times 10^{-2} = 0.0005 + 0.00001 = 0.00051\\)",
|
|
"gt_answers": "0 . 5 < 0 . 5 0 1 < 0 . 5 1 < 0 . 5 1 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1658.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 - 8x + 8 = 0.\"",
|
|
"gt_answers": "x > \\frac { 1 } { 8 \\sqrt { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1659.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2^{2n+1} - 2^{2n-1} = 2^{2n+1} - 2^{2n-2} + 2^{2n-1} - 2^{2n-2} = 2^{2n+1} - 2^{2n-1} - 2^{2n-2} + 2^{2n-2} = 0\\)",
|
|
"gt_answers": "\\frac { 2 + 1 3 } { 2 } + 2 - m = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1660.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula is known as the Pythagorean Theorem and is used to find the square of the hypotenuse of a right triangle.",
|
|
"gt_answers": "\\frac { a } { \\sin A } = \\frac { b } { \\sin B } = \\frac { c } { S _ { i n C } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1661.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3xy + 4y^2 = 100\\)",
|
|
"gt_answers": "( x + 3 x ) - 2 0 + 3 x - x - 1 0 0 + 5 5 = 2 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1662.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\nBd = Oe - Ac\n\nwhere Bd is the bond dissociation energy, Oe is the oxygen ionization energy, and Ac is the acetylation energy.",
|
|
"gt_answers": "\\frac { B D } { B A } = \\frac { O E } { A C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1664.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the multiplication of two fractions, each with a denominator of 2. The result is a fraction with a denominator of 4.",
|
|
"gt_answers": "x _ { 2 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1665.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the chemical formula notation, which is a standard way to represent chemical compounds. The formula is written as Zn(OH)2(NO3)2.",
|
|
"gt_answers": "Z n ( N O _ { 3 } ) _ { 2 } + C u = C u ( N O _ { 3 } ) _ { 2 } + Z n\n",
|
|
"image_path": "./data/HME100K/test_images/test_1666.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"P(A or B) = P(A) + P(B) - P(A and B).\"",
|
|
"gt_answers": "P ( 2 ) = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1667.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\right) = \\frac{1}{4} \\).",
|
|
"gt_answers": "\\frac { 1 } { a _ { n } } = \\frac { 1 } { a _ { 1 } q ^ { n - 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1668.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(ED = AB + 2(EX - 5) + 3(AB - EX) + 4(EX - 5) + 5(AB - EX)\\)",
|
|
"gt_answers": "E D = \\frac { 1 } { 2 } A B = \\frac { 1 } { 2 } \\times 1 0 = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1669.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nR = 1/2(V^2/R + I^2/R) + I/R",
|
|
"gt_answers": "R = \\frac { u } { I } = \\frac { 6 V } { 0 . 2 A } = 3 0 \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_1670.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x = \\frac { 5 \\sqrt { b a ^ { 4 } } } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1673.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{b}{x} + \\frac{b}{x^2} + \\frac{b}{x^3} + \\frac{b}{x^4} + \\frac{b}{x^5} + \\frac{b}{x^6} + \\frac{b}{x^7} + \\frac{b}{x^8} + \\frac{b}{x^9} + \\frac{b}{x^{10}} + \\frac{b}{x^{11}} + \\frac{b}{x^{12}} + \\frac{b}{x^{13}} + \\frac{b}{x^{14}} + \\frac{b}{x^{15}} + \\frac{b}{x^{16}} + \\frac{b}{x^{17}} + \\frac{b}{x^{18}} + \\frac{b}{x^{19}} + \\frac{b}{x^{20}} + \\frac{b}{x^{21}} + \\frac{b}{x^{22}} + \\frac{b}{x^{23}} + \\frac{b}{x^{24}} + \\frac{b}{x^{25}} + \\frac{b}{x^{26}} + \\frac{b}{x^{27}} + \\frac{b}{x^{28}} + \\frac{b}{x^{29}} + \\frac{b}{x^{30}} + \\frac{b}{x^{31}} + \\frac{b}{x^{32}} + \\frac{b}{x^{33}} + \\frac{b}{x^{34}} + \\frac{b}{x^{35}} + \\frac{b}{x^{36}} + \\frac{b}{x^{37}} + \\frac{b}{x^{38}} + \\frac{b}{x^{39}} + \\frac{b}{x^{40}} + \\frac{b}{x^{41}} + \\frac{b}{x^{42}} + \\frac{b}{x^{43}} + \\frac{b}{x^{44}} + \\frac{b}{x^{45}} + \\frac{b}{x^{4",
|
|
"gt_answers": "\\frac { 1 } { x - y } = b\n",
|
|
"image_path": "./data/HME100K/test_images/test_1675.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x^2 + 4x + 5 = 0.",
|
|
"gt_answers": ". ( 1 - k ^ { 2 } ) x ^ { 2 } - 4 k x - 1 0 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1677.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 4.5654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565456545654565",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1678.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\therefore \\Delta = ( - 1 ) ^ { 2 } - 4 ( a - 1 ) \\leq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1679.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(C_6H_{12}O_{6} + 6H_{2}O \\rightarrow 6CO_{2} + 6H_{2}O + 6H_{2}CO_{3}\\)",
|
|
"gt_answers": "c = - 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1681.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "a + b = 1 5 \\times 2 = 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1682.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\n\\(2\\pi r^2 = 4\\pi r^2 - 4\\pi r^2\\cos(2\\theta)\\)\n\nThe formula is written in LaTeX format, with the variables r and \u03b8 representing the radius and angle of a circle, respectively.",
|
|
"gt_answers": "\\angle 2 = 4 2 ^ { \\circ } ( p i v e n )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1684.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC + AC = AC +",
|
|
"gt_answers": "A C = A E + C E = 5 + 5 = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1685.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(G_s = \\frac{1}{2} \\left( \\frac{1}{cos(2\\pi f_s t)} + \\frac{1}{cos(4\\pi f_s t)} \\right)\\)\n\nThe formula represents the group delay of a sinusoidal signal with a frequency of f_s and a period of T. The group delay is defined as the time difference between the peak of the signal and its first zero crossing.",
|
|
"gt_answers": "C O _ { 3 } C = 1 \\cos C = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1686.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4} \\left( 1 + 1 \\right) = \\frac{1}{4} \\cdot 2 = \\frac{1}{2} \\cdot 2 = \\frac{1}{4} \\cdot 1 = \\frac{1}{8} = \\frac{1}{4} \\cdot \\frac{1}{2} = \\frac{1}{8} \\cdot 1 = \\frac{1}{16} = \\frac{1}{4} \\cdot \\frac{1}{4} = \\frac{1}{16} \\cdot 1 = \\frac{1}{32} = \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} = \\frac{1}{32} \\cdot 1 = \\frac{1}{64} = \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} = \\frac{1}{64} \\cdot 1 = \\frac{1}{128} = \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} = \\frac{1}{128} \\cdot 1 = \\frac{1}{256} = \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} = \\frac{1}{256} \\cdot 1 = \\frac{1}{512} = \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} \\cdot \\frac{1}{4} = \\frac{1}{512} \\cdot ",
|
|
"gt_answers": "O E \\bot D C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1688.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LEBF = 90%.\"",
|
|
"gt_answers": "\\angle E B F = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1690.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CacO+H2O = CaCO3 + H2O\".",
|
|
"gt_answers": "C a ( O H ) _ { 2 } + H _ { 2 } S O _ { 4 } = C a S O _ { 4 } + 2 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1691.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(100 \\times 100 \\times 100 = 10,000\\)",
|
|
"gt_answers": "\\frac { 1 5 } { 1 0 0 } x - \\frac { 9 } { 1 0 0 } = \\frac { 7 } { 1 0 0 } x + \\frac { 3 1 } { 1 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1692.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "5 0 \\times 2 0 0 m L = 1 0 0 0 0 m L\n",
|
|
"image_path": "./data/HME100K/test_images/test_1693.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 0\\)",
|
|
"gt_answers": "x ^ { 2 } + 4 x + 4 - 1 6 - 3 x + 6 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1694.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as sin(3) = 0.5.",
|
|
"gt_answers": "\\sin \\beta = \\frac { \\sqrt { 1 0 } } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1697.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `x^2 + 20x - 7 = 0`.",
|
|
"gt_answers": "x = \\frac { 2 0 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1698.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nR = 3V/0.002A\n\nThis formula represents the resistance (R) in Ohms (\u03a9) of a circuit with a voltage (V) of 3 volts (V) and a current (A) of 0.002 amperes (A).",
|
|
"gt_answers": "R = \\frac { V } { 2 } = \\frac { 3 V } { 0 . 2 5 A } = 1 2 \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_1699.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( x - 2 y ) ( x - y ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1700.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"8/8 = 1.\"",
|
|
"gt_answers": "x = \\frac { 2 5 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1701.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5d/1500m = 0.0033333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
|
|
"gt_answers": "5 d m = ( 5 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1702.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(L_{AJ} = 90^{\\circ} - 30^{\\circ} = 60^{\\circ}\\)",
|
|
"gt_answers": "\\angle O A C = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1703.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"45064.4565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564565645656456564",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1704.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis equation is a simple algebraic expression that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "3 ( x - 2 ) - ( x - 1 ) = x ^ { 2 } - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1705.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. In this case, the variable is x, and the square of x is x^2. The variable y is also squared, resulting in y^2. The equation is then simplified by adding the two squares together, which results in the expression x^2 + y^2 = 1.",
|
|
"gt_answers": "a = \\frac { 9 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1706.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 5x - 6 = 0\\)\n\nThis formula represents a quadratic equation, where x is the unknown variable and the other terms represent constants.",
|
|
"gt_answers": "\\frac { 5 x - 1 3 } { 5 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1707.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 7 = 0\\)",
|
|
"gt_answers": "( x - 4 y - 5 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1709.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(x + 1) - 3(x - 2) = 12.",
|
|
"gt_answers": "\\frac { 5 } { 6 } - \\frac { 1 } { 6 } = \\frac { 4 } { 6 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1710.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{1}{2} \\left(x^2 - 3x + 2\\right) + 1\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(y = \\frac{1}{2} \\left(x^2 - 3x + 2\\right) + 1\\)",
|
|
"gt_answers": "y - \\frac { 6 } { y } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1711.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"sin(x) = 0.5 sin(2x) + 0.5 sin(3x) + 0.5 sin(4x) + 0.5 sin(5x) + 0.5 sin(6x) + 0.5 sin(7x) + 0.5 sin(8x) + 0.5 sin(9x) + 0.5 sin(10x) + 0.5 sin(11x) + 0.5 sin(12x) + 0.5 sin(13x) + 0.5 sin(14x) + 0.5 sin(15x) + 0.5 sin(16x) + 0.5 sin(17x) + 0.5 sin(18x) + 0.5 sin(19x) + 0.5 sin(20x) + 0.5 sin(21x) + 0.5 sin(22x) + 0.5 sin(23x) + 0.5 sin(24x) + 0.5 sin(25x) + 0.5 sin(26x) + 0.5 sin(27x) + 0.5 sin(28x) + 0.5 sin(29x) + 0.5 sin(30x) + 0.5 sin(31x) + 0.5 sin(32x) + 0.5 sin(33x) + 0.5 sin(34x) + 0.5 sin(35x) + 0.5 sin(36x) + 0.5 sin(37x) + 0.5 sin(38x) + 0.5 sin(39x) + 0.5 sin(40x) + 0.5 sin(41x) + 0.5 sin(42x) + 0.5 sin(43x) + 0.5 sin(44x) + 0.5 sin(45x) + 0.5 sin(46x) + 0.5 sin(47x)",
|
|
"gt_answers": "- \\frac { 1 } { 2 } \\leq \\sin \\alpha < \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1712.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{10^{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "9 9 9 \\times 9 9 9 9 + 1 9 9 9 9 = 9 9 9 9 ^ { 2 } + 2 \\times 9 9 9 9 + 1 = ( 9 9 9 9 + 1 ) ^ { 2 } = 1 0 0 0 0 ^ { 2 } = 1 0 ^ { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1713.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "A B = \\sqrt { A E ^ { 2 } - R E ^ { 2 } } = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1714.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/2(n + 1) - 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) + 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) + 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) + 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) + 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) + 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) + 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) + 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) + 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) + 1/2(n - 1) = 1/2(n + 1) - 1/2(n - 2) + 1/2(n - 1) + 1/2(n - 1) = 1/2(n +",
|
|
"gt_answers": "k 1 4 m + b n - 4 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_1715.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "2 x ^ { 2 } + x = 2 x ^ { 2 } - 4 x - 2 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1717.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x2 - 2x4x5 = 6.",
|
|
"gt_answers": "3 \\cdot 6 x = 2 . 4 \\times 0 . 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1718.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"30 SH 1974-1975.\"",
|
|
"gt_answers": "\\Delta h = \\frac { 3 0 } { 1 9 } \\approx 1 \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_1720.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x ^ { 2 } = \\frac { 1 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1721.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 0.93555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555",
|
|
"gt_answers": "9 3 . 5 \\div 1 0 0 0 = 0 . 0 9 3 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1722.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 + c^2 = (a + b + c)^2\\)",
|
|
"gt_answers": "( - 2 a ^ { 2 } b ^ { 3 } ) ( - 3 a )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1723.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(4(x-1) + 4(x-1) = 4x^2 - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - ",
|
|
"gt_answers": "\\frac { 4 } { 9 } ( 1 0 ^ { n } - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1724.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a fraction, with the numerator being 4 and the denominator being 3.",
|
|
"gt_answers": "\\frac { 4 } { 3 } a = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1725.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(F_{ISN} = \\frac{T_{ISN}}{T_{ISN} + T_{N}}\\)\n\nwhere:\n\n* F_{ISN} is the force of the internal stress (ISN)\n* T_{ISN} is the total internal stress (ISN)\n* T_{N} is the total normal stress (N)\n\nThe formula calculates the ratio of the internal stress (ISN) to the sum of the internal stress (ISN) and the normal stress (N).",
|
|
"gt_answers": "F _ { 1 } = \\frac { F _ { 2 } l _ { 2 } } { l _ { 1 } } = \\frac { 3 0 } { 2 } = 1 5 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_1726.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5}\\)",
|
|
"gt_answers": "\\frac { 1 } { 7 } ( 3 x - \\frac { 2 } { 3 } x - 4 ) = \\frac { 7 } { 3 } ( x - 3 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1727.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\cos B = \\frac { B D } { B F }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1728.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"GICCEDC = 1/2 (GICCEDC + GICCEDC).\"",
|
|
"gt_answers": "C _ { 1 } C = D C , \\angle C _ { 1 } C D = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1730.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 5x + 3 = 0\\)",
|
|
"gt_answers": "( 1 0 \\times \\frac { 3 } { 5 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1731.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LPEF = 5 + 2 * LBFE.\"",
|
|
"gt_answers": "\\angle P E F = \\frac { 1 } { 2 } \\angle B E F\n",
|
|
"image_path": "./data/HME100K/test_images/test_1732.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"D.064 x L.076.\"",
|
|
"gt_answers": "0 . 6 4 < x < 0 . 7 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1733.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as y = 2x - 5.",
|
|
"gt_answers": "y = - \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1734.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 2x + 3.",
|
|
"gt_answers": "y = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1735.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 2x + 4 = 0`.",
|
|
"gt_answers": "\\frac { x - 1 } { 4 } - 1 = \\frac { 2 x + 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1737.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"Cd + CdT = CdT + CdT\".",
|
|
"gt_answers": "C a C O _ { 3 } + 2 H C l = C a C l _ { 2 } + H _ { 2 } O + C O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_1738.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SACCb = 1/2 (SACC + Co-Denominator).\"",
|
|
"gt_answers": "S _ { \\Delta C D O } : S _ { \\Delta C B D } = 1 \\frac { 1 } { 2 } C O \\cdot D E 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1739.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is represented by the letter \"c,\" the side opposite the right angle is represented by \"a,\" and the side adjacent to the right angle is represented by \"b.\"",
|
|
"gt_answers": "= ( a + b i ) ( a - b i ( a + b ) ( a - b )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1740.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98} = 18^{99} - 18^{98}",
|
|
"gt_answers": "1 8 - 9 \\textcircled { = }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1741.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 1 0 x + 4 0 } { 1 } . 5 - \\frac { 1 0 x - 3 } { 1 } - 2 = 1 . 6 \\times 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1742.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 100 = 0\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(x^2 + 2x + 100 = 0\\)\n\nThe LaTeX code for the formula is:\n\n\\begin{equation}\nx^2 + 2x + 100 = 0\n\\end{equation}\n\nThe equation is written in the form of an equation with two variables, x and y, and an expression involving the variables. The equation is also written in the form of an equation with two terms, the first term being the left side of the equation, and the second term being the right side of the equation.",
|
|
"gt_answers": "6 0 0 ( x + 2 0 ) = 6 0 0 x + x ^ { 2 } + 2 0 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1743.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nS = 2 + 2 \\* 2 + 2 \\* 2 \\* 2 + 2 \\* 2 \\* 2 \\* 2 + 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* 2 \\* ",
|
|
"gt_answers": "S = 1 + 2 + 2 ^ { 2 } + 2 ^ { 3 } + \\cdots + 2 ^ { 2 0 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1744.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 7x = 4993.",
|
|
"gt_answers": "7 \\times 7 = 4 9 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1745.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(e^{x} = \\cosh(x) + i \\sinh(x)\\)\n\nThis formula represents the exponential function in terms of the hyperbolic cosine and hyperbolic sine functions.",
|
|
"gt_answers": "y = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1746.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 0\\)",
|
|
"gt_answers": "t \\overrightarrow { n } \\cdot \\overrightarrow { n } + \\overrightarrow { n } ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1747.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{2x^2 + 2y^2 - 4xy}{x^2 - y^2} = 1\n\\end{aligned}\n\\end{equation}\n\nThis equation can be simplified further by factoring out the common denominator:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{2x^2 + 2y^2 - 4xy}{x^2 - y^2} = \\frac{2x^2 + 2y^2}{x^2 - y^2} \\cdot \\frac{1}{x^2 - y^2} = \\frac{4xy}{x^2 - y^2}\n\\end{aligned}\n\\end{equation}\n\nThis simplified equation can be further simplified by dividing both sides by 2:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{4xy}{x^2 - y^2} = \\frac{2xy}{x^2 - y^2} \\cdot \\frac{2}{2} = \\frac{xy}{x^2 - y^2}\n\\end{aligned}\n\\end{equation}\n\nFinally, the simplified equation can be written as:\n\n\\begin{equation}\n\\begin{aligned}\nxy = \\frac{xy}{x^2 - y^2}\n\\end{aligned}\n\\end{equation}\n\nThis is the final expression of the formula in the image.",
|
|
"gt_answers": "x ^ { 2 } - 2 x ^ { 2 } + 4 x - 2 - x ^ { 2 } + x = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1748.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4A + LB = ISO\".",
|
|
"gt_answers": "\\angle A + \\angle B = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1749.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(s + 2t) = 649 + 784.",
|
|
"gt_answers": "3 7 6 + 9 6 = 4 7 2 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1750.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, and the constant 10. The equation states that the sum of the products of x and y is equal to 10.",
|
|
"gt_answers": "8 0 \\div 4 0 = \\frac { 1 0 } { 4 0 } = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1751.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, but it can be translated to English as \"300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\theta \\in ( \\frac { \\pi } { 2 } + 2 k \\pi , \\frac { 3 } { 2 } \\pi + 2 k \\pi )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1752.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x^2 + 4x - 1 = 0`.",
|
|
"gt_answers": "2 x + y - 4 = 0 . 1 2 . 5 1 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1753.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4p-a2r2t3.",
|
|
"gt_answers": "\\angle P M O = \\arctan \\frac { \\sqrt { 1 0 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1754.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"C = 1/2 (A + B)\" using LaTeX format.",
|
|
"gt_answers": "c = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1757.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = r^2\\)",
|
|
"gt_answers": "A F = \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1758.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1",
|
|
"gt_answers": "5 9 . 0 2 > 5 8 . 5 2 > 5 8 . 1 7 > 5 8 . 0 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_1759.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 9600/14000 = 0.6875.",
|
|
"gt_answers": "9 8 0 0 \\div 1 4 0 = 7 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1760.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(A + B = 2(A - B)\\)\n\nThis formula can be represented using the following LaTeX code:\n\n\\(A + B = 2(A - B)\\)",
|
|
"gt_answers": "\\frac { 6 } { A B } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1761.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten format, but it can be represented in LaTeX as follows:\n\n\\(x^2 + y^2 = r^2\\)",
|
|
"gt_answers": "x _ { 2 } = - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1764.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "9 7 + 2 7 = \\textcircled { 3 . 2 x + 5 x } < 5 x - 3 . 2 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1765.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Greek letters, which can be represented in LaTeX as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\text{A} \\cdot \\text{B} \\cdot \\text{C} \\cdot \\text{D} \\cdot \\text{E} \\cdot \\text{F} \\cdot \\text{G} \\cdot \\text{H} \\cdot \\text{I} \\cdot \\text{J} \\cdot \\text{K} \\cdot \\text{L} \\cdot \\text{M} \\cdot \\text{N} \\cdot \\text{O} \\cdot \\text{P} \\cdot \\text{Q} \\cdot \\text{R} \\cdot \\text{S} \\cdot \\text{T} \\cdot \\text{U} \\cdot \\text{V} \\cdot \\text{W} \\cdot \\text{X} \\cdot \\text{Y} \\cdot \\text{Z}\n\\end{aligned}\n\\end{equation}\n\nThe formula is written in a way that each letter represents a variable, and the multiplication sign is used to combine the variables. The Greek letters are used to represent the variables, as they are commonly used in mathematics and science.",
|
|
"gt_answers": "\\Delta D E B \\sim \\Delta E B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1767.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x = 1 \\frac { 7 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1768.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{3}x^3 + \\frac{1}{4}x^4 + \\frac{1}{5}x^5 + \\frac{1}{6}x^6 + \\frac{1}{7}x^7 + \\frac{1}{8}x^8 + \\frac{1}{9}x^9 + \\frac{1}{10}x^{10} + \\frac{1}{11}x^{11} + \\frac{1}{12}x^{12} + \\frac{1}{13}x^{13} + \\frac{1}{14}x^{14} + \\frac{1}{15}x^{15} + \\frac{1}{16}x^{16} + \\frac{1}{17}x^{17} + \\frac{1}{18}x^{18} + \\frac{1}{19}x^{19} + \\frac{1}{20}x^{20} + \\frac{1}{21}x^{21} + \\frac{1}{22}x^{22} + \\frac{1}{23}x^{23} + \\frac{1}{24}x^{24} + \\frac{1}{25}x^{25} + \\frac{1}{26}x^{26} + \\frac{1}{27}x^{27} + \\frac{1}{28}x^{28} + \\frac{1}{29}x^{29} + \\frac{1}{30}x^{30} + \\frac{1}{31}x^{31} + \\frac{1}{32}x^{32} + \\frac{1}{33}x^{33} + \\frac{1}{34}x^{34} + \\frac{1}{35}x^{35} + \\frac{1}{36}x^{36} + \\frac{1}{37}x^{37} + \\frac{1}{38}x",
|
|
"gt_answers": "\\frac { 2 } { 6 } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1769.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nm = 2(2 + 3) - 7\n\nThe formula is a quadratic equation, where m represents the unknown variable, and the other terms represent known values. The equation can be solved using the quadratic formula, which is:\n\nm = (-b + or - sqrt(b^2 - 4ac)) / 2a\n\nIn this case, the quadratic formula simplifies to:\n\nm = (-2 + or - sqrt(4 + 12 - 4(2 + 3))) / 2(2 + 3)\n\nSolving for m, we get:\n\nm = (-2 + or - sqrt(16)) / 4\n\nThe possible values for m are:\n\nm = -2, 0, or 2\n\nThe solution is m = 2.",
|
|
"gt_answers": "m = - \\frac { 8 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1770.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4.506456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456456",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1771.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_A = \\frac{A}{B} + \\frac{B}{C} + \\frac{C}{A}\\)\n\nThis formula can be interpreted as the sum of the reciprocals of the ratios of the areas of the three triangles formed by the sides of the given triangle.",
|
|
"gt_answers": "C B = \\frac { 1 } { 2 } A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_1772.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 2y = 10.\"",
|
|
"gt_answers": "y _ { 1 } = 0 y _ { 2 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1773.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 4 = 0\\)",
|
|
"gt_answers": "x - 3 x + 1 \\leq x + 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1774.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "O P ^ { 2 } = x ^ { 2 } + ( - x + 6 ) ^ { 2 }\n",
|
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"image_path": "./data/HME100K/test_images/test_1775.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 100 - 0.10 = 99.90.",
|
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"gt_answers": "\\frac { 1 . 4 6 g } { 1 4 6 g } = 0 . 1 = 1 0 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_1776.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(4\\times 5\\times 6\\times 7\\times 8\\times 9\\times 10\\times 11\\times 12\\times 13\\times 14\\times 15\\times 16\\times 17\\times 18\\times 19\\times 20\\times 21\\times 22\\times 23\\times 24\\times 25\\times 26\\times 27\\times 28\\times 29\\times 30\\times 31\\times 32\\times 33\\times 34\\times 35\\times 36\\times 37\\times 38\\times 39\\times 40\\times 41\\times 42\\times 43\\times 44\\times 45\\times 46\\times 47\\times 48\\times 49\\times 50\\times 51\\times 52\\times 53\\times 54\\times 55\\times 56\\times 57\\times 58\\times 59\\times 60\\times 61\\times 62\\times 63\\times 64\\times 65\\times 66\\times 67\\times 68\\times 69\\times 70\\times 71\\times 72\\times 73\\times 74\\times 75\\times 76\\times 77\\times 78\\times 79\\times 80\\times 81\\times 82\\times 83\\times 84\\times 85\\times 86\\times 87\\times 88\\times 89\\times 90\\times 91\\times 92\\times 93\\times 94\\times 95\\times 96\\times 97\\times 98\\times 99\\times 100\\times 101\\times 102\\times 10",
|
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"gt_answers": "\\frac { 1 } { 2 } \\cdot \\vert y \\vert \\cdot 2 = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1777.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so I cannot provide a LaTeX representation of it. However, the image shows a mathematical formula with the number 3 written in Japanese characters.",
|
|
"gt_answers": "x = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1778.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "2 x = \\frac { 5 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1779.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is known as the equation of motion for a particle with mass m and energy E. It states that the total energy of a particle is equal to its mass multiplied by the square of its speed of light, c.",
|
|
"gt_answers": "m = \\frac { 5 \\cdot } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1780.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2-3x+2=0\\)",
|
|
"gt_answers": "( 2 - a ) x = 5 - a\n",
|
|
"image_path": "./data/HME100K/test_images/test_1781.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\ny = 2x^2 + 3x + 4",
|
|
"gt_answers": "y _ { 1 } = 2 , y _ { 2 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1783.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1",
|
|
"gt_answers": "( b + c ) \u3001 ( a + c ) \u3001 ( b + a )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1784.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "x = \\frac { 1 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1785.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(I^2 = J^2 + K^2 + L^2\\)",
|
|
"gt_answers": "\\pm \\sqrt { c - 2 } = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1786.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nRi = 60 + 0.07 x 3020\n\nThe formula uses the variables Ri (resistance in ohms) and 3020 (resistance in ohms) to calculate the resistance in ohms. The Ri variable represents the resistance of the resistor in the circuit, while the 3020 variable represents the resistance of another resistor in the circuit. The formula combines these two resistances to calculate the total resistance in the circuit.",
|
|
"gt_answers": "R _ { 1 } = \\frac { V _ { 1 } } { I _ { 1 } } = \\frac { 6 V } { 0 . 2 A } = 3 0 \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_1787.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 900x600 = 5400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "9 0 \\times 6 0 = 5 4 0 0 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1788.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"dollars per hour.\"",
|
|
"gt_answers": "D C \\bot A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_1789.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "= r ^ { 2 } ( 2 \\cos ^ { 2 } \\theta + \\cos \\theta - 1 ) = r ^ { 2 } ( 2 \\cos \\theta - 1 ) ( \\cos \\theta + 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1790.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(f(x) = 3x^2 - 2x + 1\\)",
|
|
"gt_answers": "\\frac { 1 } { 4 } : \\frac { 1 } { 9 } = \\frac { 1 } { 3 } : x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1791.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\sum_{i=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{j=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{k=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{l=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{m=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{n=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{o=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{p=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{q=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{r=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{s=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{t=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{u=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{v=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{w=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{x=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{y=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{z=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{aa=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{bb=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{cc=1}^{n} \\left( \\frac{1}{2} \\left( \\sum_{dd=1}^{n} \\left( \\frac{1",
|
|
"gt_answers": "\\angle A B M = \\angle A M N , A B = B C , A M = M N\n",
|
|
"image_path": "./data/HME100K/test_images/test_1792.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "y - \\frac { 3 } { 4 } = - \\frac { 1 } { 2 } ( x - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1793.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "y ^ { 2 } = \\frac { b ^ { 2 } ( a ^ { 2 } - 1 ) } { a ^ { 2 . } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1794.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2(x - 1) - 1.",
|
|
"gt_answers": "\\frac { 3 a ^ { - 2 } } { 2 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1795.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(m_1 + m_2 + m_3 + m_4 = 4m\\)\n\nwhere m1, m2, m3, and m4 are the masses of four objects, and m is the total mass of the four objects.",
|
|
"gt_answers": "( 2 ) x _ { 1 } x _ { 2 } = \\frac { c } { a } = \\frac { \\frac { m } { 4 } } { m } = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1796.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 49\\)",
|
|
"gt_answers": "W = - x ^ { 2 } + 7 x + 4 8 = - ( x - 3 . 5 ) ^ { 2 } + 6 0 . 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1797.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: (x + y)2 = (x2 + y2) + 2xy.",
|
|
"gt_answers": "\\frac { y } { y + 9 } = \\frac { 4 - \\frac { 2 } { 3 } x } { 9 - \\frac { 2 } { 3 } x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1799.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "x = \\frac { a - 5 } { a - 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1800.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 54988+5455=59443.",
|
|
"gt_answers": "4 5 9 + 8 6 = 5 4 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1801.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 6x + 6 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1803.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "2 x - ( - 7 . 8 ) = - \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1804.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 49.\"",
|
|
"gt_answers": "S _ { \\Delta } P C O = \\frac { 1 } { 2 } \\times t \\times 3 = \\frac { 3 } { 2 } t\n",
|
|
"image_path": "./data/HME100K/test_images/test_1805.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "1 2 a ^ { 2 } - 5 + x ^ { 2 } + 2 a x = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1806.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1807.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 400.\"",
|
|
"gt_answers": "\\overrightarrow { x } = \\frac { 1 \\times 2 0 + 1 . 5 \\times 1 2 0 + 2 \\times 6 0 } { 2 0 + 1 2 0 + 6 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1808.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 15x + 15 = 15x + 15.",
|
|
"gt_answers": "x = \\frac { 1 5 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1809.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "6 8 3 - 8 = 6 7 7 \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_1810.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 247-7+14cm.",
|
|
"gt_answers": "2 4 - 7 = 1 4 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1811.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(f(x) = 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { D F } { C E } = \\frac { O D } { D C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1814.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times 0.03 \\times ",
|
|
"gt_answers": "\\frac { x } { 0 . 3 } - \\frac { 0 . 2 3 - 0 . 2 x } { 0 . 0 7 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1815.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(R = \\frac{2\\pi\\omega}{4\\pi\\omega^2 + 4\\pi\\omega\\cos(2\\pi\\omega t)} \\tag{1}\\label{formula1}`",
|
|
"gt_answers": "R = \\frac { V } { I } = \\frac { 2 v } { 0 . 5 A } = 4 \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_1816.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2) + 4(x^2 + y^2",
|
|
"gt_answers": ". 1 . 3 . 1 4 \\times 4 ^ { 2 } \\times 1 2 = 6 0 2 . 8 8 l m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1817.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(O_{B} + O_{C} + O_{D} + O_{E} + O_{F} + O_{G} + O_{H} + O_{I} + O_{J} + O_{K} + O_{L} + O_{M} + O_{N} + O_{O} + O_{P} + O_{Q} + O_{R} + O_{S} + O_{T} + O_{U} + O_{V} + O_{W} + O_{X} + O_{Y} + O_{Z} = 100\\)",
|
|
"gt_answers": "O B = \\frac { 1 } { 2 } B D . O C = \\frac { 1 } { 2 } A C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1818.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 59.02 + 0.0259 + 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "5 9 . 0 2 > 5 8 . 5 2 > 5 8 . 1 7 > 5 8 . 0 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_1819.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"UV = 1/2 (U + V)\" using LaTeX format.",
|
|
"gt_answers": "\\frac { F C } { C N } = \\frac { D F } { D N }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1820.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 4x + 4 = 16\\)",
|
|
"gt_answers": "y _ { 2 } = 4 y _ { 4 } = - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1821.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 2y = 10.\"",
|
|
"gt_answers": "\\frac { 2 } { 3 } = \\frac { 8 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1824.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3(4-1) + 4(4-1) = 12(4-1) + 4(4-1) = 12(2) + 4(2) = 24 + 8 = 32.",
|
|
"gt_answers": "- \\frac { 3 } { 1 4 } - \\frac { 4 } { 1 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1825.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} \\right) = \\frac{x^2 + y^2}{2}\n\\end{equation}\n\nThis formula can be interpreted as the average of the squares of the two sides of a right triangle, where the hypotenuse is equal to the sum of the squares of the two sides.",
|
|
"gt_answers": "x + 2 \\sqrt { x + 4 } + x + 4 - 2 x - x = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1826.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "( 8 0 ) - 4 0 = 4 0 . ( 8 0 ) + 3 0 = 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1827.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 3x + 5 = 10.",
|
|
"gt_answers": "3 - \\frac { 2 x - 1 } { 5 } = \\frac { x + 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1828.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the half of the half of a whole, which is equal to one fourth.",
|
|
"gt_answers": "S _ { \\Delta B E } = 9 s = 2 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1829.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 3x + 18.",
|
|
"gt_answers": "y - 3 = \\frac { 1 8 } { y }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1830.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( y + 2 ) ^ { 2 } - y ^ { 2 } = - 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1831.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x = \\frac { 2 \\pm \\sqrt { 4 8 } } { 2 } = 1 \\pm 2 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1832.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4 x 10^4000 = 16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 \\times 4 0 0 0 0 = 1 6 0 0 0 0 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1833.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3y^2 + 4xy + 5y + 6x + 7 = 0\\)",
|
|
"gt_answers": "8 1 ( 2 x + 1 ) = x ^ { 2 } - 6 2 y + 9 6 1 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1834.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\n\\(Fe^{2+}(OH)_{2}Cl^{3+} \\rightarrow Fe^{3+}(OH)_{2}Cl^{2+}\\)\n\nThe formula represents the chemical reaction between iron(II) hydroxide and iron(III) chloride to form iron(III) hydroxide and iron(II) chloride.",
|
|
"gt_answers": "F e _ { 2 } O _ { 3 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1835.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "v c = r A - 1 7 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1836.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888",
|
|
"gt_answers": "3 8 \\div 8 8 = \\frac { 1 9 } { 4 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1837.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LABF = LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF + LABF",
|
|
"gt_answers": "\\angle A B F = \\angle F B E = \\frac { 1 } { 2 } \\angle A B E\n",
|
|
"image_path": "./data/HME100K/test_images/test_1838.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = 2x^2\n\\end{equation}\n\nThis formula is a simple algebraic expression that can be used to find the sum of the squares of two variables.",
|
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"gt_answers": "\\frac { 1 } { 1 2 } \\times 6 \\times \\vert y - 3 \\vert = b\n",
|
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"image_path": "./data/HME100K/test_images/test_1839.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E_{elapse} = \\frac{t_{elapse}}{t_{total}}\\)\n\nwhere `t_{elapse}` is the elapsed time and `t_{total}` is the total time.",
|
|
"gt_answers": "E F \\bot A D : \\angle A P F = 9 0 ^ { \\circ }\n",
|
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"image_path": "./data/HME100K/test_images/test_1841.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is known as the equation of motion for a particle with mass m and energy E. It states that the total energy of a particle is equal to its mass multiplied by the square of its speed of light, c.",
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"gt_answers": "C E = \\sqrt { E F ^ { 2 } + C F ^ { 2 } } = \\sqrt { ( \\sqrt { 3 } ) ^ { 2 } + ( \\frac { 3 } { 2 } ) ^ { 2 } } = \\frac { \\sqrt { 2 1 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1842.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x < \\frac { 2 } { \\sqrt { 5 } - 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1843.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a negative sign in front of a number, which could be written as:\n\n-n + 4",
|
|
"gt_answers": "1 3 + x = ( 4 7 + x ) \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1844.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 9/10 - 10/16.",
|
|
"gt_answers": "\\frac { 9 } { 1 6 } - \\frac { 9 \\cdot } { 1 6 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1846.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "( b + 1 ) x ^ { 2 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1847.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(L_{AB} = L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L_{LAB} + L_{LBA} + L",
|
|
"gt_answers": "\\angle A O D = 1 8 0 ^ { \\circ } - \\angle A B D - \\angle B A O = 1 5 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1848.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(LCD = LCDP + LCDD + LCDL + LCDLCD + LCDLLCD + LCDLLLLCD + LCDLLLLLLCD + LCDLLLLLLLLCD + LCDLLLLLLLLLLCD + LCDLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLLLLLLLLLLLLCD + LCDLLLLLLLLLLLL",
|
|
"gt_answers": "\\angle B D P + \\angle C D P = \\angle 1 + \\angle B A D + \\angle C A D + \\angle 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1850.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: \"AB + BC = C.\"",
|
|
"gt_answers": "\\angle A C B = \\frac { A B } { B C } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1851.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 15x + 10 = 0\\)\n\nThis formula can be solved using the quadratic formula:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\)\n\nSubstituting the values for a, b, and c from the given expression, we get:\n\n\\(x = \\frac{-15 \\pm \\sqrt{15^2 - 4(10)(10)}}{2(10)} = \\frac{-15 \\pm 15 \\sqrt{2}}{2(10)} = \\frac{-15 \\pm 15 \\sqrt{4}}{20} = \\frac{-15 \\pm 7}{20} = \\frac{-15 \\pm 3.5}{20} = \\frac{-15 \\pm 1.75}{20} = \\frac{-15 \\pm 0.875}{20} = \\frac{-15 \\pm 0.4375}{20} = \\frac{-15 \\pm 0.21875}{20} = \\frac{-15 \\pm 0.109375}{20} = \\frac{-15 \\pm 0.0546875}{20} = \\frac{-15 \\pm 0.02734375}{20} = \\frac{-15 \\pm 0.013671875}{20} = \\frac{-15 \\pm 0.0068359375}{20} = \\frac{-15 \\pm 0.00341796875}{20} = \\frac{-15 \\pm 0.0017089375}{20} = \\frac{-15 \\pm 0.000854375}{20} = \\frac{-15 \\pm 0.0004271875}{20} = \\frac{-15 \\pm 0.00021367187",
|
|
"gt_answers": "x = \\frac { 4 0 } { 1 5 } = 2 \\frac { 1 0 } { 1 5 } = 2 \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1852.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\geq 2 \\sqrt { \\frac { 9 } { 1 } } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1853.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"S(m-t) = S(m) + (m-t) * (S(t) - S(m))\".",
|
|
"gt_answers": "S m = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1854.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(6 - 3) - 10 - 20.",
|
|
"gt_answers": "\\frac { 6 } { 2 0 } = \\frac { 3 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1855.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5x2 - 10x12.",
|
|
"gt_answers": "\\frac { 5 } { 6 } = \\frac { 5 \\times 2 } { 6 \\times 2 } = \\frac { 1 0 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1856.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\ny = 9 - 3x + 3t\n\\end{equation}\n\nThis formula represents a linear equation in two variables, where y is the dependent variable and x and t are the independent variables. The equation can be solved using the substitution method, where the variable t is replaced with the expression 3t. This results in the following equation:\n\n\\begin{equation}\ny = 9 - 3x + 3(3t)\n\\end{equation}\n\nSolving for y, we get:\n\n\\begin{equation}\ny = 9 - 3x + 9t\n\\end{equation}\n\nThis equation represents the solution to the linear equation in two variables.",
|
|
"gt_answers": "3 y - 2 = 9 - 6 \\sqrt { y + 3 } + y + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1857.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 2x + 3}{x^2 - 2x + 3}\n\\end{equation}\n\nThis is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "\\frac { 3 } { 8 } \\times 5 = \\frac { 3 \\times 5 } { 8 . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1858.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = z^2\\)",
|
|
"gt_answers": "2 \\times \\frac { \\sqrt { 3 } } { 2 } \\times \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1860.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "- \\frac { b } { 2 a } = \\frac { 1 } { 3 } ( x - 2 ) ^ { 2 } + 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1861.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(b_n = 2n^2 + 2n + 1\\)",
|
|
"gt_answers": "b _ { n } = 2 ( a _ { n } - 2 a _ { n - 1 } ) ^ { 1 } = 2 b _ { n - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1862.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2mgh - LNHG\".",
|
|
"gt_answers": "\\angle M G H = \\angle N H G\n",
|
|
"image_path": "./data/HME100K/test_images/test_1863.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\because \\angle O E D = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1864.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/5 + 1/5 = 2/5 + 1/5 = 3/5.\"",
|
|
"gt_answers": "x = \\frac { 1 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1865.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `BT = 2(UT + 4(XU + YV))`.",
|
|
"gt_answers": "1 3 + x = \\frac { 1 } { 2 } ( 4 7 + x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1866.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\ny = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1}\n\\end{equation}\n\nThis formula can be simplified to:\n\n\\begin{equation}\ny = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x +",
|
|
"gt_answers": "\\frac { 3 } { 2 } y - y ^ { 2 } - \\frac { 1 } { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1867.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{100} \\cdot \\frac{1}{1",
|
|
"gt_answers": "f ( t + 1 ) = \\vert t + 1 \\vert\n",
|
|
"image_path": "./data/HME100K/test_images/test_1868.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 3x + 1.",
|
|
"gt_answers": "y = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1869.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 3x + 2.",
|
|
"gt_answers": "y _ { 1 } = 3 y _ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1870.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { C E } { A F } = \\frac { B E } { F C } = \\frac { B C } { A C } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1871.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 400 - 200x.",
|
|
"gt_answers": "y = \\frac { 2 0 0 5 } { 4 0 0 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1872.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = \\frac{1}{2}mv^2\\)\n\nThis formula states that the energy of an object is equal to one-half the product of its mass (m) and its velocity squared (v^2).",
|
|
"gt_answers": "k _ { 1 } k _ { 2 } = \\frac { n ^ { 2 } \\times 0 ^ { 2 } - m ^ { 2 } y _ { 0 } ^ { 2 } } { 2 ( m ^ { 2 } - x _ { 0 } ^ { 2 } ) } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1873.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as E(3n + 1) = 3n^2 + 3n + 1.",
|
|
"gt_answers": "E F = 3 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1874.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\nB = 0.6 HP + 0.3 HP\n\nThe formula is a combination of two separate equations, with the first equation representing the power output of the engine (HP) and the second equation representing the power output of the engine with a higher boost pressure (HP). The equation is written in the form of a sum, where the first term represents the power output at a lower boost pressure (0.6 HP) and the second term represents the power output at a higher boost pressure (0.3 HP).",
|
|
"gt_answers": "\\frac { D H } { B O } = \\frac { H P } { O E . } = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1875.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x ^ { 2 } + x ( x + 1 ) = 2 ( x + 1 ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1876.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 3x + 5 = 9\\)",
|
|
"gt_answers": "\\frac { 3 } { 5 } \\times 3 = \\frac { 9 } { 5 } = 9 = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1877.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LDEE = 28.8\".",
|
|
"gt_answers": "\\angle D O E = 2 8 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1878.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(x+1)^2 - 2x^2.",
|
|
"gt_answers": "\\sqrt { y } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_1879.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x^2 + 4x + 2`.",
|
|
"gt_answers": "S _ { 2 } = 4 = 2 ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1880.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "y = \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1881.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SLA + LAC = 5 LAC.\"",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\angle A B C = \\frac { 1 } { 2 } \\angle A C B\n",
|
|
"image_path": "./data/HME100K/test_images/test_1882.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a(c + 2) + b(c + 3) + c(c + 4) + d(c + 5) + e(c + 6) + f(c + 7) + g(c + 8) + h(c + 9) + i(c + 10) + j(c + 11) + k(c + 12) + l(c + 13) + m(c + 14) + n(c + 15) + o(c + 16) + p(c + 17) + q(c + 18) + r(c + 19) + s(c + 20) + t(c + 21) + u(c + 22) + v(c + 23) + w(c + 24) + x(c + 25) + y(c + 26) + z(c + 27) + aa(c + 28) + bb(c + 29) + cc(c + 30) + dd(c + 31) + ee(c + 32) + ff(c + 33) + gg(c + 34) + hh(c + 35) + ii(c + 36) + jj(c + 37) + kk(c + 38) + ll(c + 39) + mm(c + 40) + nn(c + 41) + oo(c + 42) + pp(c + 43) + qq(c + 44) + rr(c + 45) + ss(c + 46) + tt(c + 47) + uu(c + 48) + vv(c + 49) + ww(c + 50) + xxx(c + 51) + yyy(c + 52) + zzz(c + 53) + aaabbbccdddeeffgghhiiijjkkllmmnooppqqrr",
|
|
"gt_answers": "C a ( O H ) _ { 2 } = 2 N a O H + C a C O _ { 3 } l\n",
|
|
"image_path": "./data/HME100K/test_images/test_1883.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3xcooDBc\".",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\times ( A D + B C )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1884.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(E_{p,q} = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2}",
|
|
"gt_answers": "\\frac { 1 } { 2 } P E \\cdot B P = \\frac { 1 } { 2 } \\cdot \\frac { 1 } { 2 } E F \\cdot B P\n",
|
|
"image_path": "./data/HME100K/test_images/test_1885.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2 + 3 = 5\" using a combination of numbers and letters.",
|
|
"gt_answers": "\\frac { 8 } { 1 4 } \\textcircled { > } \\frac { 9 } { 2 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1886.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as C2N2R.",
|
|
"gt_answers": "c = 2 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1887.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 0\\)",
|
|
"gt_answers": "y = - \\frac { 1 } { 4 } x ^ { 2 } + 2 x - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1889.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\na(a-4c) + 4(a-c) + 4c = 0\n\nThis formula can be simplified to a(a-4c) = -4(a-c) + 4c.",
|
|
"gt_answers": "( a - 4 ) ( a + 3 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1890.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "y = - \\frac { 1 } { 4 } x ^ { 2 } + 2 x - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1892.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh + 8432bh",
|
|
"gt_answers": "\\frac { 8 b + 9 a ^ { 2 } - 1 0 a } { 1 2 a ^ { 2 } b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1893.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(2 + 1) - 2(2 - 1) = 4(1 + 1) - 4(1 - 1) = 4(2) - 4(0) = 8.",
|
|
"gt_answers": "q \\in ( \\frac { 1 - \\sqrt { 5 } } { 2 } , \\frac { 1 + \\sqrt { 5 } } { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1894.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x _ { 3 } = - 2 + 2 \\sqrt { 2 } , x _ { 4 } = - 2 - 2 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1895.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 2 0 8 0 } { x y } = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1896.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: tan(b) = 4/3 * (AD - BD).",
|
|
"gt_answers": "\\tan B = \\frac { A D } { B D } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1897.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\".",
|
|
"gt_answers": "a = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_1898.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{3} + \\frac{2}{3} + \\frac{3}{3} = \\frac{1}{3} + \\frac{2}{3} + \\frac{3}{3} = \\frac{4}{3}\n\\end{equation}\n\nThis equation is a simple algebraic expression that adds three terms together to equal four. The terms are written as fractions, with the numerator representing the top number and the denominator representing the bottom number. The equation is written using the standard mathematical notation for fractions, with the fraction bar separating the numerator and denominator.",
|
|
"gt_answers": "x _ { 2 } = \\frac { 2 } { 3 } - \\frac { \\sqrt { 1 0 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1899.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x ^ { 2 } + y ^ { 2 } - 4 x + 3 - y ^ { 2 } - 2 x + 2 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1900.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\ny = 3x^2 + 2x + 1\n\nThis formula can be represented using the LaTeX code:\n\ny = 3x^2 + 2x + 1\n\nThe LaTeX code is a standard way of writing mathematical expressions and formulas in a computer-readable format. It is used in many scientific and technical fields, including mathematics, physics, and engineering.",
|
|
"gt_answers": "\\cdot - \\frac { 1 } { 2 } y - ( - 2 1 ) = y \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1901.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = \\frac{F}{m} = \\frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "5 0 m ^ { 2 } = ( 5 0 0 0 ) d m ^ { 2 } 8 0 0 0 0 c m ^ { 2 } = ( 8 ) m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1902.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x = 4 + 2 \\sqrt{2} \\cdot 2^{2} \\cdot 3^{2} \\cdot 4^{2} \\cdot 5^{2} \\cdot 6^{2} \\cdot 7^{2} \\cdot 8^{2} \\cdot 9^{2} \\cdot 10^{2} \\cdot 11^{2} \\cdot 12^{2} \\cdot 13^{2} \\cdot 14^{2} \\cdot 15^{2} \\cdot 16^{2} \\cdot 17^{2} \\cdot 18^{2} \\cdot 19^{2} \\cdot 20^{2} \\cdot 21^{2} \\cdot 22^{2} \\cdot 23^{2} \\cdot 24^{2} \\cdot 25^{2} \\cdot 26^{2} \\cdot 27^{2} \\cdot 28^{2} \\cdot 29^{2} \\cdot 30^{2} \\cdot 31^{2} \\cdot 32^{2} \\cdot 33^{2} \\cdot 34^{2} \\cdot 35^{2} \\cdot 36^{2} \\cdot 37^{2} \\cdot 38^{2} \\cdot 39^{2} \\cdot 40^{2} \\cdot 41^{2} \\cdot 42^{2} \\cdot 43^{2} \\cdot 44^{2} \\cdot 45^{2} \\cdot 46^{2} \\cdot 47^{2} \\cdot 48^{2} \\cdot 49^{2} \\cdot 50^{2} \\cdot 51^{2} \\cdot 52^{2} \\cdot 53^{2} \\cdot 54^{2} \\cdot 55^{2} \\cdot 56^{2} \\cdot 57^{2} \\cdot 58^{2} \\cdot 59^{2} \\cdot 60^{2} \\cdot 61^{2} \\cdot 62^{2} \\cdot",
|
|
"gt_answers": "\\frac { 8 } { 5 } x _ { 4 } = 2 4 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_1903.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LAEB = 45\u00b0\".",
|
|
"gt_answers": "\\angle A E B = 4 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1904.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{d}{dt} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "d = \\sqrt { 1 + k ^ { 2 } } \\cdot \\vert x _ { 1 } - x _ { 2 } \\vert\n",
|
|
"image_path": "./data/HME100K/test_images/test_1907.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(M = \\frac{1}{2} \\left( \\frac{F_1}{A_1} + \\frac{F_2}{A_2} \\right)\\)\n\nwhere M is the moment of inertia, F1 and F2 are the forces acting on the object, and A1 and A2 are the areas of the two masses.",
|
|
"gt_answers": "y = \\frac { m } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1908.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a number of symbols and characters, which could be related to a mathematical equation or a chemical formula.",
|
|
"gt_answers": "x = - \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1909.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x^2 + 4x^4 + 8x^8.\"",
|
|
"gt_answers": "x ^ { 2 } - 2 x + x ^ { 2 } + 4 x + 4 = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_1910.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\therefore y = \\frac { 1 } { 4 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1911.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 5x^2 + 6x + 7\\)",
|
|
"gt_answers": "x = \\frac { 1 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1912.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "O N / / M C , O N = M C\n",
|
|
"image_path": "./data/HME100K/test_images/test_1913.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten format, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a negative sign in front of a number, which could be a negative exponent or a negative power.",
|
|
"gt_answers": "x = - \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1914.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2(4878 + 1399 + 1000) - 2(1399 + 1000) = 2(4878 - 1399) = 2(3489) = 7978\\)",
|
|
"gt_answers": "\\frac { ( 4 8 7 - 1 8 7 ) } { 3 0 0 } - \\frac { ( 1 3 9 + 6 1 ) } { 2 0 0 } = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1915.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 - 2ab = c^2\\)\n\nThis formula can be represented using the LaTeX code:\n\n\\(a^2 + b^2 - 2ab = c^2\\)\n\nThe formula can be used to find the square of the sum of two numbers, a and b, and the square of their difference, a - b. The result, c, is the square of the difference between the sum and the difference.",
|
|
"gt_answers": "d = \\frac { a _ { 3 } - a _ { 1 } } { 3 - 1 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1916.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: A(t) = A(0) + (1/2) * t * (A(t-1) - A(t-2)).",
|
|
"gt_answers": "A E = \\frac { 2 7 6 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1917.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(m_r = \\frac{m_1 + m_2}{2}\\)\n\nThis formula represents the average mass of two objects, where m1 and m2 are the masses of the two objects, and m_r is the average mass.",
|
|
"gt_answers": "m \\geq - \\frac { 5 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1920.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{10} + 2^{11} + 2^{12} + 2^{13} + 2^{14} + 2^{15} + 2^{16} + 2^{17} + 2^{18} + 2^{19} + 2^{20} + 2^{21} + 2^{22} + 2^{23} + 2^{24} + 2^{25} + 2^{26} + 2^{27} + 2^{28} + 2^{29} + 2^{30} + 2^{31} + 2^{32} + 2^{33} + 2^{34} + 2^{35} + 2^{36} + 2^{37} + 2^{38} + 2^{39} + 2^{40} + 2^{41} + 2^{42} + 2^{43} + 2^{44} + 2^{45} + 2^{46} + 2^{47} + 2^{48} + 2^{49} + 2^{50} + 2^{51} + 2^{52} + 2^{53} + 2^{54} + 2^{55} + 2^{56} + 2^{57} + 2^{58} + 2^{59} + 2^{60} + 2^{61} + 2^{62} + 2^{63} + 2^{64} + 2^{65} + 2^{66} + 2^{67} + 2^{68} + 2^{69} + 2^{70} + 2^{71} + 2^{72} + 2^{73} + 2^{74} + 2^{75} + 2^{76} + 2^{77} + 2^{78} + 2^{79} + 2^{80",
|
|
"gt_answers": "( 1 1 - 9 ) \\div 1 1 = \\frac { 2 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1921.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = 2x^{2} - 20x + 91\\)",
|
|
"gt_answers": "+ 2 z - 2 0 y + 5 z = 9 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1923.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 244 - (13 + 4) = 244 - 17 = 227.",
|
|
"gt_answers": "W _ { 1 } = - ( x - \\frac { 7 } { 2 } ) ^ { 2 } + \\frac { 2 4 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1924.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"tan(LAPD) + bon(LACE) = 0.5 + 0.5 = 1.0.\"",
|
|
"gt_answers": "\\tan \\angle A P D = \\tan \\angle A C E = \\frac { A E } { C E } = \\frac { 5 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1926.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1/12 + 1/24 + 1/36 + 1/48 + 1/60 + 1/72 + 1/84 + 1/96 + 1/108 + 1/120 + 1/132 + 1/144 + 1/156 + 1/168 + 1/180 + 1/192 + 1/204 + 1/216 + 1/228 + 1/240 + 1/252 + 1/264 + 1/276 + 1/288 + 1/300 + 1/312 + 1/324 + 1/336 + 1/348 + 1/360 + 1/372 + 1/384 + 1/396 + 1/408 + 1/420 + 1/432 + 1/444 + 1/456 + 1/468 + 1/480 + 1/492 + 1/504 + 1/516 + 1/528 + 1/540 + 1/552 + 1/564 + 1/576 + 1/588 + 1/600 + 1/612 + 1/624 + 1/636 + 1/648 + 1/660 + 1/672 + 1/684 + 1/696 + 1/708 + 1/720 + 1/732 + 1/744 + 1/756 + 1/768 + 1/780 + 1/792 + 1/804 + 1/816 + 1/828 + 1/840 + 1/852 + 1/864 + 1/876 +",
|
|
"gt_answers": "I _ { 2 } = \\frac { 1 } { 3 } I ^ { \\prime } - \\frac { B L ^ { 2 } w } { 8 r }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1927.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 32x4 - 33x3 = 16x4 - 33x2.",
|
|
"gt_answers": "\\frac { 1 6 } { 3 } \\times 0 . 4 = \\frac { 3 2 } { 1 5 } B\n",
|
|
"image_path": "./data/HME100K/test_images/test_1928.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(N_{H_{2}O} = N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH} + N_{NaOH}",
|
|
"gt_answers": "2 N a O H + H _ { 2 } S O _ { 4 } = N a _ { 2 } S O _ { 4 } + 2 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1929.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"20 = 13 x 1.5.\"",
|
|
"gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1930.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "f ^ { \\prime } ( x ) = - \\frac { 1 } { x ^ { 2 } } - 1 + \\frac { a } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1931.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 5 = 73\\)",
|
|
"gt_answers": "x _ { 1 } = - \\frac { 7 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1933.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 12/2 = 6.",
|
|
"gt_answers": "\\vert \\frac { b ^ { 2 } } { 2 k } \\vert = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1934.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"G = 0.01 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.001 x 0.0",
|
|
"gt_answers": "1 0 = 1 . 2 k g\n",
|
|
"image_path": "./data/HME100K/test_images/test_1935.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ox bab-ox 3bab\" using the LaTeX format.",
|
|
"gt_answers": "\\textcircled { 1 } \\times b a b - \\textcircled { 2 } \\times 3 a b\n",
|
|
"image_path": "./data/HME100K/test_images/test_1936.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1270.1270 - 2.222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222",
|
|
"gt_answers": "\\frac { 5 0 + 5 1 } { 2 } = 5 0 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1939.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "2 x ^ { 2 } + x - ( 2 x - 1 ) ^ { 2 } = - 1 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_1940.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(b^2 + 2bx + x^2 = 4b^2 + 4bx + x^2\\)\n\nThis formula can be rearranged to solve for x:\n\n\\(x^2 + 2bx + b^2 = 4b^2 + 4bx + x^2\\)\n\nSolving for x:\n\n\\(x^2 + 2bx + b^2 - 4b^2 - 4bx - x^2 = 0\\)\n\n\\(x^2 + 2bx - 2b^2 - 4b^2 - 4bx - x^2 = 0\\)\n\n\\(x^2 - 2bx - 2b^2 - 4b^2 - 4bx - x^2 = 0\\)\n\n\\(x^2 - 2bx - 2b^2 - 4b^2 - 4bx - x^2 = -4b^2 - 4bx - x^2\\)\n\n\\(x^2 - 2bx - 2b^2 - 4b^2 - 4bx - x^2 = -4b^2 - 4bx - x^2 - 4b^2 - 4bx - x^2\\)\n\n\\(x^2 - 2bx - 2b^2 - 4b^2 - 4bx - x^2 = -4b^2 - 4bx - x^2 - 4b^2 - 4bx - x^2 - 4b^2 - 4bx - x^2\\)\n\n\\(x^2 - 2bx - 2b^2 - 4b^2 - 4bx - x^2 = -4b^2 - 4bx - x^2 - 4b^2 - 4bx - x^2 - 4b^2 - 4bx - x^2 - 4b^2 - 4bx - x^2 - 4b^2 - 4bx - x^2 - 4b",
|
|
"gt_answers": "x + \\frac { 8 } { x } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1941.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + 111 + ",
|
|
"gt_answers": "\\frac { 3 } { 7 } + \\frac { 1 } { 4 } = \\frac { 1 9 } { 2 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1942.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x^2 - 4x + 1 = 0.",
|
|
"gt_answers": "x = - \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1943.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4v^2 + 2v + 3 = 0.\"",
|
|
"gt_answers": "4 . 5 \\frac { V ^ { 2 } } { r . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1944.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\cos(90^\\circ - 60^\\circ) = \\cos(30^\\circ) \\cos(30^\\circ) = \\cos(30^\\circ)^2 = 1 \\).",
|
|
"gt_answers": "\\angle A B E = 9 0 ^ { \\circ } - 6 0 ^ { \\circ } = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1945.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "2 \\div 1 6 = \\frac { 2 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1946.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 0 d m ^ { 2 } = 4 0 0 0 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1948.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "9 0 \\times \\frac { 7 } { 7 + 2 } = 7 0 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1949.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x - 3 = 0\\)",
|
|
"gt_answers": "\\frac { \\frac { 1 } { 4 } x ^ { 2 } - 2 a + 3 } { x - 2 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1950.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 1 = 3.",
|
|
"gt_answers": "2 \\frac { 3 } { 2 } = \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_1951.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "2 0 \\times 6 = 1 2 0 2 0 \\times 8 = 1 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1952.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4a^2 + 4b^2 - 5c^2 = 100\\)",
|
|
"gt_answers": "4 a ^ { 2 } + a ^ { 2 } - 2 0 a + 2 5 = 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1953.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: `ax^2 + bx + c = 0`.",
|
|
"gt_answers": "a \\times b \\times c = a \\times ( b \\times c )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1954.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Wi = 29.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "W _ { 1 } = - 2 ( x - 2 0 ) ^ { 2 } + 1 8 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1955.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2}",
|
|
"gt_answers": "\\cdot \\frac { \\sin A } { \\cos A } = \\frac { \\sin B } { \\cos B } = \\frac { \\sin C } { \\sin C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1957.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Cost = 2NH4 + 2NH3 + 2N2 + 2NH2 + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N + 2NH + 2N +",
|
|
"gt_answers": "C O _ { 2 } + 2 N a O H = N a 2 C O _ { 3 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_1958.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "2 n + H 2 S O _ { - 1 } = Z u S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_1960.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\left(x + 1\\right) + 3\\left(x - 1\\right) = 5x^2 + 6x - 3\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } T _ { n } = \\frac { 2 } { 2 } + \\frac { 3 } { 2 ^ { 2 } } + \\frac { 8 } { 2 ^ { 3 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1961.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(AD = 2^{3b - 6} - 9^{9 - 3b}\\)",
|
|
"gt_answers": "A D = 3 + 6 - t = 9 - t\n",
|
|
"image_path": "./data/HME100K/test_images/test_1962.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3 + 4 = 7 + 24 = 31.\"",
|
|
"gt_answers": "3 \\div 3 = 1 2 4 \\div 4 = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_1963.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(BTx = (47 \\times t) + (x^2 - 100)^2\\)",
|
|
"gt_answers": "1 3 + x = ( 4 7 + x ) \\times \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1964.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "+ \\frac { x + 2 } { x - 2 } = \\frac { 8 } { ( x + 2 ) ( x - 2 ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1965.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2} + \\frac{x}{2} + 1\\)",
|
|
"gt_answers": "( x - 2 y ) ( x - y ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1967.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 12 - 8 + 15 - 8 = 15.",
|
|
"gt_answers": "1 2 - 8 = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_1968.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2(x + 1) - 3(x - 2) = 0.",
|
|
"gt_answers": "\\frac { 3 \\pi } { 2 } + 2 k \\pi ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_1970.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\frac { 3 7 \\pm \\sqrt { 6 9 3 . } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1971.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(5 - 3) + 5(5 - 3) = 20 - 15 + 25 - 15 = 10.",
|
|
"gt_answers": "\\frac { 1 } { 5 } + \\frac { 2 } { 5 } - \\frac { 3 } { 5 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1972.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 1 = 7x + 1\" in LaTeX format.",
|
|
"gt_answers": "\\vert - 1 - x \\vert = 3 \\vert x \\vert - 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_1973.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(x^2 + 4x - 4 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x - \\frac { x + 9 } { 4 } = a\n",
|
|
"image_path": "./data/HME100K/test_images/test_1976.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"50x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x40x4",
|
|
"gt_answers": "5 0 \\times 4 0 - 4 0 \\times 4 0 = ( 4 0 + 6 0 ) \\times\n",
|
|
"image_path": "./data/HME100K/test_images/test_1977.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"H2O = H2 + O2.\"",
|
|
"gt_answers": "C O _ { 2 } + H _ { 2 } O = H _ { 2 } C O _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1978.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "\\frac { k x _ { 1 } - 1 } { x _ { 1 } } + \\frac { k x _ { 2 } - 1 } { x _ { 2 } } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1979.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(CABD-C400 = 15\\)",
|
|
"gt_answers": "\\angle A B D = \\angle B A O = 1 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1980.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "x k m / h\n",
|
|
"image_path": "./data/HME100K/test_images/test_1981.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 5\\)",
|
|
"gt_answers": "\\frac { x } { x + 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1982.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 0.444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444",
|
|
"gt_answers": "m \\% = \\frac { 0 . 4 g } { 1 g } \\times 1 0 0 \\% = 4 0 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_1983.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x = \\frac{2\\sqrt{2} - 1}{2\\sqrt{2} + 1}\\)",
|
|
"gt_answers": "x = \\frac { a - 2 } { ( a + 2 ) ( a - 2 ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1986.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis equation is a simple algebraic expression that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "x ^ { 2 } = \\frac { 3 } { a + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1987.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n(5x)2 = 12cm",
|
|
"gt_answers": "( 5 + 1 ) \\times 2 = 1 2 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_1989.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 2x^2 + 3x + 4.",
|
|
"gt_answers": "y = \\frac { x } { k }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1990.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 405-50=8.",
|
|
"gt_answers": "4 0 5 \\div 5 0 = 8 \\cdots 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_1992.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "\\rho _ { A } = \\frac { m _ { A } } { V _ { A } } = \\frac { 4 k y } { 2 \\times 1 0 ^ { - 7 } m ^ { 3 } } = 2 \\times 1 0 ^ { 3 } k g / m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1993.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"300 x 8 x 10^20 V^2/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "y = - 8 0 \\times \\frac { 3 0 0 } { 1 7 } + 2 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_1995.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "y _ { 2 } = \\frac { 1 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1996.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\nP = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "P = \\frac { w } { t } = \\frac { 6 0 J } { \\cos } = 6 w \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_1997.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x = - \\frac { 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_1998.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 1 = 3.\"",
|
|
"gt_answers": "\\frac { x ^ { 2 } } { 3 } + y ^ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_1999.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Russian, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a negative sign, which could be a mathematical expression in any language.",
|
|
"gt_answers": "K _ { A P } + K _ { B P } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2000.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 4.\"",
|
|
"gt_answers": "x = \\frac { 7 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2001.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 140202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020",
|
|
"gt_answers": "\\angle 1 6 0 ^ { \\circ } \\angle 2 6 0 ^ { \\circ } \\angle 3 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2002.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: CM = MW + TB.",
|
|
"gt_answers": "\\frac { C M } { M A } = \\frac { M N } { A B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2003.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{K_{24}K_{60}}{K_{24}K_{60}+K_{24}K_{60}}\n\\end{equation}\n\nThis equation represents the ratio of two different concentrations of potassium ions, K24 and K60, in a solution. The first concentration, K24, is given as the numerator, while the second concentration, K60, is given as the denominator. The result of the ratio is the ratio of the two concentrations, which is equal to the fraction of K60 in the solution.",
|
|
"gt_answers": "k ^ { 2 } - 4 - k ^ { 2 } - k - 6 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2004.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\angle A O D = 3 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2005.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x + 4y = 15\\)\n\nThis formula represents a linear equation in two variables, where the variables are x and y. The equation states that the sum of the products of x and y is equal to 15.",
|
|
"gt_answers": "1 5 . 7 \\div 3 . 1 4 = 5 ( d m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2006.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 8x3+4x2+6x1+8x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x2+8x1+4x4+4x3+6x",
|
|
"gt_answers": "4 8 \\times 3 1 = 1 4 8 8 4 5 \\times 7 6 = 3 4 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2008.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)\n\nThis formula represents a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { x + 2 } { 3 } - 2 ( x - 1 ) = - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2009.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: (4x3) - (3x10) + (2x20) = 0.",
|
|
"gt_answers": "( 4 x + 3 ) : 3 = ( 1 0 x - 2 ) :\n",
|
|
"image_path": "./data/HME100K/test_images/test_2012.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"B = CN + BN,\" where B is the bond energy, CN is the covalent bond energy, and BN is the bond energy of the nitrogen atom in the nitrogen molecule.",
|
|
"gt_answers": "\\frac { B C } { M D } = \\frac { C N } { B N }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2013.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `1x + 3 = 3x`.",
|
|
"gt_answers": "\\vert x - 1 \\vert = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2014.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(6-2m) - 2(8-2m) = 12 - 4m.",
|
|
"gt_answers": "( 8 - 2 m m - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2015.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_1 = 150 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8 \\times 0.8",
|
|
"gt_answers": "( 1 + 5 0 \\% ) \\cdot 8 0 \\% x - x = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_2016.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2\\alpha + 2\\beta = 2\\alpha + 2\\beta + 2\\alpha + 2\\beta = 4\\alpha + 4\\beta\\)\n\nThis formula can be rewritten as:\n\n\\(2\\alpha + 2\\beta = 4\\alpha + 4\\beta\\)\n\nThis is a simple algebraic equation that can be solved by adding both sides of the equation together:\n\n\\(2\\alpha + 2\\beta = 4\\alpha + 4\\beta + 2\\alpha + 2\\beta\\)\n\nSolving for the unknown variables, we get:\n\n\\(2\\alpha + 2\\beta = 4\\alpha + 4\\beta + 2\\alpha + 2\\beta = 8\\alpha + 8\\beta\\)\n\nTherefore, the formula is:\n\n\\(2\\alpha + 2\\beta = 8\\alpha + 8\\beta\\)\n\nThis formula can be used to calculate the sum of two angles in a triangle, where the angles are represented by the variables \\(\\alpha\\) and \\(\\beta\\).",
|
|
"gt_answers": "A l _ { 2 } O _ { 3 } + 2 N a O H = 2 N a A l O _ { 2 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2017.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(D_s = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\overrightarrow { D S } = ( \\frac { \\sqrt { 2 } } { 2 } a\n",
|
|
"image_path": "./data/HME100K/test_images/test_2018.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 8x3 = 16.",
|
|
"gt_answers": "\\Delta O A P 6 = \\frac { 8 \\times 3 } { 2 } = 1 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2019.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(v = 93 + 30 = 123\\)",
|
|
"gt_answers": "v = a ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2020.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(c^2 + d^2 = a^2 + b^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the hypotenuse. In this case, the sides are represented by the variables c, d, and a, and the hypotenuse is represented by the variable b.",
|
|
"gt_answers": "\\cos \\frac { \\alpha } { 2 } < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2021.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "\\because \\angle E A B = \\angle E A F + \\angle F A B = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2022.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(K_{eq} = \\frac{RT}{PV} = \\frac{8.3145 J/mol \\cdot K}{10^{-5} mol \\cdot L \\cdot K} = 8.3145 \\times 10^{-5} J/mol \\cdot K\\)",
|
|
"gt_answers": "\\sqrt { 1 + k ^ { 2 } } \\vert k + \\frac { 2 } { k ^ { 2 } } \\vert = \\frac { 3 \\sqrt { 1 + k ^ { 2 } } } { k ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2023.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{12x^2 + 12y^2 + 4xy + 4y^2}{12x^2 + 12y^2 + 4xy + 4y^2}\n\\end{equation}\n\nThis equation is a quadratic equation in the variables x and y, and it can be solved using the quadratic formula.",
|
|
"gt_answers": "1 2 \\times 1 2 = 1 4 4 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2024.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LDAO_{LDBO_{50}} = 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle D A O = \\angle D B O = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2025.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a2 - 2.",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2026.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nNaOH + H2SO4 + H2O --> Na2SO4 + 2H2O",
|
|
"gt_answers": "2 N a O H + S O _ { 3 } = N a _ { 2 } S O _ { 4 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2028.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "x _ { 1 } = 1 - \\frac { 1 } { 2 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2029.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 5x + 5}{x^2 + 5x + 5} = 1\n\\end{equation}\n\nThis equation can be simplified to:\n\n\\begin{equation}\nx^2 + 5x + 5 = 1 \\cdot (x^2 + 5x + 5)\n\\end{equation}\n\nThis can be further simplified to:\n\n\\begin{equation}\nx^2 + 5x + 5 = 1\n\\end{equation}\n\nThis is the final simplified expression of the formula in the image.",
|
|
"gt_answers": "\\frac { 3 } { 4 } \\times \\frac { 4 } { 5 } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2030.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { c } { a + b } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2031.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis is a simple algebraic equation that can be solved using the addition and multiplication rules of algebra.",
|
|
"gt_answers": "x ^ { 2 } = \\frac { a ^ { 2 } } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2032.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"27 + 36 = 63.\"",
|
|
"gt_answers": "( 1 7 ) + ( 5 0 ) = ( 6 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_2033.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2H2SO4 + H2SO4 = 2H2SO4 + 2H2SO4.",
|
|
"gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_2034.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1500mm = 1500/1000m^2.",
|
|
"gt_answers": "1 5 d m ^ { 2 } = 1 5 0 0 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2036.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "a + 1 6 a - 3 6 = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_2037.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 40/9.3 = 4.266666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666",
|
|
"gt_answers": "\\frac { 4 0 } { 3 6 \\cdot 5 } = \\frac { 0 \\cdot 8 g } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2038.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 5x - 10 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 9 - 3 y } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2039.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\tan \\alpha = - \\sqrt { 3 } , \\frac { 3 \\pi } { 2 } < a < 2 \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_2040.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{3} \\left( \\frac{1}{4} \\left( \\frac{1}{5} \\left( \\frac{1}{6} \\left( \\frac{1}{7} \\left( \\frac{1}{8} \\left( \\frac{1}{9} \\left( \\frac{1}{10} \\left( \\frac{1}{11} \\left( \\frac{1}{12} \\left( \\frac{1}{13} \\left( \\frac{1}{14} \\left( \\frac{1}{15} \\left( \\frac{1}{16} \\left( \\frac{1}{17} \\left( \\frac{1}{18} \\left( \\frac{1}{19} \\left( \\frac{1}{20} \\left( \\frac{1}{21} \\left( \\frac{1}{22} \\left( \\frac{1}{23} \\left( \\frac{1}{24} \\left( \\frac{1}{25} \\left( \\frac{1}{26} \\left( \\frac{1}{27} \\left( \\frac{1}{28} \\left( \\frac{1}{29} \\left( \\frac{1}{30} \\left( \\frac{1}{31} \\left( \\frac{1}{32} \\left( \\frac{1}{33} \\left( \\frac{1}{34} \\left( \\frac{1}{35} \\left( \\frac{1}{36} \\left( \\frac{1}{37} \\left( \\frac{1}{38} \\left( \\frac{1}{39} \\left( \\frac{1}{40} \\left( \\frac{1}{41} \\left( \\frac{1}{42} \\left( \\frac{1}{43} \\left( \\frac{1}{44} \\left( \\frac{1}{45} \\left( \\frac{1}{46}",
|
|
"gt_answers": "t = - \\frac { 9 ( 1 - \\sqrt { 3 } ) } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2041.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the chemical formula notation, which is a standard way to represent chemical compounds. The formula is written as H2O2, where H represents hydrogen, O represents oxygen, and 2 represents the number of oxygen atoms.",
|
|
"gt_answers": "H _ { 2 } C O _ { 3 } = C O _ { 2 } \\uparrow + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2042.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { P ^ { 2 } } { 4 } + P ^ { 2 } = - \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2043.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2xy} = \\frac{2x^2 + 3xy + y^2}{x^2 + y^2 + 2",
|
|
"gt_answers": "x ^ { 2 } + 2 x + 1 = \\frac { 2 } { x ^ { 2 } + 2 x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2044.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 10x11 - 4x11 + 11x11.",
|
|
"gt_answers": "1 0 \\times \\frac { 5 } { 1 1 } = 4 \\frac { 6 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2045.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x^2 - 6x + 6.",
|
|
"gt_answers": "x = 6 \\div \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2047.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "- 5 \\leq x + y + z \\leq 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2048.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Oe-2aC.\"",
|
|
"gt_answers": "O E / / A C . O E = \\frac { 1 } { 2 } A C\n",
|
|
"image_path": "./data/HME100K/test_images/test_2049.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 160\\)",
|
|
"gt_answers": "1 8 0 ^ { \\circ } - 4 5 ^ { \\circ } - 8 0 ^ { \\circ } = 5 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2051.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 1234567890 + 12345678",
|
|
"gt_answers": "1 2 7 + 1 2 7 + 5 3 = 1 7 0 (\n",
|
|
"image_path": "./data/HME100K/test_images/test_2052.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5x8 = 35.",
|
|
"gt_answers": "\\frac { 1 } { 5 } \\times \\frac { 5 } { 8 } = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2053.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{4} \\right) = \\frac{1}{4}\n\\end{equation}\n\nThis formula can be interpreted as finding the quotient of two fractions with denominators of 2 and 4, respectively. The result is the fraction with a denominator of 4.",
|
|
"gt_answers": "x = \\frac { 6 } { 7 } \\div \\frac { 2 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2054.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 5.",
|
|
"gt_answers": "C H = \\frac { 2 \\sqrt { 5 } } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2055.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 3x + 2 = 10.",
|
|
"gt_answers": "x = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2057.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a few Chinese characters and some numbers.",
|
|
"gt_answers": "x _ { 2 } = \\frac { 1 - \\sqrt { 5 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2058.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a mathematical equation or a chemical formula.",
|
|
"gt_answers": "y = \\frac { 1 } { 2 } x ^ { 2 } - \\frac { 5 } { 2 } x + 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2059.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(b_n = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "b _ { n } = \\frac { 1 } { n a _ { n } } = \\frac { 1 } { 1 + n }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2060.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x^{2} + y^{2}} = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2 \\frac{xy}{x^{2} + y^{2}}\n\\end{equation}\n\nThis equation can be simplified further by rearranging terms and using the distributive property of multiplication:\n\n\\begin{equation}\n\\frac{1}{x^{2} + y^{2}} = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - \\frac{2xy}{x^{2} + y^{2}} = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - \\frac{2x}{x^{2}} - \\frac{2y}{y^{2}} = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - \\frac{2x}{x^{2}} - \\frac{2y}{y^{2}} + 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2xy + 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} - 2xy = \\frac{1}{x^{2}} + \\frac{1}{y^{2}} -",
|
|
"gt_answers": "y \\frac { - e ^ { x } } { x } ( x \\neq 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2061.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "C H _ { 3 } C O O H + C H _ { 3 } O H = N a O H \\rightarrow C H _ { 3 } C O O N a + C H _ { 3 } O H + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2062.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 - 20x + 10.",
|
|
"gt_answers": "x = 2 _ { 4 } - \\frac { 2 0 } { 3 k - 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2063.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 2x + 2 = 4x^2 + 4x + 4\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x _ { 1 } = - 2 + 2 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2064.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "s ( x + \\beta ) \\sin ( \\alpha - \\beta ) = - \\frac { 5 6 } { 6 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2066.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 9.\"",
|
|
"gt_answers": "x = \\frac { 4 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2067.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(4x^2 + 5x + 6 = 15\\)",
|
|
"gt_answers": "4 \\times 6 + ( 4 \\times 1 . 5 + 6 \\times 1 . 5 ) \\times 2 = 5 4 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2068.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x^2 + 3x - 4 = 0.",
|
|
"gt_answers": "x = \\frac { 4 \\pi } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2069.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 2y = 7.",
|
|
"gt_answers": "\\frac { 2 + x } { 2 } > \\frac { 2 x - 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2070.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"sin(a) = 4/5\".",
|
|
"gt_answers": "\\sin a = - \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2071.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x = \\frac { 1 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2072.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"13 + 6 = 22.\"",
|
|
"gt_answers": "\\frac { 1 3 } { 6 } = 1 3 \\div 6 = 2 \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2073.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x2 = 48 cm.",
|
|
"gt_answers": "4 \\times 6 \\times 2 = 4 8 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2074.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3m = 30dm.",
|
|
"gt_answers": "3 m = 3 0 d m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2075.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(m = \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left(",
|
|
"gt_answers": "1 m ^ { 2 } 5 0 d m ^ { 2 } = 1 . 5 m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2077.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as y = 4x - 3.",
|
|
"gt_answers": "y _ { 4 } = - \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2078.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "m = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2079.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "y _ { 2 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2080.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 12.",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2081.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nF = 5 x 2 x 10^(-19) x 10^(-19) = 5 x 2 x 10^(-38) x 10^(-38) = 5 x 2 x 10^(-68)",
|
|
"gt_answers": "P = \\frac { F } { S } = \\frac { 1 0 N } { 2 \\times 1 0 ^ { 2 } m ^ { 2 } } = 5 0 0 P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_2082.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: CaCO3 + CO2 = CaCO3 + CO2.",
|
|
"gt_answers": "C a ( O H ) _ { 2 } + C O _ { 2 } = C a C O _ { 3 } \\downarrow + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2087.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 2x + 3.",
|
|
"gt_answers": "x = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2088.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 3NO2 + H2O + 2HNO3 \u2192 2H2O + 2NO3- + 2H+ + 2OH-",
|
|
"gt_answers": "3 N O _ { 2 } + H _ { 2 } O \\rightarrow 2 H N O _ { 3 } + N O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2089.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4.555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2090.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 6 - 5 + 4 = 15.",
|
|
"gt_answers": "6 \\div \\frac { 1 } { 9 } = 5 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2091.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: (0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\overrightarrow { C B } = ( 0 , 4 , 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2092.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_{12}O_{6} + 2H_{2}O \\rightarrow 2CO_{2} + 3H_{2} + 2H_{2}O\\)",
|
|
"gt_answers": "\\angle 1 = \\angle B A D\n",
|
|
"image_path": "./data/HME100K/test_images/test_2093.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x^2 + 3y^2 - 9xy - 9y^2 = 0\\)\n\nThis formula can be simplified to:\n\n\\(3x^2 + 3y^2 - 9xy = 0\\)\n\nThe formula can also be written as:\n\n\\(3x^2 + 3y^2 - 9xy = 0 - 9xy\\)\n\nThis can be further simplified to:\n\n\\(3x^2 + 3y^2 - 9xy = 9xy - 9xy = 0\\)\n\nFinally, the simplified formula can be written as:\n\n\\(3x^2 + 3y^2 = 0\\)\n\nThis is the quadratic equation in two variables.",
|
|
"gt_answers": "a _ { 2 } = \\frac { 3 - \\sqrt { 1 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2094.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "A D = O G = \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2095.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as CH2Cl2.",
|
|
"gt_answers": "C H _ { 2 } = C H L O O H\n",
|
|
"image_path": "./data/HME100K/test_images/test_2096.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Sac-813\" using a handwritten font.",
|
|
"gt_answers": "S _ { \\Delta C D O } = \\frac { 3 } { 8 } \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2097.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 4 } \\times 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2098.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(Cosasina - 5) + 5.",
|
|
"gt_answers": "2 \\cos a \\sin a ^ { 5 } = - \\frac { 2 4 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2099.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x _ { 1 } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2100.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 30:20 = 6:4.",
|
|
"gt_answers": "3 0 : 2 0 = 6 : 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2101.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\n\\(S_{AB} = \\frac{1}{2} \\left( \\sqrt{A^2 + B^2} + \\sqrt{A^2 - B^2} \\right)\\)\n\nThe formula is written in LaTeX format using the `\\sqrt` function to calculate the square root of the given numbers.",
|
|
"gt_answers": "\\therefore \\frac { S _ { \\Delta A E F } } { S _ { \\Delta A B C } } = ( \\frac { A E } { A B } ) ^ { 2 } = \\frac { A E \\cdot A F } { A B \\cdot A C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2102.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( 1 - P ) ^ { 4 } = \\frac { 1 } { 8 1 } \\therefore P = \\frac { 1 } { 3 } \\therefore P = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2103.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(z^2 + 2z - 4 = 0\\)",
|
|
"gt_answers": "2 - 2 a = 4 - 2 a = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2104.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A + E = C + D.\"",
|
|
"gt_answers": "A E \\cdot C D = A D \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_2105.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b_{f} = \\frac{1}{2} \\left(b_{i} + b_{o}\\right)\\)\n\nThis formula represents the balance of forces acting on a body, where b_{f} is the net force acting on the body, b_{i} is the force acting inward, and b_{o} is the force acting outward.",
|
|
"gt_answers": "b + 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2106.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 0 0 \\times 1 0 0 \\times \\frac { 1 } { 1 0 0 0 0 0 } = 4 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2107.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 3j^2\\)",
|
|
"gt_answers": "x + 1 = \\sqrt [ 3 ] { 2 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2108.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as Fe(OH)3(s) + 2FeCl3(aq) + 3H2O(l) --> Fe3O4(s) + 6HCl(aq) + 3H2O(l).",
|
|
"gt_answers": "F e _ { 2 } O _ { 3 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2109.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07 x 0.05 x 0.07",
|
|
"gt_answers": "\\tan \\angle A D C = 0 . 7 5 = \\frac { 3 } { 4 } = \\frac { A C } { C D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2110.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3.14 \\times 10^{14} = 3.14 \\times 10^{14} \\times 10^{14} = 3.14 \\times 10^{28}\\)",
|
|
"gt_answers": "3 . 1 4 \\times 1 = 3 . 1 4 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2111.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_1 = \\frac{1068}{99 \\times 10^{0.48}} = 1.078\\)",
|
|
"gt_answers": "C \\% = \\frac { 1 0 . 6 g } { 1 1 g } \\times 1 0 0 \\% \\approx 9 6 . 4 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_2112.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(2x + 1) - 3(x - 1) = 2x^2 - 3x + 2.",
|
|
"gt_answers": "0 - \\frac { ( 1 + x ) ^ { 2 } } { 9 } = - \\frac { 1 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2114.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"2x + 13 = 20.\"",
|
|
"gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2115.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 199\\)\n\nThis formula represents a quadratic equation, where x and y are the variables and 199 is the constant. The equation can be solved using the quadratic formula, which is:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\)\n\nIn this case, the quadratic formula simplifies to:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4(199)}}{2(199)} = \\frac{-b \\pm \\sqrt{b^2 - 990}}{2(199)} = \\frac{-b \\pm \\sqrt{b^2 - 499}}{2(199)} = \\frac{-b \\pm 25}{2(199)} = \\frac{-b \\pm 12.5}{2(199)} = \\frac{-b \\pm 6}{2(199)} = \\frac{-b \\pm 3}{2(199)} = \\frac{-b \\pm 1.5}{2(199)} = \\frac{-b \\pm 0.75}{2(199)} = \\frac{-b \\pm 0.375}{2(199)} = \\frac{-b \\pm 0.1875}{2(199)} = \\frac{-b \\pm 0.09375}{2(199)} = \\frac{-b \\pm 0.046875}{2(199)} = \\frac{-b \\pm 0.0234375}{2(199)} = \\frac{-b \\pm 0.01171875}{2(199)} = \\frac{-b \\pm 0.005859375}{2(199)} = \\frac{-b \\pm 0.0029296875}{2(199)} = \\frac{-b \\pm 0.00146484375}{2(199)}",
|
|
"gt_answers": "\\frac { 1 0 6 } { 5 0 } = \\frac { 1 0 . 6 g } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2116.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: \"A(B + C) = AB + AC.\"",
|
|
"gt_answers": "A ( - 2 , 0 ) , B ( 0 , 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2118.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nK_{3} = K_{2} + K_{1}\n\nThis formula represents the relationship between the three constants K_{1}, K_{2}, and K_{3}, where K_{1} is the equilibrium constant for the reaction A + B --> C, K_{2} is the equilibrium constant for the reaction B + C --> A, and K_{3} is the equilibrium constant for the reaction C + A --> B.",
|
|
"gt_answers": "k _ { 3 } = \\frac { k _ { 1 } } { k _ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2119.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(BAC_i = \\frac{300}{100} \\times \\frac{100}{100} \\times \\frac{100}{100} = 300\\)",
|
|
"gt_answers": "\\angle B A C = 5 0 ^ { \\circ } + 3 0 ^ { \\circ } = 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2120.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(cos^2(d) + sin^2(d) = 1\\)",
|
|
"gt_answers": "\\cos ^ { 2 } \\alpha = \\frac { 1 } { 1 + \\tan ^ { 2 } \\alpha } = \\frac { 1 6 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2122.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nBa = 2ty\n\nThe formula represents the relationship between the base area (Ba) and the height (y) of a right triangle.",
|
|
"gt_answers": "B Q = \\frac { 8 } { 2 + x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2124.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x _ { 2 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2125.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "C O S A = \\frac { 5 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2126.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten format, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a few letters and numbers, which can be represented in LaTeX as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\text{Formula}\n\\end{aligned}\n\\end{equation}",
|
|
"gt_answers": "\\frac { 9 } { 6 } x = \\frac { 7 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2127.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(0.5 \\times 3 \\times 4 \\times 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 . 2 5 \\times 3 . 4 = 0 . 7 6 . 0 0 1 . 5 \\times 1 1 . 2 4 = 1 8 . 0 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2128.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "3 . 1 4 \\times ( 6 \\div 2 ) ^ { 2 } \\times 1 0 + 3 . 1 4 \\times ( 6 \\div 2 ) ^ { 2 } \\times 4 \\times \\frac { 1 } { 3 } 3 2 0 . 2 8 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2129.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 18\\)",
|
|
"gt_answers": "1 8 ( x + 5 ) + 6 ( x + 2 ) ( x - 1 ) = 5 ( x + 2 ) ( x + 5 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2130.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(y = \\frac{x^2}{2} + \\frac{x^3}{3} + \\frac{x^4}{4} + \\frac{x^5}{5} + \\frac{x^6}{6} + \\frac{x^7}{7} + \\frac{x^8}{8} + \\frac{x^9}{9} + \\frac{x^{10}}{10} + \\frac{x^{11}}{11} + \\frac{x^{12}}{12} + \\frac{x^{13}}{13} + \\frac{x^{14}}{14} + \\frac{x^{15}}{15} + \\frac{x^{16}}{16} + \\frac{x^{17}}{17} + \\frac{x^{18}}{18} + \\frac{x^{19}}{19} + \\frac{x^{20}}{20} + \\frac{x^{21}}{21} + \\frac{x^{22}}{22} + \\frac{x^{23}}{23} + \\frac{x^{24}}{24} + \\frac{x^{25}}{25} + \\frac{x^{26}}{26} + \\frac{x^{27}}{27} + \\frac{x^{28}}{28} + \\frac{x^{29}}{29} + \\frac{x^{30}}{30} + \\frac{x^{31}}{31} + \\frac{x^{32}}{32} + \\frac{x^{33}}{33} + \\frac{x^{34}}{34} + \\frac{x^{35}}{35} + \\frac{x^{36}}{36} + \\frac{x^{37}}{37} + \\frac{x^{38}}{38} + \\frac{x^{39}}{39} + \\frac{x^{40}}{40} + \\frac{x^{41}}{41} + \\frac{x^{42}}{42} + \\frac{x^{43}}{43} + \\frac{x^{44",
|
|
"gt_answers": "\\frac { x } { x ^ { 2 } y - y } \\div \\frac { x y } { x ^ { 2 } + x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2131.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x + 2y = 5\\)\n\nThis is a simple algebraic equation that can be solved using the addition and subtraction operations.",
|
|
"gt_answers": "\\frac { 4 } { 5 } + \\frac { 1 } { 5 } - \\frac { 2 } { 5 } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2132.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x - 3 = 0\\)",
|
|
"gt_answers": "x = \\alpha - \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2133.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\n2x^2 + 3x + 4 = 0\n\\end{equation}\n\nThe equation is written in the form of an equation with two variables, x and y, and an expression involving the variables. The equation is also written in the form of an equation with an equal sign, which indicates that the two sides of the equation are equal.",
|
|
"gt_answers": "x = 2 + \\frac { 2 } { 3 } y\n",
|
|
"image_path": "./data/HME100K/test_images/test_2134.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{8} \\left( \\frac{1}{16} \\left( \\frac{1}{32} \\left( \\frac{1}{64} \\left( \\frac{1}{128} \\left( \\frac{1}{256} \\left( \\frac{1}{512} \\left( \\frac{1}{1024} \\left( \\frac{1}{2048} \\left( \\frac{1}{4096} \\left( \\frac{1}{8192} \\left( \\frac{1}{16384} \\left( \\frac{1}{32768} \\left( \\frac{1}{65536} \\left( \\frac{1}{131072} \\left( \\frac{1}{262144} \\left( \\frac{1}{524288} \\left( \\frac{1}{1048576} \\left( \\frac{1}{2097152} \\left( \\frac{1}{4194304} \\left( \\frac{1}{8388608} \\left( \\frac{1}{16777216} \\left( \\frac{1}{33554432} \\left( \\frac{1}{67108864} \\left( \\frac{1}{134217728} \\left( \\frac{1}{268435456} \\left( \\frac{1}{536870912} \\left( \\frac{1}{1073741824} \\left( \\frac{1}{2147483648} \\left( \\frac{1}{4294967296} \\left( \\frac{1}{8589934592} \\left( \\frac{1}{16",
|
|
"gt_answers": "\\frac { 3 } { 5 } x \\div \\frac { 3 } { 5 } = 2 4 \\div \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2136.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "y _ { 1 } - y _ { 2 } = x _ { 1 } ^ { 2 } - x _ { 2 } ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2137.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in a different language.",
|
|
"gt_answers": "\\frac { I } { I _ { 2 } } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2138.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nb^2 + 0 = 0\n\nThis is a quadratic equation in the variable b, with the constant term 0 on the left side and the quadratic term b^2 on the right side. The equation has no solutions, as the quadratic term is zero, which means that the equation has no real roots.",
|
|
"gt_answers": "( b + 2 ) \\neq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2141.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(AB + 2AB = 2A^2 + B^2\\)\n\nThis formula can be written using the following LaTeX code:\n\n\\begin{equation}\nAB + 2AB = 2A^2 + B^2\n\\end{equation}\n\nThe equation is a quadratic equation, which means that it has the form of a quadratic function with two variables. The variables in this equation are A and B, and the function is represented by the expression AB + 2AB. The equation can be solved using the quadratic formula, which involves finding the square root of the expression on the left side of the equation.",
|
|
"gt_answers": "- \\frac { 1 } { 2 } \\frac { A B ^ { 2 } + C B ^ { 2 } - A C ^ { 2 } } { 2 A B \\cdot C B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2142.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244836244",
|
|
"gt_answers": "x = 2 \\times 4 . 8 \\div ( 2 . 4 + 3 . 6 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2143.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 + c^2 = (a + b + c)^2\\)",
|
|
"gt_answers": "a ^ { 2 } = b ^ { 2 } + c ^ { 2 } - \\frac { 4 \\sqrt { 2 } } { 3 } b c\n",
|
|
"image_path": "./data/HME100K/test_images/test_2145.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5x6-10.",
|
|
"gt_answers": "5 x = 5 \\times 6 = 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2148.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 4x + 6 = 6(x^2 + 2x + 3)\\)",
|
|
"gt_answers": "1 2 \\times 4 \\times \\frac { 1 } { 3 } = 1 6 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2149.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5x + 12.",
|
|
"gt_answers": "\\frac { 5 } { 8 } x = \\frac { 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2151.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(a + b = c\\)\n\nThis is a basic algebraic equation that represents the addition of two numbers.",
|
|
"gt_answers": "\\overrightarrow { A D } = \\frac { 1 } { 2 } ( \\overrightarrow { A B } + \\overrightarrow { A C } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2152.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "\\pm \\sqrt { m ^ { 2 } - 4 m } = - 2 + 2 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2153.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 - 12x + 60.",
|
|
"gt_answers": "\\frac { x - ( - b ) } { 2 } < 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2154.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"11m + 11n = 49.\"",
|
|
"gt_answers": "1 1 4 m + 6 n = 4 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_2155.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "\\vert - \\frac { \\sqrt { 2 } } { 3 } \\vert = \\frac { \\sqrt { 2 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2156.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1.5 x 0.005 = 0.075.",
|
|
"gt_answers": "1 . 5 \\times 0 . 5 = 0 . 7 5 m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2157.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nP = W/T\n\nwhere P is the power (watts) and T is the time (seconds).",
|
|
"gt_answers": "P = \\frac { w } { t }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2158.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "a b = 1 4 2 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_2159.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(L = \\frac{AB}{C} + \\frac{BC}{D} + \\frac{CD}{E} + \\frac{DE}{F} + \\frac{EF}{G} + \\frac{GF}{H} + \\frac{HF}{I} + \\frac{IJ}{K} + \\frac{KJ}{L} + \\frac{LL}{M} + \\frac{MN}{O} + \\frac{ON}{P} + \\frac{PQ}{R} + \\frac{RQ}{S} + \\frac{SQ}{T} + \\frac{TU}{V} + \\frac{VW}{X} + \\frac{XY}{Z} + \\frac{ZW}{AB} + \\frac{AB}{CD} + \\frac{CD}{EF} + \\frac{EF}{GH} + \\frac{GH}{IJ} + \\frac{IJ}{KL} + \\frac{KL}{MN} + \\frac{MN}{OP} + \\frac{OP}{PQ} + \\frac{PQ}{RS} + \\frac{RS}{TU} + \\frac{TU}{VW} + \\frac{VW}{XY} + \\frac{XY}{ZW} + \\frac{ZW}{AB} + \\frac{AB}{CD} + \\frac{CD}{EF} + \\frac{EF}{GH} + \\frac{GH}{IJ} + \\frac{IJ}{KL} + \\frac{KL}{MN} + \\frac{MN}{OP} + \\frac{OP}{PQ} + \\frac{PQ}{RS} + \\frac{RS}{TU} + \\frac{TU}{VW} + \\frac{VW}{XY} + \\frac{XY}{ZW} + \\frac{ZW}{AB} + \\frac{AB}{CD} + \\frac{CD}{EF} + \\frac{EF}{GH} + \\frac{GH}{IJ} + \\frac{IJ}{KL} + \\frac{KL}{MN} + \\frac{MN}{OP} + \\frac{OP}{PQ} +",
|
|
"gt_answers": "\\angle A B C = \\angle A C B = 5 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2160.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 99 - 15 + 10 = 104\\)",
|
|
"gt_answers": "\\angle A D E = 9 0 ^ { \\circ } - 7 5 ^ { \\circ } = 1 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2161.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "( 1 0 0 + 9 9 9 ) \\times 9 9 9 \\div 2 = 1 0 9 7 9 0 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2162.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A + B = C\\)",
|
|
"gt_answers": "A E = \\frac { 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2165.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LDTE = 30\u00b0.\"",
|
|
"gt_answers": "\\angle D B E = 3 0 ^ { \\circ } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_2166.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"0 = 45\".",
|
|
"gt_answers": "\\square = 4 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2167.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "z = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2168.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"DOOCC = ACAC.\"",
|
|
"gt_answers": "A O = O C = \\frac { 1 } { 2 } A C\n",
|
|
"image_path": "./data/HME100K/test_images/test_2169.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\nb^2 + 4ac = 4(a^2 + b^2)",
|
|
"gt_answers": "b ^ { 2 } - 4 a c = ( 4 + k )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2170.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(O_{DJ3} = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2}",
|
|
"gt_answers": "O D = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2172.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 9x2 + 3x3 = 18x.",
|
|
"gt_answers": "\\frac { 9 } { 1 0 } \\times \\frac { 2 } { 3 } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2174.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 1 4 \\div 7 8 . 5 = 4 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2175.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\sqrt { 2 } < k < \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2176.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"C = 2t + 3\" using LaTeX format.",
|
|
"gt_answers": "t = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2177.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ADDO, DOXL.\"",
|
|
"gt_answers": "A D + D O = A O , D O = x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2178.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x _ { 3 } = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2179.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "a _ { n } - a _ { 1 } = ( 2 \\times 1 - 1 ) + ( 2 \\times 1 - 1 ) + ( 2 \\times 4 - 1 ) + \\cdots + 2 n - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2180.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b^2 + 4ac = 4b^2 + 4ac\\)",
|
|
"gt_answers": "\\cdot b ^ { 2 } - 4 a c = 7 ^ { 2 } - 4 \\times 1 \\times 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2181.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\sin(x) = \\frac{sin(60^\\circ)}{sin(x)} \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(x) \\cdot \\sin(60^\\circ) \\cdot \\sin(",
|
|
"gt_answers": "E F = C F \\cdot \\sin C = ( 6 0 - 2 0 \\sqrt { 3 } ) \\times \\sin 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2182.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4} \\).",
|
|
"gt_answers": "y _ { 3 } = - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2183.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{P_1 + P_2 + P_3 + P_4}{4} = P_1 + P_2 + P_3 + P_4\n\\end{equation}\n\nThis formula states that the sum of the four pressures (P1, P2, P3, and P4) is equal to the sum of the four pressures divided by four.",
|
|
"gt_answers": "P F _ { 1 } ^ { 2 } + P F _ { 2 } ^ { 2 } = 4 c ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2184.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2x^2 + 3x - 5 = 0.",
|
|
"gt_answers": "5 \\frac { 1 } { 2 } - 3 \\times 1 = a + \\frac { 1 } { 4 } \\times 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2185.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(N = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) \\right) = \\frac{1}{4} + \\frac{1}{4} = \\frac{3}{4}\\)",
|
|
"gt_answers": "\\frac { 8 n } { 8 } = n\n",
|
|
"image_path": "./data/HME100K/test_images/test_2186.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(AB + BC + CA = 1\\)\n\nThis formula represents the sum of the three sides of a triangle, where A, B, and C are the lengths of the sides. The equation is written in the form of an equation with the variables A, B, and C on the left side, and the constant 1 on the right side.",
|
|
"gt_answers": "A B ^ { 2 } = B C ^ { 2 } + C A ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2188.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 400 - 200 = 200.",
|
|
"gt_answers": "\\frac { 4 0 } { 1 0 0 } = \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2189.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle A E B = \\angle 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2190.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(q = \\frac{p}{9}\\)\n\nwhere q is the quotient and p is the numerator.",
|
|
"gt_answers": "9 = \\frac { 9 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2191.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x - 4.",
|
|
"gt_answers": "x \\leq 4 \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2192.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(C_2O_3 + O_2 + CO_2 = 2CO + 2H_2O\\)",
|
|
"gt_answers": "\\frac { C D } { C B } = \\frac { \\sqrt { 2 } } { 3 \\sqrt { 3 } } = \\frac { 1 } { 3 } = \\frac { O A } { O C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2193.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the Greek alphabet, and it is not possible to write it out in LaTeX format without knowing the exact Greek letters used. However, the image shows a formula that involves the Greek letters \"alpha,\" \"beta,\" \"gamma,\" and \"delta.\"",
|
|
"gt_answers": "\\Delta A B C \\sim \\Delta B P D \\sim \\Delta A P F\n",
|
|
"image_path": "./data/HME100K/test_images/test_2194.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "( 2 x + 3 ) ^ { 2 } - ( 3 x + 3 ) = 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2195.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 2y^2 + 2z^2 + 2xy + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + 2xz + 2yz + ",
|
|
"gt_answers": "\\frac { 1 - a } { 2 - 4 a + 2 a ^ { 3 } } = \\frac { a + 3 } { 2 ( a + 3 ) ( a - 1 ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2196.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3xy + 4y^2 = 100x + 102y + 104\\)\n\nThe formula can be written in LaTeX as follows:\n\n\\(2x^2 + 3xy + 4y^2 = 100x + 102y + 104\\)\n\nThe formula is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "\\frac { 1 0 0 } { x } - 1 = \\frac { 1 3 5 } { 2 5 - x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2197.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written in the form of a mathematical equation, with the letters \"A\" and \"B\" representing variables. The formula is written in a way that it can be easily read and understood by those familiar with the notation.",
|
|
"gt_answers": "\\Delta A O B \\cong \\Delta C O D ( A S A )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2198.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x = 0.795 \\times 30 \\times 0.007\\)",
|
|
"gt_answers": "1 5 x + ( 3 0 + 1 5 ) \\times 0 . 0 7 = 7 . 9 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2199.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\ce{CaCO3 + 2H2O -> Ca(OH)2 + CO2 + H2}\n\\end{equation}\n\nThis formula represents the chemical reaction between calcium carbonate (CaCO3) and water (H2O) to produce calcium hydroxide (Ca(OH)2), carbon dioxide (CO2), and water (H2).",
|
|
"gt_answers": "C a ( O H ) _ { 2 } + C O _ { 2 } = C a C O _ { 3 } \\downarrow + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2200.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 10.\"",
|
|
"gt_answers": "2 5 2 \\div 2 + 5 6 = 1 8 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2201.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{3x + 2y}{x + 2y} = 3 + \\frac{2y}{x + 2y}\n\\end{equation}\n\nThis equation can be simplified by rearranging the terms and using the distributive property of multiplication:\n\n\\begin{equation}\n\\frac{3x + 2y}{x + 2y} = \\frac{3x}{x + 2y} + \\frac{2y}{x + 2y} = 3 + \\frac{2y}{x + 2y}\n\\end{equation}\n\nThe simplified equation can be further simplified by using the fact that 3 + 2y = 5:\n\n\\begin{equation}\n\\frac{3x + 2y}{x + 2y} = 5\n\\end{equation}\n\nThis equation can be written in a more compact form using the fraction bar notation:\n\n\\begin{equation}\n\\frac{3x + 2y}{x + 2y} = \\frac{3x + 2y}{5}\n\\end{equation}\n\nThe final expression of the formula is:\n\n\\begin{equation}\n\\frac{3x + 2y}{x + 2y} = \\frac{3x + 2y}{5}\n\\end{equation}\n\nThis equation can be further simplified by using the fact that 5 is a common factor of both the numerator and denominator:\n\n\\begin{equation}\n\\frac{3x + 2y}{x + 2y} = \\frac{3x + 2y}{5} = \\frac{3x + 2y}{5 \\cdot 1} = \\frac{3x + 2y}{5}\n\\end{equation}\n\nThe final expression of the formula is:\n\n\\begin{equation}\n\\frac{3x + 2y}{x + 2y} = \\frac{3x + 2y}{5}\n\\end{equation}\n\nThis equation can be written in a more compact form using the fraction bar notation:\n\n\\begin{equation}\n\\frac{3x + ",
|
|
"gt_answers": "\\frac { 3 } { 2 } x + \\frac { x } { 5 } = \\frac { 3 } { \\pi } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2202.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(AS = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "- \\frac { b } { 2 a } = \\frac { 2 } { - 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2203.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{28} - 2^{27} + 2^{26} - 2^{25} + 2^{24} - 2^{23} + 2^{22} - 2^{21} + 2^{20} - 2^{19} + 2^{18} - 2^{17} + 2^{16} - 2^{15} + 2^{14} - 2^{13} + 2^{12} - 2^{11} + 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 1 = 5898749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918749187491874918",
|
|
"gt_answers": "2 8 1 - 2 2 3 = 5 8 ( g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2204.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\nGlu + H2O + H2S = Cus + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2S + H2O + H2",
|
|
"gt_answers": "C u O + H _ { 2 } S O _ { 4 } = C u S O _ { 4 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2205.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1/x^2 + 1/x + 1 = 0.",
|
|
"gt_answers": "\\frac { 7 } { 8 } \\{ x + 7 x - 1 - 7 \\} = 1 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2206.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4x^2 + 4x + 4 = 16.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x - \\frac { 1 } { 4 } x - \\frac { 1 } { 4 } = \\frac { 2 } { 3 } x - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2207.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with two variables, x and y, and an expression involving the square root of x squared and y squared.",
|
|
"gt_answers": "x - y = \\frac { 1 } { 2 - \\sqrt { 3 } } - \\frac { 1 } { 2 + \\sqrt { 3 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2208.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/2 + 1/2 = 1\".",
|
|
"gt_answers": "x - 1 = \\pm 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2209.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 3x + 2 = 0.\"",
|
|
"gt_answers": "x = - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2210.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\ny = a(x - h)2 + k\n\nwhere y is the output variable, a is a constant, x is the input variable, h is the offset, and k is the constant.",
|
|
"gt_answers": "y = a ( x - h + 2 ) ^ { 2 } + k\n",
|
|
"image_path": "./data/HME100K/test_images/test_2211.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 - 5x + 15.",
|
|
"gt_answers": "x _ { 4 } = - \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2212.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\cos \\angle A C B = \\sqrt { 1 - \\sin ^ { 2 } \\angle A C B } = \\frac { 2 \\sqrt { 7 } } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2213.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(g = \\frac{GMm}{r^2}\\)\n\nwhere:\n\n* `g` is the gravitational constant, which is a constant value equal to 6.67408 \u00d7 10^{-11} m^3 kg^-1 s^-2.\n* `M` is the mass of the object, which is the mass of the Earth in this case.\n* `m` is the mass of the object being considered, which is the mass of the person in the image.\n* `r` is the distance between the object and the center of the Earth.",
|
|
"gt_answers": "9 - \\frac { m } { 9 } =\n",
|
|
"image_path": "./data/HME100K/test_images/test_2214.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "y _ { 2 } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2215.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(x - 9) + 4.",
|
|
"gt_answers": "M < - \\frac { 9 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2217.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"a(b + c) + a(b - c) = a^2(b^2 + c^2) + a^2(b^2 - c^2)\".",
|
|
"gt_answers": "A C E N \\cong A C F B ( S \\cdot A \\cdot A )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2218.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"H2Cu2O4.\"",
|
|
"gt_answers": "H _ { 2 } + C u O \\xrightarrow { \\Delta } C u + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2221.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/3 + 1/9 = 1/2.",
|
|
"gt_answers": "\\frac { 1 } { 3 } = \\frac { 3 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2222.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"C128T 20011 16376 35000\" in LaTeX format.",
|
|
"gt_answers": "( 1 2 8 + 2 0 9 + 1 6 3 ) \\times 7 = 3 5 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2223.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(R_{i} = \\frac{I_{i}}{V_{i}} = \\frac{16 \\text{ mA}}{1.5 \\text{ V}} = 10 \\text{ \u03a9}\\)",
|
|
"gt_answers": "\\Delta I = \\frac { U } { \\Delta P } = \\frac { 1 6 V } { 1 6 W } = 1 A\n",
|
|
"image_path": "./data/HME100K/test_images/test_2225.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AE = AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE + AE",
|
|
"gt_answers": "A E = A F + E F = 4 0 +\n",
|
|
"image_path": "./data/HME100K/test_images/test_2226.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Korean.",
|
|
"gt_answers": "( x + y ) ^ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2228.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\cdot S _ { \\Delta } P D O - S _ { \\Delta } C D O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2229.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"a^2 + b^2 = c^2.\"",
|
|
"gt_answers": "a = 2 \\sqrt { 2 } o r a \\geq 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2230.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = (x + y)^2\\)",
|
|
"gt_answers": "( a + b ) \\times c = a \\times c + b \\times c\n",
|
|
"image_path": "./data/HME100K/test_images/test_2232.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(PQ = \\frac{C_{s} \\cdot Q_{s}}{3 \\cdot V_{d}} \\cdot \\frac{3 \\cdot V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}} \\cdot \\frac{V_{d}}{V_{s}} \\cdot \\frac{V_{s}}{V_{d}}",
|
|
"gt_answers": "P Q = C Q \\sin c = 3 0 ( \\sqrt { 3 } - 1 ) c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2233.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "m x + 2 n x + 5 x + m y - n y - 3 m - 3 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2234.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 13x + 13 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 1 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2235.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x^2 + 4x + 5 = 0.\"",
|
|
"gt_answers": "x = 3 \\times \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2236.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + 2x + 3 = 10\n\\end{aligned}\n\\end{equation}",
|
|
"gt_answers": "2 x + 2 x ^ { 2 } + 3 x - 3 = x + x ^ { 2 } - 1 - x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2237.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 3x + 4 = 12.",
|
|
"gt_answers": "x = 3 \\cdot \\frac { 7 } { 3 } - 4 = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2238.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "\\angle H E M = \\angle E N M = \\frac { 1 } { n } \\angle B M N .\n",
|
|
"image_path": "./data/HME100K/test_images/test_2239.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{a^2 + b^2}{a^2 - b^2} = \\frac{a^2 + b^2}{a^2 - b^2}\n\\end{equation}\n\nThis is a simple algebraic expression that can be easily solved using the distributive property of multiplication.",
|
|
"gt_answers": "l _ { n } = \\sqrt { a _ { n } } + \\sqrt { a _ { 2 a b } - n }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2240.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "e = \\frac { - 5 + 1 1 } { 4 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2241.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6x30 + 1500 = 1650\" and is expressed using the mathematical notation for addition.",
|
|
"gt_answers": "5 0 \\times 3 0 \\times 1 0 = 1 5 0 0 0 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2242.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/31 - 24/31 = 1/31 - 1/31 = 0.",
|
|
"gt_answers": "y = \\frac { 3 1 } { 2 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2243.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(T_n = \\frac{n^2}{2} + \\frac{n}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n) + \\frac{1}{2} \\ln(n)",
|
|
"gt_answers": "n \u3001 H ^ { \\prime } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2244.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 4x16t16b16 = 16x16t16b16.",
|
|
"gt_answers": "4 x ^ { 2 } - 1 6 x + 1 6 = 2 0 x - 1 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2245.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(4x2) + 4(2x2) + 8(4x2) + 8(2x2) + 4(4x2) + 4(2x2) + 2(4x2) + 4(2x2) + 8(4x2) + 8(2x2) + 4(4x2) + 4(2x2) + 2(4x2) + 4(2x2) + 8(4x2) + 8(2x2) + 4(4x2) + 4(2x2) + 2(4x2) + 4(2x2) + 8(4x2) + 8(2x2) + 4(4x2) + 4(2x2) + 2(4x2) + 4(2x2) + 8(4x2) + 8(2x2) + 4(4x2) + 4(2x2) + 2(4x2) + 4(2x2) + 8(4x2) + 8(2x2) + 4(4x2) + 4(2x2) + 2(4x2) + 4(2x2) + 8(4x2) + 8(2x2) + 4(4x2) + 4(2x2) + 2(4x2) + 4(2x2) + 8(4x2) + 8(2x2) + 4(4x2) + 4(2x2) + 2(4x2) + 4(2x2) + 8(4x2) + 8(2x2) + 4(4x2) + 4(2x2) + 2(4x2) + 4(2x2) + 8(4x2) + 8(2x2) + 4(4x2) + 4(2x2) + 2(4x2) + 4(2x2) + 8(4x",
|
|
"gt_answers": "\\angle 1 + \\angle 3 = 1 8 0 ^ { \\circ } , \\angle 2 + \\angle 4 = 1 8 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2246.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(sin(q) = \\frac{sin(0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\sin \\angle G O _ { 1 } O = \\frac { G O } { O _ { 1 } O } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2247.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y^2} = \\frac{4x^2 + 4y^2}{4x^2 - 4y",
|
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"gt_answers": "\\frac { x } { 1 6 } = \\frac { 4 x + 5 } { 8 } + 2\n",
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"image_path": "./data/HME100K/test_images/test_2248.jpg",
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"model_name": "mPLUG"
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|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x} + \\frac{1}{y} = \\frac{1}{x + y}\n\\end{equation}\n\nThis formula represents the basic algebraic identity of addition of fractions.",
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|
"gt_answers": "\\frac { 1 } { x - y } = V\n",
|
|
"image_path": "./data/HME100K/test_images/test_2249.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation in two variables, where x and y represent the two unknowns. The expression represents the square of the sum of the two variables, which must equal 1.",
|
|
"gt_answers": "x = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2252.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x = \\frac { - 1 + \\sqrt { 2 1 } } { 2 } , x = \\frac { - 1 - \\sqrt { 2 1 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2253.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written in the form of a matrix, with the letters O, B, D, and C representing the four elements of the matrix. The formula is written in the order OBDC, which is the order of the elements in the matrix.",
|
|
"gt_answers": "O B = B D = O C = C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_2254.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "C G - B F = B L\n",
|
|
"image_path": "./data/HME100K/test_images/test_2257.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"V(x) = 2x^2 - 3xh + 2h^2.\"",
|
|
"gt_answers": "V = \\pi \\times ( R ^ { 2 } - r ^ { 2 } ) \\times h\n",
|
|
"image_path": "./data/HME100K/test_images/test_2258.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "y _ { 4 } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2260.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as y = 5/2x + 1.",
|
|
"gt_answers": "y _ { 2 } = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2261.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4\\cdot 2^{2} + 4\\cdot 2^{3} + 4\\cdot 2^{4} + 4\\cdot 2^{5} + 4\\cdot 2^{6} + 4\\cdot 2^{7} + 4\\cdot 2^{8} + 4\\cdot 2^{9} + 4\\cdot 2^{10} + 4\\cdot 2^{11} + 4\\cdot 2^{12} + 4\\cdot 2^{13} + 4\\cdot 2^{14} + 4\\cdot 2^{15} + 4\\cdot 2^{16} + 4\\cdot 2^{17} + 4\\cdot 2^{18} + 4\\cdot 2^{19} + 4\\cdot 2^{20} + 4\\cdot 2^{21} + 4\\cdot 2^{22} + 4\\cdot 2^{23} + 4\\cdot 2^{24} + 4\\cdot 2^{25} + 4\\cdot 2^{26} + 4\\cdot 2^{27} + 4\\cdot 2^{28} + 4\\cdot 2^{29} + 4\\cdot 2^{30} + 4\\cdot 2^{31} + 4\\cdot 2^{32} + 4\\cdot 2^{33} + 4\\cdot 2^{34} + 4\\cdot 2^{35} + 4\\cdot 2^{36} + 4\\cdot 2^{37} + 4\\cdot 2^{38} + 4\\cdot 2^{39} + 4\\cdot 2^{40} + 4\\cdot 2^{41} + 4\\cdot 2^{42} + 4\\cdot 2^{43} + 4\\cdot 2^{44} + 4\\cdot 2^{45} + 4\\cdot 2^{46} + 4\\cdot 2^{4",
|
|
"gt_answers": "\\angle 1 + \\angle C A F = \\angle 2 + \\angle C A F\n",
|
|
"image_path": "./data/HME100K/test_images/test_2262.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(H_2O + CO_2 \\rightarrow 2H_2O + CO_2\\)",
|
|
"gt_answers": "1 \\div 1 2 = \\frac { 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2264.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(OH^2 + H_2O \\rightarrow CO_2 + 2H_2\\)",
|
|
"gt_answers": "O H \\bot C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_2268.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(E_{k} = \\frac{h}{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\right)^{2} \\left( \\frac{1}{\\sqrt{2m}} \\",
|
|
"gt_answers": "E _ { k } = e U _ { c } = h v - W _ { 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2269.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "V = \\frac { \\lambda } { T } = \\frac { 1 . 2 } { 0 . 4 } = 3 m / s\n",
|
|
"image_path": "./data/HME100K/test_images/test_2273.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"sum(4x^2 + 4y^2 + 4x + 4y + 4)\".",
|
|
"gt_answers": "3 ( m ^ { 2 } y ^ { 2 } + 4 + 4 m y ) + 4 y ^ { 2 } = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2274.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x = \\pm \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2276.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "O E = \\sqrt { B E ^ { 2 } - O E ^ { 2 } } = \\sqrt { \\frac { 5 2 } { 9 } } = \\frac { 2 \\sqrt { 1 3 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2277.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(n^2 + n^3 + n^4 + n^5 + n^6 + n^7 + n^8 + n^9 + n^{10} + n^{11} + n^{12} + n^{13} + n^{14} + n^{15} + n^{16} + n^{17} + n^{18} + n^{19} + n^{20} + n^{21} + n^{22} + n^{23} + n^{24} + n^{25} + n^{26} + n^{27} + n^{28} + n^{29} + n^{30} + n^{31} + n^{32} + n^{33} + n^{34} + n^{35} + n^{36} + n^{37} + n^{38} + n^{39} + n^{40} + n^{41} + n^{42} + n^{43} + n^{44} + n^{45} + n^{46} + n^{47} + n^{48} + n^{49} + n^{50} + n^{51} + n^{52} + n^{53} + n^{54} + n^{55} + n^{56} + n^{57} + n^{58} + n^{59} + n^{60} + n^{61} + n^{62} + n^{63} + n^{64} + n^{65} + n^{66} + n^{67} + n^{68} + n^{69} + n^{70} + n^{71} + n^{72} + n^{73} + n^{74} + n^{75} + n^{76} + n^{77} + n^{78} + n^{79} + n^{80} + n^{81} + n^{82} + n^{83} + n^{84} + n^{85} + n^{86} +",
|
|
"gt_answers": "n ^ { 2 } + n = n \\times ( n + 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2278.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 12\\)",
|
|
"gt_answers": "x > \\frac { 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2279.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { E F } { C H } = \\frac { A F } { A H } = \\frac { E F } { - x ^ { 2 } + 4 x } = \\frac { 2 } { 4 - x } \\Rightarrow E F = 2 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2280.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 33-3 = 30.",
|
|
"gt_answers": "x _ { 3 } = - \\frac { 8 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2282.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `5x^2 + 2x^2 - 7x^2 = 0`.",
|
|
"gt_answers": "\\frac { 4 } { 5 } x \\div 2 \\times 2 = \\frac { 7 } { 1 6 } \\times 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2283.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2Fe(OH)2 + 4H2O = 2Fe(OH)3 + 3H2.",
|
|
"gt_answers": "F e _ { 2 } O _ { 3 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2284.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2x3 - 5 = 10.",
|
|
"gt_answers": "\\frac { 2 \\times 3 } { 5 } = \\frac { 6 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2285.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a number and a symbol, which could be a mathematical operator or a variable.",
|
|
"gt_answers": "- \\sqrt { 2 x - 3 } = x - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2286.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3xy + 4y^2 = 10x^2 + 12xy + 12y^2\\)",
|
|
"gt_answers": "y = \\sqrt { 8 9 - 8 x } ( 0 < x < w )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2287.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3xy + 4y^2 = 5x^2 + 6xy + 7y^2\\)",
|
|
"gt_answers": "5 ^ { 2 } + ( 1 0 - t ) ^ { 2 } = 1 0 ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2289.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\nLZA_7 = 2^{7} - 1\n\\end{equation}\n\nThis is the formula for the 7th bit of the Lempel-Ziv-Welch (LZW) compression algorithm. The LZW algorithm is a lossless data compression technique that uses a dictionary of previously compressed data to compress new data. The 7th bit of the LZW algorithm is used to determine whether the next bit of data is a new symbol or a symbol that has already been seen in the dictionary.",
|
|
"gt_answers": "\\angle 2 = A D = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2292.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LA+LC+LADC=360\u00b0\".",
|
|
"gt_answers": "\\angle A + \\angle A B C + \\angle C + \\angle A D C = 3 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2293.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2\\pi r^2 \\cdot \\sin(2\\theta) = 2",
|
|
"gt_answers": "t ^ { \\prime } = \\frac { S } { V } = \\frac { 2 5 k m } { 1 0 0 k m / h } = 0 . 2 5 h\n",
|
|
"image_path": "./data/HME100K/test_images/test_2294.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(b^2 - 6t^2) + 3b - 4t.",
|
|
"gt_answers": "2 B = \\frac { 8 } { 6 } \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_2295.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given by:\n\n\\(L = 48 \\cdot \\sin(30^\\circ) = 48 \\cdot \\frac{\\sin(30^\\circ)}{\\cos(30^\\circ)} = 48 \\cdot \\frac{1}{\\sqrt{2}} = 24\\)",
|
|
"gt_answers": "\\angle _ { 1 } = 4 8 ^ { \\circ } ( g i v e n )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2296.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "g = - \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2297.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"GUH+H2SO4 = CUSHY + H2O.\"",
|
|
"gt_answers": "C u O + H _ { 2 } S O _ { 4 } = C u S O _ { 4 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2299.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x3=12.",
|
|
"gt_answers": "+ \\textcircled { 4 } : 4 x = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2300.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 18/90 = 0.20.",
|
|
"gt_answers": "\\frac { 1 8 } { 9 0 } ( 1 8 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2301.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x ^ { 2 } + x - 2 < 0 \\Rightarrow ( x - 1 ) ( x + 2 ) < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2302.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"L = 15\u00b0 + 15\u00b0 = 30\u00b0.\"",
|
|
"gt_answers": "\\angle A B O = \\angle B A O = 1 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2303.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"X^2 + 3200 = 10000.\"",
|
|
"gt_answers": "x + y = 3 2 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2304.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nx^2 + 2x + 1 = 0\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2305.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 14x + 14 = 0`.",
|
|
"gt_answers": "x = \\frac { 1 4 } { 1 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2306.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `a^2 + b^2 = c^2`.",
|
|
"gt_answers": "a = b = c = 3 ^ { \\frac { 1 } { 6 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2308.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x - 5 = 0\\)",
|
|
"gt_answers": "x - 2 = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2309.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBLEd = 180\u00b0 - 30\u00b0 - 90\u00b0 = 120\u00b0.\"",
|
|
"gt_answers": "\\angle B D E = \\angle B E D = \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } - 3 0 ^ { \\circ } ) = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2310.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "4 y ^ { 2 } + 9 + 1 2 y + y ^ { 2 } = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_2313.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LUHM = 90\u00b0.\"",
|
|
"gt_answers": "\\angle O H M = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2314.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x + 3 = 9.",
|
|
"gt_answers": "2 : 9 = \\frac { 1 } { 3 } : x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2315.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis equation is a simple algebraic expression that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "\\frac { 4 } { 3 } x = 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2316.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a = \\frac{b}{c}\\)\n\nThis formula represents the relationship between three variables, a, b, and c, where a is equal to the quotient of b divided by c.",
|
|
"gt_answers": "a : b = \\frac { 3 } { \\sqrt { 5 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2317.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 6x + 3 = 0`.",
|
|
"gt_answers": "x = \\frac { 6 } { 5 } \\div 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2318.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "1 6 8 0 \\div 3 = 5 6 0 2 8 0 0 \\div 5 = 5 6 0 3 9 2 0 \\div 7 = 5 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2319.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 13\\)\n\nThis formula represents a square with side length 13 units.",
|
|
"gt_answers": "= - \\frac { 1 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2320.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(7.9 - 14.1 = 7.0 - 14.0\\)",
|
|
"gt_answers": "\\frac { 1 4 2 } { 7 . 1 g } = \\frac { 1 1 7 } { y }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2321.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(1007 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 = 7 - 1000 =",
|
|
"gt_answers": "1 0 0 x = 4 0 0 - 9 0 = 9 0 + 1 0 0 \\times 3 . 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2322.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\ce{2H2O + O2 -> 2H2O2 + 2H2}\n\\end{equation}\n\nThis formula represents the chemical reaction between water and oxygen to produce hydrogen peroxide and hydrogen gas.",
|
|
"gt_answers": "2 H _ { 2 } O _ { 2 } \\xlongequal { M n O _ { 2 } } 2 H _ { 2 } O + O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_2323.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 3x + 2 = 0\\)",
|
|
"gt_answers": "\\vert b + 1 \\vert = \\vert \\frac { b } { 2 } - 1 \\vert \\times 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2324.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n$$500 + 600 = 1100$$",
|
|
"gt_answers": "5 9 0 + 6 0 = 6 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2325.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"sna4 + co2 = 4\".",
|
|
"gt_answers": "\\sin \\alpha = - \\frac { 4 } { 5 } < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2326.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
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"gt_answers": "5 1 2 \\div 8 5 = 6 \\cdots 2 5 1 2 \\div 8 9 = 5 \\cdots 6 7\n",
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"image_path": "./data/HME100K/test_images/test_2327.jpg",
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"model_name": "mPLUG"
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|
},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written as follows: 2(DBC + EBC) = 5(xb + yb) + 6(xb - yb) + 7(xb + yb) + 8(xb - yb) + 9(xb + yb) + 10(xb - yb) + 11(xb + yb) + 12(xb - yb) + 13(xb + yb) + 14(xb - yb) + 15(xb + yb) + 16(xb - yb) + 17(xb + yb) + 18(xb - yb) + 19(xb + yb) + 20(xb - yb) + 21(xb + yb) + 22(xb - yb) + 23(xb + yb) + 24(xb - yb) + 25(xb + yb) + 26(xb - yb) + 27(xb + yb) + 28(xb - yb) + 29(xb + yb) + 30(xb - yb) + 31(xb + yb) + 32(xb - yb) + 33(xb + yb) + 34(xb - yb) + 35(xb + yb) + 36(xb - yb) + 37(xb + yb) + 38(xb - yb) + 39(xb + yb) + 40(xb - yb) + 41(xb + yb) + 42(xb - yb) + 43(xb + yb) + 44(xb - yb) + 45(xb + yb) + 46(xb - yb) + 47(xb + yb) + 48(xb - yb) + 49(xb + yb) + ",
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"gt_answers": "\\angle D B C + \\angle E C B = \\frac { 1 } { 2 } \\times 1 2 0 ^ { \\circ } = 6 0 ^ { \\circ }\n",
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"image_path": "./data/HME100K/test_images/test_2328.jpg",
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"model_name": "mPLUG"
|
|
},
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{
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|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written as 2x + 4 = 5.",
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"gt_answers": "x = \\frac { 1 } { 2 } : \\frac { 3 } { 4 }\n",
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"image_path": "./data/HME100K/test_images/test_2329.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as: 1/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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"gt_answers": "O E \\bot O F\n",
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"image_path": "./data/HME100K/test_images/test_2330.jpg",
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"model_name": "mPLUG"
|
|
},
|
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{
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|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a Chinese character in the middle, which could be a symbol or a word.",
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"gt_answers": "\\therefore \\frac { D F } { C D } = \\frac { 1 } { 3 } \\cdot\n",
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"image_path": "./data/HME100K/test_images/test_2332.jpg",
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"model_name": "mPLUG"
|
|
},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
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"gt_answers": "- 2 < a < 0 \\therefore M = 4 a + 2 ( a + 2 ) + 2\n",
|
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"image_path": "./data/HME100K/test_images/test_2333.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
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"gt_answers": "x - y = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2334.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
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"gt_answers": "f ^ { \\prime } ( x ) = 2 a + \\frac { b } { x ^ { 2 } } + \\frac { 1 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2335.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( O B + \\overrightarrow { O C } ) ( \\overrightarrow { O C } - \\overrightarrow { O B } ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2336.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the chemical formula notation, which is a standard way to represent chemical compounds. The formula is written as Fe2+ + H2O = Fe(OH)2.",
|
|
"gt_answers": "B . ( 1 ) F e + H _ { 2 } S O _ { 4 } = F e S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_2337.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\overrightarrow { A M } = ( 1 - \\lambda ) \\overrightarrow { A B } + \\lambda \\overrightarrow { A C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2338.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Kt-28t\".",
|
|
"gt_answers": "[ k \\pi - \\frac { 3 } { 8 } \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_2339.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 4x - 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\sqrt { x + a } = \\sqrt { 2 x - 4 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2340.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"gx^8 + gx^7 + gx^6 + gx^5 + gx^4 + gx^3 + gx^2 + gx + 1.\"",
|
|
"gt_answers": "6 x + 8 \\square\n",
|
|
"image_path": "./data/HME100K/test_images/test_2341.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{",
|
|
"gt_answers": "t = L\n",
|
|
"image_path": "./data/HME100K/test_images/test_2342.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"G(x) = 1 + 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8 + 10x^9 + 11x^10 + 12x^11 + 13x^12 + 14x^13 + 15x^14 + 16x^15 + 17x^16 + 18x^17 + 19x^18 + 20x^19 + 21x^20 + 22x^21 + 23x^22 + 24x^23 + 25x^24 + 26x^25 + 27x^26 + 28x^27 + 29x^28 + 30x^29 + 31x^30 + 32x^31 + 33x^32 + 34x^33 + 35x^34 + 36x^35 + 37x^36 + 38x^37 + 39x^38 + 40x^39 + 41x^40 + 42x^41 + 43x^42 + 44x^43 + 45x^44 + 46x^45 + 47x^46 + 48x^47 + 49x^48 + 50x^49 + 51x^50 + 52x^51 + 53x^52 + 54x^53 + 55x^54 + 56x^55 + 57x^56 + 58x^57 + 59x^58 + 60x^59 + 61x^60 + 62x^61 + 63x^62 + 64x^63 + 65x^64 + ",
|
|
"gt_answers": "( \\frac { 9 } { 2 } \\leq t \\leq \\frac { 1 3 } { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2344.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{2b-1} - 2^{2a-1} = 2^{2b-2} - 2^{2a-2} + 2^{2b-2} - 2^{2a-2} = 2^{2b-2} - 2^{2a-2} - 2^{2b-2} + 2^{2a-2} = 0\\)",
|
|
"gt_answers": "1 - 2 a b + a ^ { 2 } b ^ { 2 } > a ^ { 2 } + b ^ { 2 } - 2 a b\n",
|
|
"image_path": "./data/HME100K/test_images/test_2345.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(S_{AF} = \\frac{A \\cdot F}{P \\cdot G} \\cdot 12\\)\n\nwhere:\n\n* SAF = the surface area of the face of the cube\n* A = the area of the face of the cube\n* F = the number of faces of the cube\n* P = the perimeter of the cube\n* G = the number of edges of the cube\n\nThe formula can be rearranged to solve for the surface area of the cube:\n\n\\(S_{AF} = \\frac{A \\cdot F}{P \\cdot G} \\cdot 12 = \\frac{A \\cdot F}{P \\cdot G} \\cdot \\frac{P \\cdot G}{12} = \\frac{A \\cdot F}{P \\cdot G} \\cdot \\frac{P}{12} = \\frac{A \\cdot F}{P \\cdot G} \\cdot \\frac{P}{12} \\cdot 12 = \\frac{A \\cdot F}{P \\cdot G} \\cdot 12 \\cdot 12 = \\frac{A \\cdot F}{P \\cdot G} \\cdot 144 = \\frac{A \\cdot F}{P \\cdot G} \\cdot 12 \\cdot 12 \\cdot 12 = \\frac{A \\cdot F}{P \\cdot G} \\cdot 144 \\cdot 12 = \\frac{A \\cdot F}{P \\cdot G} \\cdot 168 = \\frac{A \\cdot F}{P \\cdot G} \\cdot 12 \\cdot 12 \\cdot 12 \\cdot 12 = \\frac{A \\cdot F}{P \\cdot G} \\cdot 192 = \\frac{A \\cdot F}{P \\cdot G} \\cdot 12 \\cdot 12 \\cdot 12 \\cdot 12 \\cdot 12 = \\frac{A \\cdot F}{P \\cdot G} \\cdot 256 = \\frac{A \\cdot F}{P \\cdot G} \\cdot 12 \\cdot 12 \\cdot 12 \\cdot 12 \\cdot 12 \\cdot 12 = \\frac{A \\cdot F}{",
|
|
"gt_answers": "S _ { \\Delta } A O F = \\frac { 1 } { 2 } A D . F G = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2346.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(4x^2 + 4y^2 + 4z^2 + 4xy + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + 4xz + 4yz + ",
|
|
"gt_answers": "\\Delta = b ^ { 2 } - 4 a c = 4 + 4 k + 4 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2347.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "- \\pi < - B < - \\frac { 1 } { 2 } \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_2348.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(m(OH) = 4.89 \\times 10^{-4} \\times 0.029 \\times 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "m ( N a O H ) = 4 . 8 g \\times 5 \\% = 0 . 2 4 g\n",
|
|
"image_path": "./data/HME100K/test_images/test_2349.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(CaCO3 + H_{2}O \\rightarrow Ca(OH)_{2} + CO_{2}\\)\n\nThis formula represents the chemical reaction between calcium carbonate (CaCO3) and water (H2O) to produce calcium hydroxide (Ca(OH)2) and carbon dioxide (CO2).",
|
|
"gt_answers": "C a ( O H ) _ { 2 } + C O _ { 2 } = C a C O _ { 3 } \\downarrow + H _ { 2 } O \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_2350.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 8\\)",
|
|
"gt_answers": "x - 2 y + 8 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2351.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(5x \\times 8 = 40\\)",
|
|
"gt_answers": "\\frac { 5 } { 1 2 } \\times 8 = \\frac { 5 \\times 8 } { 1 2 } = \\frac { 1 0 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2352.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nG = 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "p = \\frac { F } { S } = \\frac { G } { S } = \\frac { 9 8 N } { 2 \\times 1 0 ^ { - 2 } m ^ { 2 } } = 4 9 0 0 P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_2353.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"22/16 = 1.4166666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666",
|
|
"gt_answers": "7 ^ { 2 } = 8 ^ { 2 } + c ^ { 2 } - 1 6 c \\cdot \\cos 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2354.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 - 2x + 1 = 0.\"",
|
|
"gt_answers": "x = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2355.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m_1 + m_2 = m_3 + m_4\\)",
|
|
"gt_answers": "b = \\frac { m - 4 } { 3 } < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2356.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "( 4 0 + x - 3 0 ) ( 6 0 0 - 1 0 8 ) = 1 0 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2357.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nb = 2(a + b) - 3a\n\nThis formula can be represented using the LaTeX code:\n\nb = 2(a + b) - 3a\n\nThe formula is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "b = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2358.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"NX2 + NX1 = NX4,\" where NX1 and NX2 are the two numbers on the left side of the equation, and NX4 is the number on the right side.",
|
|
"gt_answers": "( 3 \\times 4 ) ^ { 2 } = 1 2 \\times 1 2 = 1 4 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2359.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6 in a sin B = 2 sin A sin B.\"",
|
|
"gt_answers": "\\cdot \\sin A \\sin B = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2360.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2700 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times ",
|
|
"gt_answers": "S _ { 1 } = \\frac { v } { u } = \\frac { 8 1 0 c m ^ { 3 } } { 3 c m } = 2 7 0 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2362.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3a^2 + 2b^2 - 3ab - 2b^2 = 0\\)\n\nThis formula represents the quadratic equation with the variables a and b.",
|
|
"gt_answers": "\\frac { 3 a - 2 b } { a + b } = - \\frac { 1 } { 3 } \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_2363.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: F(x) = 3x^2 + 4x + 13.",
|
|
"gt_answers": "F e _ { 2 } O _ { 3 } + 6 H C 1 = 3 H _ { 2 } O + 2 F e C l _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2365.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"y = 2x + 3.\"",
|
|
"gt_answers": "y ^ { 2 } + y = 1 y ^ { 2 } - y = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2366.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.",
|
|
"gt_answers": "a _ { n } = a _ { 1 } + ( n - 1 ) d\n",
|
|
"image_path": "./data/HME100K/test_images/test_2367.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{a^2 + b^2}{a^2 - b^2} = \\frac{a^2 + b^2}{a^2 - b^2}\n\\end{equation}\n\nThis is a simple algebraic expression that demonstrates the identity property of the square root function.",
|
|
"gt_answers": "\\frac { a } { b + c } + \\frac { b } { a + c } + \\frac { c } { b + a } = ( - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2369.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(240 \\times 240 + 250 \\times 250 = 600000\\)",
|
|
"gt_answers": "1 6 5 0 + [ ( 2 8 0 - 2 4 0 ) \\div 8 ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_2372.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x _ { 2 } = \\frac { 1 + \\sqrt { 1 0 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2373.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "- 1 4 0 x - 3 0 x ^ { 2 } - 2 1 - 1 1 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_2374.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{a_1x^2 + a_2x^3 + a_3x^4 + a_4x^5 + a_5x^6 + a_6x^7 + a_7x^8 + a_8x^9 + a_9x^{10} + a_{10}x^{11}}{b_1x + b_2x^2 + b_3x^3 + b_4x^4 + b_5x^5 + b_6x^6 + b_7x^7 + b_8x^8 + b_9x^{9} + b_{10}x^{10} + b_{11}x^{11}} \\tag{LaTeX formula}\n\nThe formula is a polynomial expression in the variable x, with coefficients a1 through a11 and constants b1 through b11.",
|
|
"gt_answers": "= a ^ { 3 } + a ^ { 2 } + a - 2 a ^ { 2 } - 2 a - 2 +\n",
|
|
"image_path": "./data/HME100K/test_images/test_2375.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 200x45 = 900km.",
|
|
"gt_answers": "2 0 0 \\times 4 . 5 = 9 0 0 ( k m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2376.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nS = 2452.16 m^2",
|
|
"gt_answers": "S = ( 4 5 2 . 1 6 ) m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2377.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 9800px^2\\)",
|
|
"gt_answers": "x 0 . 1 m = 9 8 0 p a\n",
|
|
"image_path": "./data/HME100K/test_images/test_2379.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2}x^2 + \\frac{1}{2}y^2 + \\frac{1}{2}z^2 + \\frac{1}{2}w^2 + \\frac{1}{2}xy + \\frac{1}{2}yz + \\frac{1}{2}xz + \\frac{1}{2}yw + \\frac{1}{2}yz + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xz + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yz + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{2}xw + \\frac{1}{2}yw + \\frac{1}{",
|
|
"gt_answers": "x _ { 1 } = 2 , x _ { 2 } = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2381.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a few Chinese characters and some numbers.",
|
|
"gt_answers": "y = 1 3 \\times \\frac { 9 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2382.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"VRBC = 323.\"",
|
|
"gt_answers": "V _ { p A B C } = \\frac { 3 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2383.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LEFAT + 2CDB = 180\u00b0.\"",
|
|
"gt_answers": "\\angle E F A + \\angle C D B = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2384.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, but it can be translated to English as \"Rei Zero: Zero Time Dilemma - The Answer.\"",
|
|
"gt_answers": "x \\in ( 2 k \\pi + \\pi , 2 k \\pi + 2 \\pi ) ( k \\in z )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2385.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(M = \\frac{m_1 + m_2}{2}\\)\n\nwhere M represents the mass of the object, m1 and m2 represent the masses of the two objects being added together, and the division sign \"/\" represents the mathematical operation of division.",
|
|
"gt_answers": "M _ { x } = \\frac { 2 \\sqrt { 3 } } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2386.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(AB = \\frac{1}{2} \\left( \\sqrt{A^2 + B^2} + \\sqrt{C^2 + D^2} \\right)\\)",
|
|
"gt_answers": "A B = \\sqrt { ( - 5 + 1 ) ^ { 2 } + ( 1 - 3 ) ^ { 2 } } = \\sqrt { 1 6 + 4 } = \\sqrt { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2387.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\pi r^2 + 2\\pi r\\cdot r' + 2\\pi r\\cdot r'' + 2\\pi r\\cdot r''' + 2\\pi r\\cdot r'''' + 2\\pi r\\cdot r'''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r\\cdot r'''''''' + 2\\pi r",
|
|
"gt_answers": "2 ^ { 2 } \\times 3 . 1 4 \\times 1 . 5 \\times \\frac { 1 } { 3 } = 6 . 2 8 c m ^ { 2 } \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_2388.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x4 + 6 = 15\" in LaTeX format.",
|
|
"gt_answers": "S _ { \\Delta A B C } = 3 \\times 4 \\times \\frac { 1 } { 2 } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2389.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(v = \\sqrt{2 \\cdot g \\cdot h}\\)\n\nwhere v is the velocity, g is the gravitational constant, and h is the height of the object.",
|
|
"gt_answers": "V = \\frac { s m } { b } ( k m / h )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2390.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: PM2.5 = 12.5 + 5.",
|
|
"gt_answers": "P _ { M = } \\frac { 1 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2392.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot",
|
|
"gt_answers": "( y - x + z ) x = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2393.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(A + B + C = 3(C + 3A + B)\\)",
|
|
"gt_answers": "A B = \\sqrt { ( - 3 - 3 ) ^ { 2 } + ( - 3 - 4 ) ^ { 2 } } = \\sqrt { 8 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2394.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 33.",
|
|
"gt_answers": "4 = 3 \\frac { 2 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2396.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{44} + 2^{43} + 2^{42} + 2^{41} + 2^{40} + 2^{39} + 2^{38} + 2^{37} + 2^{36} + 2^{35} + 2^{34} + 2^{33} + 2^{32} + 2^{31} + 2^{30} + 2^{29} + 2^{28} + 2^{27} + 2^{26} + 2^{25} + 2^{24} + 2^{23} + 2^{22} + 2^{21} + 2^{20} + 2^{19} + 2^{18} + 2^{17} + 2^{16} + 2^{15} + 2^{14} + 2^{13} + 2^{12} + 2^{11} + 2^{10} + 2^{9} + 2^{8} + 2^{7} + 2^{6} + 2^{5} + 2^{4} + 2^{3} + 2^{2} + 2^{1} + 2^{0} = 10^{44} + 10^{43} + 10^{42} + 10^{41} + 10^{40} + 10^{39} + 10^{38} + 10^{37} + 10^{36} + 10^{35} + 10^{34} + 10^{33} + 10^{32} + 10^{31} + 10^{30} + 10^{29} + 10^{28} + 10^{27} + 10^{26} + 10^{25} + 10^{24} + 10^{23} + 10^{22} + 10^{21",
|
|
"gt_answers": "2 0 \\times 0 . 4 + 0 . 5 \\times 2 0 + 0 . 5 x = 4 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2397.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as m1 + m2 = 2m.",
|
|
"gt_answers": "\\vert m \\vert - 2 = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2398.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 811:9 + 471:11.",
|
|
"gt_answers": "8 + 1 = 9 4 + 7 = 1 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2399.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(E = \\frac{1}{2}mv^2\\)\n\nwhere E is the energy, m is the mass of the object, and v is its velocity.",
|
|
"gt_answers": "D C = t , E C = \\frac { 4 } { 3 } t\n",
|
|
"image_path": "./data/HME100K/test_images/test_2400.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\ny = \\frac{1}{2} \\left( \\frac{x^2}{a^2} + \\frac{b^2}{c^2} \\right)\n\\end{equation}\n\nThe equation is a quadratic equation in the variable \"y\" and the variables \"x\" and \"b\". The expression is written using the \"equation\" environment, which provides a clean and professional look to the equation.",
|
|
"gt_answers": "y _ { 1 } = 6 , y _ { 2 } = - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2401.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1 + 6 = 7\" using the LaTeX formula notation.",
|
|
"gt_answers": "a _ { n + 1 } = \\frac { 1 } { 6 } + \\frac { 1 } { 6 a n }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2402.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 0.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": ". 2 + 0 . 6 = 0 . 8 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2405.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 5x^2 + 6x + 7\\)\n\nThe formula is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "\\frac { 4 } { 5 } \\times \\frac { 3 } { 2 } \\times = \\frac { 1 2 } { 5 } \\times\n",
|
|
"image_path": "./data/HME100K/test_images/test_2406.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 5.\"",
|
|
"gt_answers": "\\frac { 1 } { \\sqrt { 3 + 1 } } = \\frac { \\sqrt { 3 } - 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2408.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 3x + 2 = 0.\"",
|
|
"gt_answers": "x = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2409.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "2 x ^ { 2 } + 3 x - k = 2 x ^ { 2 } + 2 x n + 8 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2410.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(L_A = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) \\left( \\frac{1}{x^2} + \\frac{1}{y^2} \\right) \\left( \\frac{1}{x^4} + \\frac{1}{y^4} \\right) \\left( \\frac{1}{x^6} + \\frac{1}{y^6} \\right) \\left( \\frac{1}{x^8} + \\frac{1}{y^8} \\right) \\left( \\frac{1}{x^{10}} + \\frac{1}{y^{10}} \\right) \\left( \\frac{1}{x^{12}} + \\frac{1}{y^{12}} \\right) \\left( \\frac{1}{x^{14}} + \\frac{1}{y^{14}} \\right) \\left( \\frac{1}{x^{16}} + \\frac{1}{y^{16}} \\right) \\left( \\frac{1}{x^{18}} + \\frac{1}{y^{18}} \\right) \\left( \\frac{1}{x^{20}} + \\frac{1}{y^{20}} \\right) \\left( \\frac{1}{x^{22}} + \\frac{1}{y^{22}} \\right) \\left( \\frac{1}{x^{24}} + \\frac{1}{y^{24}} \\right) \\left( \\frac{1}{x^{26}} + \\frac{1}{y^{26}} \\right) \\left( \\frac{1}{x^{28}} + \\frac{1}{y^{28}} \\right) \\left( \\frac{1}{x^{30}} + \\frac{1}{y^{30}} \\right) \\left( \\frac{1}{x^{32}} + \\frac{1}{y^{32}} \\right) \\left( \\frac{1}{x^{34}} + \\frac{1}{y^{34}} \\right) \\left( \\frac{1}{x^{3",
|
|
"gt_answers": "\\angle A O C = \\frac { 3 } { 1 0 } \\times 1 8 0 = 5 4 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2411.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(E = \\frac{1}{2} \\cdot \\left(F \\cdot D \\cdot T \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2} \\cdot \\left(F \\cdot D \\right) \\right) \\cdot \\left( \\frac{1}{2",
|
|
"gt_answers": "\\frac { E G } { A G } = \\frac { E F } { A D } = \\frac { 2 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2412.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { E G } { D C } = \\frac { A E } { A C } = \\frac { 3 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2413.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"NVT = 1/T + 1/V + 1/P.\"",
|
|
"gt_answers": "\\lambda = V . T\n",
|
|
"image_path": "./data/HME100K/test_images/test_2414.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 12.\"",
|
|
"gt_answers": "x _ { 2 } = - \\frac { 5 - \\sqrt { 5 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2415.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is: Fe(OH)3 + FeSO4 + 2H2O = Fe3O4 + 2FeSO4 + 3H2O.",
|
|
"gt_answers": "2 . F e + H _ { 2 } S O _ { 4 } = F e S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_2416.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"NaOH + H2O = Na+ + H3O+\".",
|
|
"gt_answers": "N a _ { 2 } O + H _ { 2 } O = 2 N a O H\n",
|
|
"image_path": "./data/HME100K/test_images/test_2417.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 27 + 7x + 27x^2 + 7x^3 + 27x^4 + 7x^5 + 27x^6 + 7x^7 + 27x^8 + 7x^9 + 27x^{10} + 7x^{11} + 27x^{12} + 7x^{13} + 27x^{14} + 7x^{15} + 27x^{16} + 7x^{17} + 27x^{18} + 7x^{19} + 27x^{20} + 7x^{21} + 27x^{22} + 7x^{23} + 27x^{24} + 7x^{25} + 27x^{26} + 7x^{27} + 27x^{28} + 7x^{29} + 27x^{30} + 7x^{31} + 27x^{32} + 7x^{33} + 27x^{34} + 7x^{35} + 27x^{36} + 7x^{37} + 27x^{38} + 7x^{39} + 27x^{40} + 7x^{41} + 27x^{42} + 7x^{43} + 27x^{44} + 7x^{45} + 27x^{46} + 7x^{47} + 27x^{48} + 7x^{49} + 27x^{50} + 7x^{51} + 27x^{52} + 7x^{53} + 27x^{54} + 7x^{55} + 27x^{56} + 7x^{57} + 27x^{58} + 7x^{59} + 27x^{60",
|
|
"gt_answers": "y = \\pm \\frac { 2 \\sqrt { 7 } } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2418.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3b4 = 4.",
|
|
"gt_answers": "3 \\sqrt { - 6 4 } = - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2419.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "A C = 2 A N = 2 \\sqrt { A O _ { 1 } ^ { 2 } - O _ { 1 } N ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2420.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + y^2 = 4`.",
|
|
"gt_answers": "x ^ { 2 } - 6 x = x ^ { 2 } - 7 x + 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2421.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A0:OC0-0Z33\".",
|
|
"gt_answers": "A O = O C = O E = 3 .\n",
|
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"image_path": "./data/HME100K/test_images/test_2422.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "D F + C F = E F + A F . A E = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2423.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x _ { 1 } = - 2 , x _ { 2 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2424.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "( 1 0 \\times 6 + 1 0 \\times 5 + 6 \\times 5 ) \\times 2 = 2 8 0 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2425.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 10\\)\n\nThis formula can be represented using the LaTeX code:\n\n\\(x^2 + 2x + 3 = 10\\)\n\nThe LaTeX code uses the `\\( \\)` and `\\)` symbols to denote the beginning and end of the formula, respectively. The `x` variable is represented using the `\\(x\\)` command, and the `+` and `=` signs are represented using the `\\+` and `\\=` commands, respectively. The `+` sign is placed between the `x` and `2x` terms, and the `=` sign is placed between the `x` and `3` terms.",
|
|
"gt_answers": "1 6 \\times 1 6 + 1 2 \\times 1 2 = ( 1 2 8 - 2 x ) + \\frac { 1 } { 2 } \\times 1 2 \\times ( 1 2 - x ) ^ { - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2426.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(x + 1) - 3x = 4.",
|
|
"gt_answers": "7 . \\sqrt { 9 } + ( - \\frac { 1 } { 2 } ) ^ { - 1 } - \\sqrt { 2 } \\sin 4 5 ^ { \\circ } + ( \\sqrt { 3 } - 2 ) ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2427.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{1 + \\left(\\frac{x}{100}\\right)^2}\n\\end{equation}\n\nThis formula represents the inverse of the square of the ratio of x to 100.",
|
|
"gt_answers": "\\frac { 1 } { 1 0 } x = 1 \\frac { 2 } { 1 0 } + 1 \\frac { 5 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2428.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{3} \\left( \\frac{1}{4} \\left( \\frac{1}{5} \\left( \\frac{1}{6} \\left( \\frac{1}{7} \\left( \\frac{1}{8} \\left( \\frac{1}{9} \\left( \\frac{1}{10} \\left( \\frac{1}{11} \\left( \\frac{1}{12} \\left( \\frac{1}{13} \\left( \\frac{1}{14} \\left( \\frac{1}{15} \\left( \\frac{1}{16} \\left( \\frac{1}{17} \\left( \\frac{1}{18} \\left( \\frac{1}{19} \\left( \\frac{1}{20} \\left( \\frac{1}{21} \\left( \\frac{1}{22} \\left( \\frac{1}{23} \\left( \\frac{1}{24} \\left( \\frac{1}{25} \\left( \\frac{1}{26} \\left( \\frac{1}{27} \\left( \\frac{1}{28} \\left( \\frac{1}{29} \\left( \\frac{1}{30} \\left( \\frac{1}{31} \\left( \\frac{1}{32} \\left( \\frac{1}{33} \\left( \\frac{1}{34} \\left( \\frac{1}{35} \\left( \\frac{1}{36} \\left( \\frac{1}{37} \\left( \\frac{1}{38} \\left( \\frac{1}{39} \\left( \\frac{1}{40} \\left( \\frac{1}{41} \\left( \\frac{1}{42} \\left( \\frac{1}{43} \\left( \\frac{1}{44} \\left( \\frac{1}{45} \\left( \\frac{1",
|
|
"gt_answers": "F e C l _ { 3 } + 3 N a O H = F e ( O H ) _ { 2 } \\downarrow + 3 N a C l\n",
|
|
"image_path": "./data/HME100K/test_images/test_2429.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 5x + 6 = 0\\)",
|
|
"gt_answers": "x = \\frac { 5 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2430.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nCa(OH)2 + 2NaCl + 2H2SO4 \u2192 CaSO4 + 2NaOH + 2H2O + 2Cl2",
|
|
"gt_answers": "( N H _ { 4 } ) _ { 2 } S O _ { 4 } + C a ( O H ) _ { 2 } = C a S O _ { 4 } + N H _ { 3 } \\uparrow + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_2431.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LC = LA + 100\".",
|
|
"gt_answers": "\\angle C = 1 8 0 ^ { \\circ } - \\angle A = 1 4 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2432.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle B A D = \\angle E A G = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_2435.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(1 + 4 \\times 2 + 3 \\times 3 + 2 \\times 2 + 1 \\times 1 = 13\\)",
|
|
"gt_answers": "1 + 4 y + 4 y ^ { 2 } + y ^ { 2 } = 1 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2436.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{d m}{d t} = \\frac{dm}{dt}\n\\end{equation}\n\nThis equation is a mathematical statement that states that the derivative of the mass with respect to time is equal to the derivative of the mass with respect to time.",
|
|
"gt_answers": "\\frac { c d } { m } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2437.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "x ( a - 1 ) = 6 t _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2438.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"DOE = DOD - D2D,\" where DOE stands for Design of Experiments, DOD stands for Design of Data, and D2D stands for Design of Data.",
|
|
"gt_answers": "O E ^ { 2 } = D O \\cdot D\n",
|
|
"image_path": "./data/HME100K/test_images/test_2439.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"130 kg = 0.13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
|
|
"gt_answers": "1 3 0 k g = 0 . 1 3 t\n",
|
|
"image_path": "./data/HME100K/test_images/test_2442.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: `2x^2 + 4x - 3 = 0`.",
|
|
"gt_answers": "( x ^ { 2 } - 4 ) ( x ^ { 2 } + 1 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2443.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(R = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2",
|
|
"gt_answers": "k = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2444.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LANDLEGIC-90.\"",
|
|
"gt_answers": "\\angle A B D + \\angle E B C = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2445.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "T = \\frac { 1 } { 3 0 } s\n",
|
|
"image_path": "./data/HME100K/test_images/test_2446.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 5x + 2 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 2 x + 1 } { 5 } \\leq \\frac { x + 1 } { 2 } \\textcircled { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2448.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 9.",
|
|
"gt_answers": "x = \\frac { 9 } { 1 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2449.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 24000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 0 1 . 4 4 + 5 0 . 2 4 \\times 2 = 4 0 1 9 2 d m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2450.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "P \\cap \\theta = \\{ x \\vert \\frac { 3 } { 2 } \\leq x < 2 \\}\n",
|
|
"image_path": "./data/HME100K/test_images/test_2452.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f_{o} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO_{3}^{2-} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO_{3}^{2-} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO_{3}^{2-} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO_{3}^{2-} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO_{3}^{2-} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO_{3}^{2-} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO_{3}^{2-} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO_{3}^{2-} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO_{3}^{2-} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO_{3}^{2-} + 6H_{2}O + 6CO_{2} + 6H_{2}CO_{3} + 6CO_{3}^{2-} + 6HCO",
|
|
"gt_answers": "F e _ { 2 } O _ { 3 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2453.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2\\sqrt{3} - 3 = 0\\)",
|
|
"gt_answers": "\\frac { 1 } { y } - 3 y - 2 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2455.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\sqrt { a ^ { 2 } - 1 0 a + 2 5 } \\geqslant 0 , ( b - 2 ) ^ { 2 } \\geqslant 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2456.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x + 4 = 0.",
|
|
"gt_answers": "\\sqrt { 2 x + 1 } = x - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2457.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x2 + 9x9 - 2x8.",
|
|
"gt_answers": "\\frac { 4 } { 9 } = \\frac { 4 \\times 2 } { 9 \\times 2 } = \\frac { 8 } { 1 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2458.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is known as the equation of motion for a particle with mass m and energy E. It states that the total energy of a particle is equal to its mass multiplied by the square of its speed of light, c.",
|
|
"gt_answers": "V = \\frac { \\lambda } { T } = \\frac { 4 } { a 1 6 } = 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2459.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "9 x - x = 1 2 x + 2 = 5 x + 5 - 1 7 x = 7 - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2460.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2nh + 2hs = 2(2h + h) = 2(2h + 1h) = 2(3h) = 6h.",
|
|
"gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_2461.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle S _ { \\Delta } A O P = S _ { \\Delta } P X\n",
|
|
"image_path": "./data/HME100K/test_images/test_2462.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 5x + 2y = 10.",
|
|
"gt_answers": "S _ { 5 } = 5 ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2463.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\nGg + Gb + Gd + Gf = Gn + Gm + Go + Gp + Gq + Gs + Gt + Gu + Gv + Gw + Gx + Gy + Gz = Gn + Gm + Go + Gp + Gq + Gs + Gt + Gu + Gv + Gw + Gx + Gy + Gz + Gg + Gb + Gd + Gf = Gn + Gm + Go + Gp + Gq + Gs + Gt + Gu + Gv + Gw + Gx + Gy + Gz + Gg + Gb + Gd + Gf = Gn + Gm + Go + Gp + Gq + Gs + Gt + Gu + Gv + Gw + Gx + Gy + Gz + Gg + Gb + Gd + Gf = Gn + Gm + Go + Gp + Gq + Gs + Gt + Gu + Gv + Gw + Gx + Gy + Gz + Gg + Gb + Gd + Gf = Gn + Gm + Go + Gp + Gq + Gs + Gt + Gu + Gv + Gw + Gx + Gy + Gz + Gg + Gb + Gd + Gf = Gn + Gm + Go + Gp + Gq + Gs + Gt + Gu + Gv + Gw + Gx + Gy + Gz + Gg + Gb + Gd + Gf = Gn + Gm + Go + Gp + Gq + Gs + Gt + Gu + Gv + Gw + Gx + Gy + Gz + Gg + Gb + Gd + Gf = Gn + Gm + Go + Gp + Gq + Gs + Gt + Gu + Gv + Gw + Gx + Gy + Gz + Gg + Gb + Gd + Gf = Gn + Gm + Go + Gp + Gq + Gs + Gt + Gu + Gv + Gw + Gx + Gy + Gz + Gg + Gb + Gd + Gf =",
|
|
"gt_answers": "\\Delta G = G - G ^ { \\prime } = 6 0 N - 4 0 N = 2 0 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_2464.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 3x - 9 = 0`.",
|
|
"gt_answers": "x = \\sqrt [ 3 ] { - 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2465.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 H _ { 2 } O _ { 2 } \\xlongequal { M n O _ { 2 } } 2 H _ { 2 } O + O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_2466.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "A E \\bot B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_2468.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 2 = 10.\"",
|
|
"gt_answers": "x = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2469.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 4x - 10.",
|
|
"gt_answers": "( 3 y ) ^ { 2 } - 2 ( 3 y ) y + y ^ { 2 } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2471.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2m - 3m - 2",
|
|
"gt_answers": "1 - 2 m , x = - 3 m - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2472.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a negative sign, which can be represented in LaTeX as follows:\n\n\\(f(x) = -x^2\\)",
|
|
"gt_answers": "u = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2474.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 19.0506 x 10^6.",
|
|
"gt_answers": "\\frac { 9 } { 1 6 } \\approx 0 . 5 0 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2475.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x = \\frac { 9 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2476.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "A D = 1 2 ^ { c m } \\cdot A B = 6 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2477.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(R_i = \\frac{V_i}{I_i} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot \\frac{1}{R_0} \\cdot \\frac{1}{R_i}} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot \\frac{1}{R_0} \\cdot \\frac{1}{R_i} \\cdot \\frac{1}{R_0 \\cdot R_i}} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot \\frac{1}{R_0} \\cdot \\frac{1}{R_i^2}} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot \\frac{1}{R_0^2}} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot \\frac{1}{R_0}} \\cdot \\frac{1}{R_i^2} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot R_0 \\cdot R_i^2} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot R_0 \\cdot R_i} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot R_0 \\cdot R_i} \\cdot \\frac{1}{R_i} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot R_0 \\cdot R_i} \\cdot \\frac{1}{R_i} \\cdot \\frac{1}{R_i} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot R_0 \\cdot R_i} \\cdot \\frac{1}{R_i^2} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot R_0 \\cdot R_i^2} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot R_0 \\cdot R_i} = \\frac{V_i}{4 \\pi \\mu_0 \\cdot R_0 \\cdot R_i} \\cdot \\frac{1}{R_i} = \\frac{V_i}{4 \\pi \\mu_",
|
|
"gt_answers": "R _ { 1 } = \\frac { V _ { 1 } } { I _ { 1 } } = \\frac { 4 V } { 0 . 8 A } = 5 \\Omega .\n",
|
|
"image_path": "./data/HME100K/test_images/test_2478.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/",
|
|
"gt_answers": "x - \\frac { 1 } { 6 } + \\frac { 1 } { 6 } = \\frac { 3 } { 6 } t \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2479.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 492-50=6-12.",
|
|
"gt_answers": "4 9 2 \\div 8 0 = 6 \\cdots 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2481.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"50-2+2=48\".",
|
|
"gt_answers": "S O _ { 3 } ^ { 2 } + C l _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2482.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(x^2 + y^2 = 25\\)",
|
|
"gt_answers": "( x - 2 > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2483.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3 = 5.",
|
|
"gt_answers": "x _ { 1 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2484.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `x^2 + 3x + 4 = 64`.",
|
|
"gt_answers": "x = - \\frac { 6 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2485.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": ": \\angle B D N + \\angle N + \\angle D B N = 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2486.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis equation represents the multiplication of two fractions, each with a denominator of 2. The result is a fraction with a denominator of 4.",
|
|
"gt_answers": "h ( x ) \\leq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2490.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Sadho Saadho Saadho\" using the LaTeX formula.",
|
|
"gt_answers": "S _ { \\Delta } D H O = S _ { \\Delta } A C D + S _ { \\Delta } A O C + S _ { \\Delta } C O H - S _ { \\Delta } A O D\n",
|
|
"image_path": "./data/HME100K/test_images/test_2491.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 360/12 = 30.",
|
|
"gt_answers": "1 2 \\div \\frac { 1 } { 3 } = 3 6 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2492.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x^2 + 2x - 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\sqrt [ 3 ] { 6 \\frac { 6 } { 2 1 5 } } = 6 \\sqrt [ 3 ] { \\frac { 6 } { 2 1 5 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2494.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(t = \\frac{1}{8} \\left(1 + \\sqrt{16 \\left(1 - \\frac{1}{8} \\right)}\\right)\\)",
|
|
"gt_answers": "t = \\frac { 1 2 } { 6 . 4 } = 1 . 8 8 ( s )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2495.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(100 \\div 100 = 100\\)",
|
|
"gt_answers": "\\frac { O D } { D A } = \\frac { O F } { O C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2497.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"S = 2(1/2) + 3(1/3) + 4(1/4) + 5(1/5) + 6(1/6) + 7(1/7) + 8(1/8) + 9(1/9) + 10(1/10) + 11(1/11) + 12(1/12) + 13(1/13) + 14(1/14) + 15(1/15) + 16(1/16) + 17(1/17) + 18(1/18) + 19(1/19) + 20(1/20) + 21(1/21) + 22(1/22) + 23(1/23) + 24(1/24) + 25(1/25) + 26(1/26) + 27(1/27) + 28(1/28) + 29(1/29) + 30(1/30) + 31(1/31) + 32(1/32) + 33(1/33) + 34(1/34) + 35(1/35) + 36(1/36) + 37(1/37) + 38(1/38) + 39(1/39) + 40(1/40) + 41(1/41) + 42(1/42) + 43(1/43) + 44(1/44) + 45(1/45) + 46(1/46) + 47(1/47) + 48(1/48) + 49(1/49) + 50(1/50) + 51(1/51) + 52(1/52) + 53(1/",
|
|
"gt_answers": "S = \\frac { 1 } { 2 } a t ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2498.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3.843 \\times 10^{10} \\div 201 \\times 10^{3} \\div 3.843 \\times 10^{10} = 1.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
|
|
"gt_answers": "- \\vert - \\frac { 2 0 } { 7 } \\vert , - ( - \\frac { 3 } { 5 } ) , - 3 , 8 , 4 , 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2499.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2258866 x 100 = 225886600.",
|
|
"gt_answers": "\\frac { 5 2 + 3 8 + 1 6 } { 2 0 0 } = \\frac { x } { 1 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2500.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a negative sign, which is likely a mathematical expression in Japanese.",
|
|
"gt_answers": "x _ { 1 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2501.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x + 5 = 12.",
|
|
"gt_answers": "\\frac { 2 } { 5 } x = \\frac { 1 0 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2502.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 333 - 333 = 0.",
|
|
"gt_answers": "x = \\frac { 3 2 3 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2503.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(A = \\frac{1}{2} \\left( \\sqrt{3} \\left( \\sqrt{2} - 1 \\right) \\right)^2 + \\frac{1}{2} \\left( \\sqrt{3} \\left( \\sqrt{2} + 1 \\right) \\right)^2\\)",
|
|
"gt_answers": "a _ { 1 } = \\frac { 3 + \\sqrt { 1 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2504.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as b = 10/100.",
|
|
"gt_answers": "b = - \\frac { 2 0 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2506.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x = 1 , y = 3 - \\sqrt { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2507.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 1 } { 3 } ( \\frac { 1 } { m } + \\frac { 4 } { n } ) ( m + n ) = \\frac { 1 } { 2 } ( 5 + \\frac { n } { m } + \\frac { 4 m } { n } ) \\geqslant .\n",
|
|
"image_path": "./data/HME100K/test_images/test_2508.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(4 \\times BD = 9\\)\n\nThe formula is written using the LaTeX equation editor, which is a standard notation for mathematical equations. The equation consists of the variables \"4\" and \"BD\" on the left side, and the equal sign (=) in the middle. The right side of the equation contains the result of multiplying the two variables, which is 9.",
|
|
"gt_answers": "\\frac { 4 } { B D } = \\frac { 8 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2509.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(P(A \\land B) = P(A) \\cdot P(B) \\cdot P(A \\land B) / P(A \\land B \\land C) \\cdot P(C) \\cdot P(A \\land B \\land C) / P(A \\land B \\land C \\land D) \\cdot P(D) \\cdot P(A \\land B \\land C \\land D) / P(A \\land B \\land C \\land D \\land E) \\cdot P(E) \\cdot P(A \\land B \\land C \\land D \\land E) / P(A \\land B \\land C \\land D \\land E \\land F) \\cdot P(F) \\cdot P(A \\land B \\land C \\land D \\land E \\land F) / P(A \\land B \\land C \\land D \\land E \\land F \\land G) \\cdot P(G) \\cdot P(A \\land B \\land C \\land D \\land E \\land F \\land G) / P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H) \\cdot P(H) \\cdot P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H) / P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I) \\cdot P(I) \\cdot P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I) / P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I \\land J) \\cdot P(J) \\cdot P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I \\land J) / P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I \\land J \\land K) \\cdot P(K) \\cdot P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H",
|
|
"gt_answers": "P ( C ) = C _ { 4 } ^ { 2 } ( \\frac { 1 } { 3 } ) ^ { 2 } ( \\frac { 2 } { 3 } ) ^ { 2 } = \\frac { 8 } { 2 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2510.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "\\frac { 2 } { 3 } \\times 0 . 3 = \\frac { 1 } { 5 } \\frac { 5 } { 8 } \\times 0 . 8 = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2511.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{10} + \\frac{1}{20} + \\frac{1}{30} + \\frac{1}{40} + \\frac{1}{50} + \\frac{1}{60} + \\frac{1}{70} + \\frac{1}{80} + \\frac{1}{90} + \\frac{1}{100} = 1\n\\end{equation}\n\nThis equation can be interpreted as the sum of the first 10 terms of the geometric series, which is equal to 1.",
|
|
"gt_answers": "S ^ { L } = \\frac { ( 5 - 7 ) ^ { 2 } + ( 5 - 7 ) ^ { 2 } + ( 5 - 7 ) ^ { 2 } + ( 8 - 7 ) ^ { 2 } + ( 9 - 7 ) ^ { 2 } } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2512.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nFet + FeSO4 + CuSO4 + Cu(OH)2 + Cu(NO3)2 + Cu(OH)3 + Cu(NO3)3 + Cu(OH)4 + Cu(NO3)4 + Cu(OH)5 + Cu(NO3)5 + Cu(OH)6 + Cu(NO3)6 + Cu(OH)7 + Cu(NO3)7 + Cu(OH)8 + Cu(NO3)8 + Cu(OH)9 + Cu(NO3)9 + Cu(OH)10 + Cu(NO3)10 + Cu(OH)11 + Cu(NO3)11 + Cu(OH)12 + Cu(NO3)12 + Cu(OH)13 + Cu(NO3)13 + Cu(OH)14 + Cu(NO3)14 + Cu(OH)15 + Cu(NO3)15 + Cu(OH)16 + Cu(NO3)16 + Cu(OH)17 + Cu(NO3)17 + Cu(OH)18 + Cu(NO3)18 + Cu(OH)19 + Cu(NO3)19 + Cu(OH)20 + Cu(NO3)20 + Cu(OH)21 + Cu(NO3)21 + Cu(OH)22 + Cu(NO3)22 + Cu(OH)23 + Cu(NO3)23 + Cu(OH)24 + Cu(NO3)24 + Cu(OH)25 + Cu(NO3)25 + Cu(OH)26 + Cu(NO3)26 + Cu(OH)27 + Cu(NO3)27 + Cu(OH)28 + Cu(NO3)28 + Cu(OH)29 + Cu(NO3)29 + Cu(OH)30 + Cu(NO3)30 + Cu(OH)31 + Cu(NO3)31 + Cu(OH)32 + Cu(NO3)32 + Cu(OH)33 + Cu(NO3)33 + Cu(OH)34 + Cu(NO3)34 + Cu(OH)35 + Cu(",
|
|
"gt_answers": "F e + C u S O _ { 4 } = F e S O _ { 4 } + C u\n",
|
|
"image_path": "./data/HME100K/test_images/test_2513.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: X04 + BaCl4 + XCl4.",
|
|
"gt_answers": "x S O _ { 4 } + B a C l _ { 2 } \\rightarrow B a S O _ { 4 } + x C l _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2515.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2\\times\\sin(30^\\circ) + 2\\times\\sin(60^\\circ) + 2\\times\\sin(90^\\circ) = 2\\times\\sin(30^\\circ) + 2\\times\\sin(60^\\circ) + 2\\times\\sin(90^\\circ) + 2\\times\\sin(120^\\circ) + 2\\times\\sin(150^\\circ) + 2\\times\\sin(180^\\circ) = 2\\times\\sin(30^\\circ) + 2\\times\\sin(60^\\circ) + 2\\times\\sin(90^\\circ) + 2\\times\\sin(120^\\circ) + 2\\times\\sin(150^\\circ) + 2\\times\\sin(180^\\circ) + 2\\times\\sin(240^\\circ) = 2\\times\\sin(30^\\circ) + 2\\times\\sin(60^\\circ) + 2\\times\\sin(90^\\circ) + 2\\times\\sin(120^\\circ) + 2\\times\\sin(150^\\circ) + 2\\times\\sin(180^\\circ) + 2\\times\\sin(240^\\circ) + 2\\times\\sin(300^\\circ) = 2\\times\\sin(30^\\circ) + 2\\times\\sin(60^\\circ) + 2\\times\\sin(90^\\circ) + 2\\times\\sin(120^\\circ) + 2\\times\\sin(150^\\circ) + 2\\times\\sin(180^\\circ) + 2\\times\\sin(240^\\circ) + 2\\times\\sin(300^\\circ) = 2\\times\\sin(30^\\circ) + 2\\times\\sin(60^\\circ) + 2\\times\\sin(90^\\circ) + 2\\times\\sin(120^\\circ) + 2\\times\\sin(15",
|
|
"gt_answers": "\\alpha = 3 6 0 ^ { \\circ } - \\angle M A G = 3 6 0 ^ { \\circ } - 6 0 ^ { \\circ } = 3 0 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2516.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 9x^2 + 9y^2 = 18.",
|
|
"gt_answers": "x = \\frac { 9 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2519.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 2 } { x } = \\frac { x } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2520.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(m = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
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"gt_answers": "( m - 1 ) ^ { 2 } = ( \\sqrt { 2 0 1 9 } + 1 ) - 1 ) ^ { 2 } = 2 0 1 9\n",
|
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"image_path": "./data/HME100K/test_images/test_2521.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac",
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"gt_answers": "\\vert x + \\frac { 1 } { 2 } \\vert + \\vert x - \\frac { 3 } { 2 } \\vert \\leq 3\n",
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"image_path": "./data/HME100K/test_images/test_2523.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(U = \\frac{1}{2} \\left( \\frac{V^2}{R} + \\frac{P^2}{R} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{L} + \\frac{P^2}{L} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{C} + \\frac{P^2}{C} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{R} + \\frac{P^2}{R} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{L} + \\frac{P^2}{L} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{C} + \\frac{P^2}{C} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{R} + \\frac{P^2}{R} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{L} + \\frac{P^2}{L} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{C} + \\frac{P^2}{C} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{R} + \\frac{P^2}{R} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{L} + \\frac{P^2}{L} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{C} + \\frac{P^2}{C} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{R} + \\frac{P^2}{R} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{L} + \\frac{P^2}{L} \\right) + \\frac{1}{2} \\left( \\frac{V^2}{C} + \\frac{P^2}{C} \\",
|
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"gt_answers": "P = \\frac { U _ { 1 } ^ { 2 } } { R _ { 1 } }\n",
|
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"image_path": "./data/HME100K/test_images/test_2526.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2B = CB + 40\".",
|
|
"gt_answers": "\\angle B A E = \\frac { 1 } { 2 } \\angle B A C = 4 0\n",
|
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"image_path": "./data/HME100K/test_images/test_2527.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LCD = \\frac{BG + AG}{2} = \\frac{BG + AG}{2} \\cdot \\frac{BG - AG}{BG + AG} = \\frac{BG \\cdot AG}{BG + AG} = \\frac{BG}{BG + AG} \\cdot \\frac{AG}{BG + AG} = \\frac{BG}{2} \\cdot \\frac{AG}{2} = BG \\cdot AG\\)",
|
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"gt_answers": "\\angle C A D = \\angle B D G , B G = A C\n",
|
|
"image_path": "./data/HME100K/test_images/test_2528.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "1 2 . 9 1 < 1 2 . 9 5 < 1 2 . 9 8 < 1 3 . 0 0 < 1 3 . 1 2 < 1 3 . 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2530.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 6x^2 - 6x + 6 = 0.",
|
|
"gt_answers": "a ^ { 2 } + a - 6 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2531.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{20x-15}{x-10}\n\\end{equation}\n\nThis equation represents the ratio of the difference between 20 and 15, divided by the difference between x and 10.",
|
|
"gt_answers": "4 x ^ { 2 } - 4 x ^ { 2 } + 2 0 x - 2 5 - 1 5 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2534.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b^2 + 4ac = 0\\)",
|
|
"gt_answers": "= \\frac { b } { 2 c } = \\frac { 2 a } { 4 } = \\frac { 9 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2535.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `a^2 + 2b^2 - 2ab + b^2 - 1 = 0`.",
|
|
"gt_answers": "a _ { 9 } : 2 \\times 9 - 1 = 1 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_2537.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444",
|
|
"gt_answers": "1 4 4 - 4 8 y + 4 y ^ { 2 } - 3 6 y + 6 y ^ { 2 } + 2 y ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2538.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LCL = LAC + 45\u00b0\".",
|
|
"gt_answers": ". \\angle C O D = \\angle A O C = 4 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2539.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(c_d = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{",
|
|
"gt_answers": "c > d\n",
|
|
"image_path": "./data/HME100K/test_images/test_2540.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"n + 1\" in LaTeX format.",
|
|
"gt_answers": "u < f\n",
|
|
"image_path": "./data/HME100K/test_images/test_2541.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BDBIAC Loading 15.\"",
|
|
"gt_answers": "B D / / A C \\angle O A C = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2543.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(20 = 20 \\times 100 = 2000\\)",
|
|
"gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2544.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\n\\(F = \\frac{Gm_1m_2}{r^2}\\)\n\nwhere F is the force between the two objects, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.",
|
|
"gt_answers": "F = G = m g = 1 \\times 1 0 ^ { 3 } k g \\times 1 0 N / k g = 1 \\times 1 0 ^ { 4 } N\n",
|
|
"image_path": "./data/HME100K/test_images/test_2545.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = z^2\\)",
|
|
"gt_answers": "F G = \\frac { 1 } { 2 } \\times 1 0 0 = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2546.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^{2} + 4x + 100 = 0\\)\n\nThis formula can be solved using the quadratic formula:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^{2} - 4ac}}{2a}\\)\n\nIn this case, the quadratic formula simplifies to:\n\n\\(x = \\frac{-4 \\pm \\sqrt{4^{2} - 4(4)(100)}}{2(4)} = \\frac{-4 \\pm \\sqrt{16}}{2} = \\frac{-4 \\pm 4}{2} = \\frac{-4 \\pm 2}{2} = \\frac{-2 \\pm 1}{2} = \\frac{-1 \\pm 1}{2} = \\frac{-1}{2} = -0.5\\)\n\nTherefore, the solution to the formula is -0.5.",
|
|
"gt_answers": "x _ { 1 1 2 } = \\frac { 4 \\pm \\sqrt { 1 6 0 } } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2547.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4x3 - 12x2 + 15x + 12.",
|
|
"gt_answers": "\\frac { 4 } { 3 } = \\frac { 4 \\times 3 } { 3 \\times 3 } = \\frac { 1 2 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2548.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 5\\)",
|
|
"gt_answers": "y = \\pm 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2551.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "5 9 . 0 2 > 5 8 . 5 2 > 5 8 . 1 7 > 5 8 . 0 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_2553.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x = 12/7\".",
|
|
"gt_answers": "x = - \\frac { 1 2 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2554.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as (wz-10) / (wz-5) where w is the weight of the object and z is the number of times the object is weighed.",
|
|
"gt_answers": "( \\sqrt { 2 } - 1 , 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2555.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2}",
|
|
"gt_answers": "A D = D C = 5 \\cdot \\frac { A B } { A C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2556.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `x^2 - 2x + 1 = 0`.",
|
|
"gt_answers": "( 9 - c ) ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2557.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 10x314 = 314x10.",
|
|
"gt_answers": "1 0 ^ { 2 } \\times 3 . 1 4 = 3 1 4 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2558.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"C4:C6 + C6:C8 + C8:C10 + C10:C12 + C12:C14 + C14:C16 + C16:C18 + C18:C20 + C20:C22 + C22:C24 + C24:C26 + C26:C28 + C28:C30 + C30:C32 + C32:C34 + C34:C36 + C36:C38 + C38:C40 + C40:C42 + C42:C44 + C44:C46 + C46:C48 + C48:C50 + C50:C52 + C52:C54 + C54:C56 + C56:C58 + C58:C60 + C60:C62 + C62:C64 + C64:C66 + C66:C68 + C68:C70 + C70:C72 + C72:C74 + C74:C76 + C76:C78 + C78:C80 + C80:C82 + C82:C84 + C84:C86 + C86:C88 + C88:C90 + C90:C92 + C92:C94 + C94:C96 + C96:C98 + C98:C100 + C100:C102 + C102:C104 + C104:C106 + C106:C108 + C108:C110 + C110:C112 + C112:C114 + C114:C116 + C116:C118 + C118:C120 + C120:C122 + C122:C124 + C1",
|
|
"gt_answers": "C _ { 4 } ^ { 1 } \\cdot C _ { 6 } ^ { 3 } \\cdot = 8 : 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2559.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 20/13 = 1.566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666",
|
|
"gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2560.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `x^2 + 54 = 100`.",
|
|
"gt_answers": "x + \\frac { 2 1 } { 2 5 } = \\pm \\frac { 5 4 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2562.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 5\\)",
|
|
"gt_answers": "2 0 + 2 3 = 4 3 ( s\n",
|
|
"image_path": "./data/HME100K/test_images/test_2563.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 4x + 3 = 0.\"",
|
|
"gt_answers": "x = \\frac { 3 } { 4 } - \\frac { 2 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2564.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(P_{a} = \\frac{F_{a}}{A} = \\frac{F_{a}}{S_{n} \\cdot N_{n}} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A \\cdot \\pi} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A \\cdot \\pi \\cdot r^{2}} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A \\cdot \\pi \\cdot r^{2}} \\cdot \\frac{r^{2}}{r^{2}} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A \\cdot \\pi \\cdot r^{2}} \\cdot \\frac{r^{2}}{r^{2}} \\cdot \\frac{r^{2}}{r^{2}} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A \\cdot \\pi \\cdot r^{2}} \\cdot \\frac{r^{4}}{r^{4}} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A \\cdot \\pi \\cdot r^{2}} \\cdot \\frac{r^{4}}{r^{4}} \\cdot \\frac{r^{2}}{r^{2}} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A \\cdot \\pi \\cdot r^{2}} \\cdot \\frac{r^{6}}{r^{6}} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A \\cdot \\pi \\cdot r^{2}} \\cdot \\frac{r^{6}}{r^{6}} \\cdot \\frac{r^{2}}{r^{2}} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A \\cdot \\pi \\cdot r^{2}} \\cdot \\frac{r^{8}}{r^{8}} = \\frac{F_{a}}{S_{n} \\cdot N_{n} \\cdot A \\cdot \\pi \\cdot r^{2}} \\cdot \\frac{r^{8",
|
|
"gt_answers": "P A = \\frac { F A } { S A } = \\frac { G A } { a ^ { 2 } } = \\frac { 8 N } { 0 . 0 1 m ^ { 2 } } = 8 0 0 P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_2565.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 5x^2 + 6x + 7\\)\n\nThe formula is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "\\cos \\frac { 2 3 \\pi } { 3 } = \\cos ( \\pi + \\frac { 2 } { 3 } \\pi ) = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2566.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 3x + 5 = 0\\)",
|
|
"gt_answers": "\\cos \\alpha = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2567.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\nb = \\frac{1}{2} \\left(a + \\sqrt{a^2 + 4b^2}\\right)\n\\end{equation}\n\nThis formula is used to find the value of b when given the value of a and the square root of a squared plus 4b squared.",
|
|
"gt_answers": "b = \\frac { 7 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2568.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `b^2 + y^2 = 1`.",
|
|
"gt_answers": "b ^ { 2 } y ^ { 2 } + y ^ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2569.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\ny = 2x + 1\n\nThis formula represents a linear equation in two variables, where y is the dependent variable and x is the independent variable. The constant 2 is the slope of the line, and 1 is the y-intercept.",
|
|
"gt_answers": "y = \\frac { 5 1 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2570.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 8x + 10 = 0\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(x^2 + 8x + 10 = 0\\)\n\nThe LaTeX code for the formula is:\n\n\\begin{equation}\nx^2 + 8x + 10 = 0\n\\end{equation}\n\nThe LaTeX code for the expression is:\n\n\\begin{equation}\nx^2 + 8x + 10\n\\end{equation}",
|
|
"gt_answers": "x ^ { 2 } + \\frac { 1 4 } { 3 } x + \\frac { 8 } { 3 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2571.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(A + B = C\\)\n\nThis formula represents the basic algebraic equation of addition, where A, B, and C are variables representing the three terms of the equation.",
|
|
"gt_answers": "\\frac { A B } { C E } = \\frac { B O } { E O } = \\frac { A O } { C O }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2572.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/2 + 1/3 = 1/6.\"",
|
|
"gt_answers": "- \\frac { 1 } { 2 } x = 1 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2574.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Sapco-x = 3x + 2.\"",
|
|
"gt_answers": "S _ { \\Delta P C O } = \\frac { 1 } { 2 } \\times 3 \\times \\vert x \\vert = \\frac { 3 \\vert x \\vert } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2575.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\ce{Fe2O3 + 2H2SO4 -> FeSO4 + 2H2O + O2}\n\\end{equation}\n\nThis formula represents the chemical reaction between iron(III) oxide (Fe2O3) and sulfuric acid (H2SO4) to produce iron(II) sulfate (FeSO4), water (H2O), and oxygen (O2).",
|
|
"gt_answers": "2 A g N O _ { 3 } + F e = F e ( N O _ { 3 } ) _ { 2 } + 2 A g\n",
|
|
"image_path": "./data/HME100K/test_images/test_2576.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "2 [ \\frac { 4 } { 3 } x - \\frac { 2 } { 3 } x + \\frac { 1 } { 2 } ] = \\frac { 3 } { 4 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2577.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 0.08 x 100 = 8%.",
|
|
"gt_answers": "0 . 0 8 = \\frac { 8 } { 1 0 0 } = 8 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_2578.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 11 + 3 = 14.",
|
|
"gt_answers": "\\frac { 1 7 } { 3 } y = \\frac { 1 7 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2579.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 0.02m.",
|
|
"gt_answers": "0 . 5 m o l\n",
|
|
"image_path": "./data/HME100K/test_images/test_2580.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BD = 0.055.\"",
|
|
"gt_answers": "\\frac { A B } { B D } = 0 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2581.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. In this case, the variable is x, and the square of x is x^2. The variable y is also involved in the equation, and its square is y^2. The equation is solved by setting the two sides equal to each other, which results in the equation x^2 + y^2 = 1.",
|
|
"gt_answers": "x = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2582.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x + 2y = 10.",
|
|
"gt_answers": "\\frac { 3 } { 1 + 1 } - \\frac { x } { x - 1 } + 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2583.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as (2/3) + (1/4) - (1/6) + (1/7) - (1/8) - (1/9) - (1/10) - (1/11) - (1/12) - (1/13) - (1/14) - (1/15) - (1/16) - (1/17) - (1/18) - (1/19) - (1/20) - (1/21) - (1/22) - (1/23) - (1/24) - (1/25) - (1/26) - (1/27) - (1/28) - (1/29) - (1/30) - (1/31) - (1/32) - (1/33) - (1/34) - (1/35) - (1/36) - (1/37) - (1/38) - (1/39) - (1/40) - (1/41) - (1/42) - (1/43) - (1/44) - (1/45) - (1/46) - (1/47) - (1/48) - (1/49) - (1/50) - (1/51) - (1/52) - (1/53) - (1/54) - (1/55) - (1/56) - (1/57) - (1/58) - (1/59) - (1/60) - (1/61) - (1/62) - (1/63) - (1/64) - (1/65) - (1/66) - (1/67) - (1/68) - (1/69) - (1/70) - (1/71) - (1/72) - (1/73) - (1/74) - (1/75) - (1/76",
|
|
"gt_answers": "( 1 ) 1 2 . 5 6 \\div 3 . 1 4 = 4 d m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2584.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `60 = 1/2 x (x + 1)^2`.",
|
|
"gt_answers": "1 2 x = 1 2 \\times 5 = 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2586.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6.755149072941185 + 5.149072941185275 - 1.072941185275275 + 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "6 . 6 . 7 . \\sqrt { 3 } 8 \\sqrt { 2 } - 1 9 1 0 1 0 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_2588.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3 = 5.",
|
|
"gt_answers": "x = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2589.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"P(A or B) = P(A) + P(B) - P(A and B).\"",
|
|
"gt_answers": "P _ { a } : P _ { b } = 4 : 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2590.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "- 3 ^ { 2 } - ( - 1 \\frac { 2 } { 5 } ) \\div 1 \\frac { 5 } { 9 } \\times ( - \\frac { 5 } { 6 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2591.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(L_{RF} = 90 \\cdot \\left( \\frac{RF}{RF_{max}} \\right)^{0.5}\\)\n\nThis formula calculates the ratio of the received field strength (RF) to the maximum received field strength (RF_{max}) as a function of the ratio of the reflectance factor (RF) to the maximum reflectance factor (RF_{max}).",
|
|
"gt_answers": "\\angle 2 + \\angle B C F = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2592.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x(11-2x12) = 11x11 - 2x12x11 + 2x12x11x11 - 2x12x11x12\".",
|
|
"gt_answers": "1 2 x + m - 1 1 \\leq 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2593.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{50644 \\cdot 56 \\cdot 65}{4 \\cdot 5 \\cdot 6}\n\\end{aligned}\n\\end{equation}\n\nThe formula is a multiplication of four numbers, with the first three numbers multiplied together and the last number multiplied by the first three numbers. The result is then divided by the first three numbers.",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2594.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 31.44% = 44/100.",
|
|
"gt_answers": "3 . 6 : x = 4 8 \\% : \\frac { 3 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2595.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3 \\times 4 + 1 \\times 2 + 1 \\times 3 + 2 \\times 4 + 1 \\times 5 + 2 \\times 6 + 3 \\times 7 + 4 \\times 8 + 5 \\times 9 + 6 \\times 10 + 7 \\times 11 + 8 \\times 12 + 9 \\times 13 + 10 \\times 14 + 11 \\times 15 + 12 \\times 16 + 13 \\times 17 + 14 \\times 18 + 15 \\times 19 + 16 \\times 20 + 17 \\times 21 + 18 \\times 22 + 19 \\times 23 + 20 \\times 24 + 21 \\times 25 + 22 \\times 26 + 23 \\times 27 + 24 \\times 28 + 25 \\times 29 + 26 \\times 30 + 27 \\times 31 + 28 \\times 32 + 29 \\times 33 + 30 \\times 34 + 31 \\times 35 + 32 \\times 36 + 33 \\times 37 + 34 \\times 38 + 35 \\times 39 + 36 \\times 40 + 37 \\times 41 + 38 \\times 42 + 39 \\times 43 + 40 \\times 44 + 41 \\times 45 + 42 \\times 46 + 43 \\times 47 + 44 \\times 48 + 45 \\times 49 + 46 \\times 50 + 47 \\times 51 + 48 \\times 52 + 49 \\times 53 + 50 \\times 54 + 51 \\times 55 + 52 \\times 56 + 53 \\times 57 + 54 \\",
|
|
"gt_answers": "3 = a ^ { 2 } + 1 - 2 a \\cos \\frac { 2 \\pi } { 3 } ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_2596.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} = \\frac{1}{27}\n\\end{equation}\n\nThis formula represents the multiplication of three identical fractions, each with a denominator of 3. The result is a fraction with a denominator of 27.",
|
|
"gt_answers": "( 3 ^ { \\frac { 1 } { 3 } } \\times 5 ^ { \\frac { 1 } { 3 } } ) ^ { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2597.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis equation is a simple algebraic expression that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "2 x - 3 y = 6 2 x - . 3 y\n",
|
|
"image_path": "./data/HME100K/test_images/test_2598.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "5 S _ { 1 } + 3 S _ { 2 } = 2 S _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2600.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis is a simple algebraic equation that can be solved using the addition and subtraction operations.",
|
|
"gt_answers": "< ^ { 2 } - \\frac { 1 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2601.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 4\\)",
|
|
"gt_answers": "y _ { 2 } = \\frac { 2 } { k } + 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2602.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 4x - 4 = 0\\)",
|
|
"gt_answers": "\\frac { 4 } { x ^ { 2 } - 4 } = \\frac { x + 1 } { x + 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2603.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"a^2 + b^2 = c^2.\"",
|
|
"gt_answers": "a = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2604.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = -3x^2 + 2x + 1\\)",
|
|
"gt_answers": "\\frac { 1 } { 3 } y - y = - \\frac { 1 } { 3 } - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2605.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b(169) - 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "( 3 a + 1 ) ( 6 a - 1 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2606.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "x _ { 1 } = 0 , x _ { 2 } = \\frac { - 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2607.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: (4x + 10x^2 + 3x^3) + (10x + 3x^2 + 5x^3) + (5x + 10x^2 + 7x^3) + (10x + 7x^2 + 9x^3) + (7x + 10x^2 + 11x^3) + (10x + 11x^2 + 12x^3) + (11x + 10x^2 + 13x^3) + (10x + 13x^2 + 14x^3) + (13x + 10x^2 + 15x^3) + (10x + 15x^2 + 16x^3) + (15x + 10x^2 + 17x^3) + (10x + 17x^2 + 18x^3) + (17x + 10x^2 + 19x^3) + (10x + 19x^2 + 20x^3) + (19x + 10x^2 + 21x^3) + (10x + 21x^2 + 22x^3) + (21x + 10x^2 + 23x^3) + (23x + 10x^2 + 24x^3) + (24x + 10x^2 + 25x^3) + (25x + 10x^2 + 26x^3) + (26x + 10x^2 + 27x^3) + (27x + 10x^2 + 28x^3) + (28x + 10x^2 + 29x^3) + (29x + 10x^2 + 30x^3) + (30x + 10x^2 + 31x^3) + (31x + 10x^",
|
|
"gt_answers": "4 ( x - 1 ) - 1 0 x + 1 > 3 ( 2 x - 3 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2609.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(N_{a} + N_{b} = N_{a} + N_{b} + N_{c} + N_{d} + N_{e} + N_{f} + N_{g} + N_{h} + N_{i} + N_{j} + N_{k} + N_{l} + N_{m} + N_{n} + N_{o} + N_{p} + N_{q} + N_{r} + N_{s} + N_{t} + N_{u} + N_{v} + N_{w} + N_{x} + N_{y} + N_{z} + N_{aa} + N_{bb} + N_{cc} + N_{dd} + N_{ee} + N_{ff} + N_{gg} + N_{hh} + N_{ii} + N_{jj} + N_{kk} + N_{ll} + N_{mm} + N_{nn} + N_{oo} + N_{pp} + N_{qq} + N_{rr} + N_{ss} + N_{tt} + N_{uu} + N_{vv} + N_{ww} + N_{xx} + N_{yy} + N_{zz} + N_{aaa} + N_{bbb} + N_{ccc} + N_{ddd} + N_{eee} + N_{fff} + N_{ggg} + N_{hhh} + N_{iii} + N_{jjj} + N_{kkk} + N_{lll} + N_{mmm} + N_{nnn} + N_{ooo} + N_{ppp} + N_{qqq} + N_{rrr} + N_{sss} + N_{ttt} + N_{uuu} + N_{vvv} + N_{www} + N_{xxx} + N_{yyy} + N_{zzz} + N_{aaaa} + N_{bbbb} + N_{cccg} + N_{dddd} + N_{eeee} + N_{fffg} + N_{gggg} + N_{hhhh} + N_{iiiq} + N_{jjjj} + N_{kkkk",
|
|
"gt_answers": "2 2 N a O H + C O _ { 2 } = N a _ { 2 } C O _ { 3 } + H _ { 2 } O (\n",
|
|
"image_path": "./data/HME100K/test_images/test_2611.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x2 + 2x2 = 4x2.",
|
|
"gt_answers": "2 = \\frac { 1 } { 2 } \\times 2 \\times Q H\n",
|
|
"image_path": "./data/HME100K/test_images/test_2612.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(12 + 12 = 24\\)",
|
|
"gt_answers": "\\frac { 5 } { 1 2 } + \\frac { 5 } { 1 2 } - \\frac { 7 } { 1 2 } = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2614.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(A = \\sqrt{B^2 + C^2}\\)",
|
|
"gt_answers": "A C = 2 ( \\sqrt { 3 } + 1 ) m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2615.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left(",
|
|
"gt_answers": "m _ { 1 } = 1 0 m _ { 2 } = 1 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2616.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"IDB = SMC * (1 - SMC)\".",
|
|
"gt_answers": "\u3001 D \u3001 B ^ { \\prime } C = 5 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2617.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right) + 0.06 \\left( 0.08 + 0.03 \\right)",
|
|
"gt_answers": "0 . 8 - 0 . 7 = 0 . 1 1 . 9 + 0 . 4 = 2 . 3 1 . 6 - 0 . 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_2620.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\sqrt{2} - 2\\sqrt{3} = 2\\sqrt{2} - 2\\sqrt{6} = 2\\sqrt{2} - 2\\sqrt{12} = 2\\sqrt{2} - 2\\sqrt{24} = 2\\sqrt{2} - 2\\sqrt{36} = 2\\sqrt{2} - 2\\sqrt{72} = 2\\sqrt{2} - 2\\sqrt{144} = 2\\sqrt{2} - 2\\sqrt{288} = 2\\sqrt{2} - 2\\sqrt{576} = 2\\sqrt{2} - 2\\sqrt{1152} = 2\\sqrt{2} - 2\\sqrt{2304} = 2\\sqrt{2} - 2\\sqrt{4608} = 2\\sqrt{2} - 2\\sqrt{9216} = 2\\sqrt{2} - 2\\sqrt{18432} = 2\\sqrt{2} - 2\\sqrt{36656} = 2\\sqrt{2} - 2\\sqrt{73280} = 2\\sqrt{2} - 2\\sqrt{146432} = 2\\sqrt{2} - 2\\sqrt{293040} = 2\\sqrt{2} - 2\\sqrt{586080} = 2\\sqrt{2} - 2\\sqrt{1172160} = 2\\sqrt{2} - 2\\sqrt{2344320} = 2\\sqrt{2} - 2\\sqrt{4688640} = 2\\sqrt{2} - 2\\sqrt{9376960} = 2\\sqrt{2} - 2\\sqrt{18753840} = 2\\sqrt{2} - 2\\sqrt{37597600} = 2\\sqrt{2} -",
|
|
"gt_answers": "\\frac { 2 1 } { x } = \\frac { 2 . 5 } { 1 } = 2 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2621.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2LG + 2",
|
|
"gt_answers": "\\angle C G E = \\angle D E G + \\angle G D E\n",
|
|
"image_path": "./data/HME100K/test_images/test_2622.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows: `P(A or B) = P(A) + P(B) - P(A and B)`.",
|
|
"gt_answers": "1 . ( x + y ) ^ { 2 } + 6 ( x + y ) + 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_2623.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 29.97 + 0.0325 * 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "x = \\frac { 2 9 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2624.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{x^2 + 2x + 1}{x^2 + 3x + 2} \\tag{1}\\label{formula1}`",
|
|
"gt_answers": "\\frac { 1 } { x + y } + \\frac { 2 } { x - y } = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2625.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(y = 35x^2 + 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "y _ { 2 } = 3 5 \\times 8 0 0 + 2 0 0 0 0 = 4 8 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2626.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "D = \\frac { v } { t } = \\frac { 1 . 2 \\times 1 0 6 J } { 6 0 0 s } = 2 0 0 0 W\n",
|
|
"image_path": "./data/HME100K/test_images/test_2627.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x^2 + 3x + 4 = 0.\"",
|
|
"gt_answers": "S x _ { 1 } = \\sqrt { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2628.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 0.044444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444",
|
|
"gt_answers": "\\cdot 6 V + 0 . 4 A ( \\frac { 9 } { 4 } R _ { b } ) = 0 . 3 A \\times ( 4 0 \\Omega + R _ { b } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2629.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{3} \\cdot \\frac{1}{2} \\cdot \\frac{1}{4} = \\frac{1}{12}\n\\end{equation}\n\nThe equation is a multiplication of three fractions, each with a denominator of 12. The result is a fraction with a denominator of 12.",
|
|
"gt_answers": "8 + 3 = - \\frac { 1 } { 2 } - a\n",
|
|
"image_path": "./data/HME100K/test_images/test_2630.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Korean.",
|
|
"gt_answers": "x ^ { 2 } - x y + 4 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2631.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"cos(x) + sin(x) = 1.\"",
|
|
"gt_answers": "\\cos ( \\frac { \\pi } { 2 } + x ) = - \\sin x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2633.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x - 4.",
|
|
"gt_answers": "x = - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2634.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(O_{B} = \\frac{O_{A}}{O_{C}}\\)\n\nThis formula represents the ratio of the output of the B component to the output of the A component, where OA is the output of the A component and OB is the output of the B component.",
|
|
"gt_answers": "\\frac { . O B } { O E } = \\frac { O D } { O C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2635.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{x^2 + y^2 + z^2} = \\frac{1}{x^2} + \\frac{1}{y^2} + \\frac{1}{z^2} + \\frac{2}{x^2y^2} + \\frac{2}{x^2z^2} + \\frac{2}{y^2z^2} + \\frac{2}{x^2yz} + \\frac{2}{y^2zx} + \\frac{2}{x^2yzx} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxxy} + \\frac{2}{x^2yzxxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} + \\frac{2}{y^2zxy} + \\frac{2}{x^2yzxy} +",
|
|
"gt_answers": "( \\frac { 3 } { 5 } x - \\frac { 4 } { 1 1 } ) + ( - \\frac { 1 } { 2 } ) = \\frac { x } { 1 1 0 } x - 1 = \\frac { 7 ^ { n } } { 1 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2636.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(13 - 1) + 3(2 - 1) + 4(3 - 1) + 5(4 - 1) + 6(5 - 1) + 7(6 - 1) + 8(7 - 1) + 9(8 - 1) + 10(9 - 1) + 11(10 - 1) + 12(11 - 1) + 13(12 - 1) + 14(13 - 1) + 15(14 - 1) + 16(15 - 1) + 17(16 - 1) + 18(17 - 1) + 19(18 - 1) + 20(19 - 1) + 21(20 - 1) + 22(21 - 1) + 23(22 - 1) + 24(23 - 1) + 25(24 - 1) + 26(25 - 1) + 27(26 - 1) + 28(27 - 1) + 29(28 - 1) + 30(29 - 1) + 31(30 - 1) + 32(31 - 1) + 33(32 - 1) + 34(33 - 1) + 35(34 - 1) + 36(35 - 1) + 37(36 - 1) + 38(37 - 1) + 39(38 - 1) + 40(39 - 1) + 41(40 - 1) + 42(41 - 1) + 43(42 - 1) + 44(43 - 1) + 45(44 - 1) + 46(45 - 1) + 47(46 - 1) + 48(47 - 1",
|
|
"gt_answers": "\\frac { 1 3 } { 2 1 } - \\frac { ( 1 2 ) } { 2 1 } + \\frac { 4 } { 2 1 } = \\frac { 5 } { 2 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2637.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x ^ { 2 } + 2 x - 2 x ^ { 2 } + \\varphi x - x - k + x ^ { 2 } - \\varphi = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2638.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "C _ { 2 } = y = - x ^ { 2 } + 2 x + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2639.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "- x ^ { 2 } + 6 x + x ^ { 2 } - x - 4 = k\n",
|
|
"image_path": "./data/HME100K/test_images/test_2640.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(EM = 12 + 13 = 25\\)",
|
|
"gt_answers": "\\frac { E M } { 1 2 } = \\frac { \\frac { 1 3 } { 2 } } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2641.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 5\\)",
|
|
"gt_answers": "x _ { 1 } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2642.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CuSO4 + H2SO4 = CuSO4\\+H2SO4\".",
|
|
"gt_answers": "C u O + H _ { 2 } S O _ { 4 } = C u S O _ { 4 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2643.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 x ^ { 2 } + ( 4 n - 4 ) x + n ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2644.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `DCM = 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 2 c m = 1 2 0 0 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2645.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "f ( 2 ) = e ^ { 2 } f ( 4 ) = \\frac { e ^ { 4 } } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2646.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: G = 45 + 1/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 1 } { C _ { 1 0 } ^ { 2 } } = \\frac { 1 } { 4 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2647.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{s_n - s_{n-1}}{n} = \\frac{s_n - s_{n-2}}{n-1} + \\frac{s_{n-1} - s_{n-2}}{n-1} = \\frac{s_n - s_{n-2}}{n-1} + \\frac{s_{n-1} - s_{n-3}}{n-2} + \\frac{s_{n-2} - s_{n-3}}{n-2} + \\frac{s_{n-3} - s_{n-4}}{n-3} + \\cdots + \\frac{s_{2} - s_{3}}{2} + \\frac{s_{3} - s_{4}}{3} + \\frac{s_{4} - s_{5}}{4} + \\cdots + \\frac{s_{n-5} - s_{n-4}}{n-5} + \\frac{s_{n-4} - s_{n-3}}{n-4} + \\frac{s_{n-3} - s_{n-2}}{n-3} + \\frac{s_{n-2} - s_{n-1}}{n-2}\n\\end{equation}\n\nThis is a general formula for the nth term of a geometric sequence, where s_n is the nth term and s_1 is the first term.",
|
|
"gt_answers": "S _ { n - 1 } = \\frac { 3 n - n ^ { 2 } - 2 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2648.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2(x + 1) - 3(x - 1) = 0.",
|
|
"gt_answers": "z = - \\frac { 1 7 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2649.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(6x^2 + 6x + 6 = 3(2x^2 + 2x + 1)\\)",
|
|
"gt_answers": ": 3 \\times 3 \\times 6 = 5 4 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2650.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 1/5 + 1/5 = 2/5.",
|
|
"gt_answers": "\\frac { x } { 1 5 } = \\frac { 1 . 5 } { 0 . 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2651.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few words written in Japanese, which could be a mathematical expression or a phrase related to mathematics.",
|
|
"gt_answers": "2 . 5 \\times 2 . 5 = 6 . 2 5 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2652.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "\\frac { 1 } { 1 2 0 } x + \\frac { 1 } { 2 4 } + \\frac { 1 } { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2653.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\nBPE = BED + (0.8 x 0.5 x 0.5) x (0.7 x 0.7 x 0.7) x (0.6 x 0.6 x 0.6) x (0.5 x 0.5 x 0.5) x (0.4 x 0.4 x 0.4) x (0.3 x 0.3 x 0.3) x (0.2 x 0.2 x 0.2) x (0.1 x 0.1 x 0.1) x (0.05 x 0.05 x 0.05) x (0.04 x 0.04 x 0.04) x (0.03 x 0.03 x 0.03) x (0.02 x 0.02 x 0.02) x (0.01 x 0.01 x 0.01) x (0.005 x 0.005 x 0.005) x (0.004 x 0.004 x 0.004) x (0.003 x 0.003 x 0.003) x (0.002 x 0.002 x 0.002) x (0.001 x 0.001 x 0.001) x (0.0005 x 0.0005 x 0.0005) x (0.0004 x 0.0004 x 0.0004) x (0.0003 x 0.0003 x 0.0003) x (0.0002 x 0.0002 x 0.0002) x (0.0001 x 0.0001 x 0.0001) x (0.00005 x 0.00005 x 0.00005) x (0.0000",
|
|
"gt_answers": "\\angle B D E = \\angle B E D = \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } - 3 0 ^ { \\circ } ) = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2654.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2}\\)",
|
|
"gt_answers": "y = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2655.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(30 + 7 = 97\\)",
|
|
"gt_answers": "9 7 \\div 3 0 = 3 \\cdots 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_2656.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x^2 + 2x + 1 = 10\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\n3x^2 + 2x + 1 = 10\n\\end{equation}\n\nThe equation is written in the form of an equation with the variable x on the left side and the expression on the right side. The equation is also written in the standard mathematical notation, with the equal sign in the middle and the variables and expressions separated by the equal sign.",
|
|
"gt_answers": "\\frac { 1 } { 4 } = \\frac { 1 \\times 3 } { 4 \\times 3 } = \\frac { 3 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2657.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "a ^ { 2 } + b ^ { 2 } - a b = 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2658.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(P = \\frac{1}{2} \\cdot \\pi \\cdot r^2\\)\n\nwhere P is the pressure, r is the radius of the sphere, and \u03c0 is the constant pi.",
|
|
"gt_answers": "\\sqrt { 3 x + 1 } = 1 + \\sqrt { 5 x - 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2659.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: EQ = (6 sin(30 degrees) + 3 sin(60 degrees)) / 2.",
|
|
"gt_answers": "E Q = C Q \\sin C = 3 0 ( \\sqrt { 3 } - 1 ) c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2660.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\",
|
|
"gt_answers": "( 2 . 5 \\times 1 0 ^ { 3 } + 1 0 \\times 1 0 ^ { 3 } ) \\times 1 0 = 1 . 2 5 \\times 1 0 ^ { 5 } ( N\n",
|
|
"image_path": "./data/HME100K/test_images/test_2661.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(6v^2/2g = 1/2mv^2\\)\n\nThis formula relates the kinetic energy of an object to its mass and its velocity squared.",
|
|
"gt_answers": "L _ { 7 } = \\frac { 6 V } { 6 0 \\Omega } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2662.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(H_2O + NaOH \\rightarrow Na_2CO_3 + H_2O\\)",
|
|
"gt_answers": "2 N a O H + S O _ { 2 } = N a _ { 2 } S O _ { 4 } + H _ { 2 } \\uparrow \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_2663.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 + 2x + 2y + 3 = 10\\)",
|
|
"gt_answers": "\\vert x + \\frac { m - 1 } { 2 } \\vert + \\frac { 3 } { 2 } - x \\leq 3 - x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2664.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 10\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = \\frac { 4 7 } { 2 } - \\frac { 2 6 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2665.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(L_B \\cdot D_C = 60\\)\n\nThe formula represents the relationship between the length of the base (L_B) and the diameter of the center (D_C) of a circle. The result of the formula is 60.",
|
|
"gt_answers": "\\angle B O D = \\angle D O C = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2666.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 20\\)",
|
|
"gt_answers": "\\frac { 3 } { 5 } x = 3 2 0 \\times ( - \\frac { 2 } { 5 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2667.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2x^2 + 2x + 1 = 6.",
|
|
"gt_answers": "\\frac { 1 } { 3 } \\times \\frac { 1 } { 2 } = \\frac { 1 \\times 1 } { 3 \\times 2 } = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2669.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 100 \\cdot 10",
|
|
"gt_answers": "\\frac { 8 0 } { 1 1 } = 7 \\frac { 2 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2671.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"8x = 4cm.\"",
|
|
"gt_answers": "8 \\times \\pi \\times \\frac { 1 } { 2 } = 4 \\pi ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2672.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2(269) + 7 = 538.",
|
|
"gt_answers": "- 2 . 5 + a = - 1 5 + 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_2673.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: f(x) = 1/x + 1/x^2.",
|
|
"gt_answers": "f ( x ) - m \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_2674.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"soc-kats = 1-kats\" using LaTeX format.",
|
|
"gt_answers": "S _ { \\Delta } C E O = 1 \\times 2 \\times \\frac { 1 } { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2675.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"lend = 4bme.\"",
|
|
"gt_answers": "- \\frac { 1 } { 2 } \\angle E N D = \\frac { 1 } { 2 } \\angle B M E\n",
|
|
"image_path": "./data/HME100K/test_images/test_2676.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\tan ( \\frac { \\pi } { 4 } - x ) = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2677.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 260 = 30x.",
|
|
"gt_answers": "\\frac { 1 } { 2 } 6 0 = 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2678.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2.5sth + 1.5sth = 3sth.\"",
|
|
"gt_answers": "1 2 0 = 2 . 5 k + b\n",
|
|
"image_path": "./data/HME100K/test_images/test_2679.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x + 2 = 10.\"",
|
|
"gt_answers": "y _ { 4 } = - \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2681.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 0 . 5 } { 1 . 5 } = \\frac { 1 . 5 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2682.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x2 + 2x2 = 5x2.\"",
|
|
"gt_answers": "a _ { n } - 3 = 2 ( a _ { n - 1 } - 3 ) ( n \\geq 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2683.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(3x + 5y) - 3(2x + 4y) = 10x - 12y.",
|
|
"gt_answers": "\\frac { 2 y + 5 } { 6 } - \\frac { 3 y - 2 } { 8 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2684.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(A + B + C = 2(A + B) + C\\)\n\nThis formula can be written as:\n\n\\(A + B + C = 2(A + B) + C = 2A + 2B + 2C\\)\n\nThe formula can also be written as:\n\n\\(A + B + C = 2(A + B) + C = 2A + 2B + 2C = 2A + 2B + 2C + 2C\\)\n\nThe formula is a basic algebraic identity that can be used to solve equations involving addition of three terms.",
|
|
"gt_answers": "\\frac { C B } { B F } = \\frac { D B } { P C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2685.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a number and a sign, which could be a mathematical expression in any language.",
|
|
"gt_answers": "= \\frac { 5 9 } { 1 2 } = - 4 \\frac { 1 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2686.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 1/2(x + 3) - 1/2(x - 2) = 1/2(x - 1) - 1/2(x - 1) = 0.",
|
|
"gt_answers": "\\frac { 6 } { 1 0 } = \\frac { ( 1 2 ) } { 2 0 } = \\frac { 6 0 } { ( 1 0 0 ) } = \\frac { 1 8 } { ( 3 0 ) } = 3 \\div ( 5 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2687.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x + 3y = 5`.",
|
|
"gt_answers": "y _ { 2 } = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2688.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `a^2 + 5a + 1 = 0`.",
|
|
"gt_answers": "( a + 5 ) ( a - 1 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2689.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"200 + 300 = 500.\"",
|
|
"gt_answers": "2 0 0 + 3 0 0 = 5 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2690.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(K_{eq} = \\frac{RT}{PV} = \\frac{8.3144625 J/mol \\cdot K}{100000 Pa \\cdot m^3} = 8.3144625 J/mol \\cdot K\\)",
|
|
"gt_answers": "k ( \\frac { 1 } { 2 } x , x + 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2691.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"tan(CAB) = tan(C) + tan(A) - tan(B).\"",
|
|
"gt_answers": "\\tan \\angle C A B = \\frac { C M } { A M } = \\frac { 8 } { 1 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2693.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s + t + u + v + w + x + y + z = 20\\)",
|
|
"gt_answers": "\\frac { 1 } { 1 + a } + \\frac { 1 } { 1 + b } - \\frac { a } { 1 + a } - \\frac { b } { x + b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2694.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{2} + 2^{3} + 2^{4} + 2^{5} + 2^{6} + 2^{7} + 2^{8} + 2^{9} + 2^{10} + 2^{11} + 2^{12} + 2^{13} = 5529\\)",
|
|
"gt_answers": "A E = 2 \\sqrt { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2697.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(Cb_{a} + Sb_{a} = 1\\)\n\nThis formula represents the relationship between the concentration of the two species A and B in a solution, where Cb_{a} is the concentration of species A in the solution and Sb_{a} is the concentration of species B in the solution. The equation states that the sum of the concentrations of the two species must equal 1.",
|
|
"gt_answers": "\\frac { \\sin ( A + C ) } { \\sin C + \\sin A } = \\frac { C + b - a } { a - b } ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_2698.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: n(n+1)(n+2)(n+3) - (n+1)(n+2)(n+3) = 0.",
|
|
"gt_answers": "\\frac { 2 5 } { 2 } n + n = \\frac { 1 } { 2 } - ( - 5 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2699.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = 25\\)",
|
|
"gt_answers": "( a + b ) = 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2700.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x^3 - 3x^4 + 4x^5 - 5x^6 + 6x^7 - 7x^8 + 8x^9 - 9x^{10} + 10x^{11} - 11x^{12} + 12x^{13} - 13x^{14} + 14x^{15} - 15x^{16} + 16x^{17} - 17x^{18} + 18x^{19} - 19x^{20} + 20x^{21} - 21x^{22} + 22x^{23} - 23x^{24} + 24x^{25} - 25x^{26} + 26x^{27} - 27x^{28} + 28x^{29} - 29x^{30} + 30x^{31} - 31x^{32} + 32x^{33} - 33x^{34} + 34x^{35} - 35x^{36} + 36x^{37} - 37x^{38} + 38x^{39} - 39x^{40} + 40x^{41} - 41x^{42} + 42x^{43} - 43x^{44} + 44x^{45} - 45x^{46} + 46x^{47} - 47x^{48} + 48x^{49} - 49x^{50} + 50x^{51} - 51x^{52} + 52x^{53} - 53x^{54} + 54x^{55} - 55x^{56} + 56x^{57} - 57x^{58} + 58x^{59",
|
|
"gt_answers": "2 ( x + y ) = 3 - 3 k\n",
|
|
"image_path": "./data/HME100K/test_images/test_2701.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(BDE = (180\u00b0 - 30\u00b0) \\times (75\u00b0 - 30\u00b0) = 150\u00b0 \\times 45\u00b0 = 675\u00b0\\)",
|
|
"gt_answers": "\\angle B D E = \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } - 3 0 ^ { \\circ } ) = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2702.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as cos(d) = 3.",
|
|
"gt_answers": "\\cos ^ { 2 } \\alpha = \\frac { 3 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2704.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\Delta A D C \\cong \\Delta A B C ( S . S . S )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2705.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 4x + 4 = 10\\)\n\nThis formula can be represented using the LaTeX code:\n\n\\(x^2 + 4x + 4 = 10\\)\n\nThe LaTeX code uses the `\\( \\)` and `\\)` symbols to denote the beginning and end of the formula, respectively. The `\\( \\)` symbol is used to enclose the entire formula, while the `\\)` symbol is used to enclose the expression within the parentheses. The `\\( \\)` symbol is also used to separate the variables from the constants.",
|
|
"gt_answers": "x _ { 1 } = - \\frac { 2 } { 3 } , x _ { 2 } = - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2706.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{2x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{2x^2 + 3x + 4}{x^2 + 2x + 3}\n\\end{equation}\n\nThis is a simple algebraic equation that can be solved by factoring out the common factor of \"x^2 + 2x + 3\" from both sides of the equation. The result is:\n\n\\begin{equation}\n\\frac{2x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{2x^2 + 3x + 4}{x^2 + 2x + 3}\n\\end{equation}\n\nThis is the same expression as the original equation.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2707.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(sin(x) = \\frac{sin(x) - sin(x - \\pi/2)}{sin(x) + sin(x + \\pi/2)}\\)",
|
|
"gt_answers": "\\frac { A D } { \\sin 4 5 ^ { \\circ } } = \\frac { 1 5 \\sqrt { 6 } } { \\sin 6 0 ^ { \\circ } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2708.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5.\"",
|
|
"gt_answers": "\\frac { 7 } { 2 1 } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2709.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"30 - 40 = 10\" using the LaTeX formula notation.",
|
|
"gt_answers": "A N = 3 0 \\sqrt { 3 } - 3 0 + 4 0 = 3 0 \\sqrt { 3 } + 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2710.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A2B2C2 + B2C2A2 + C2A2B2 = 12cm2.\"",
|
|
"gt_answers": ": A B = 6 c m B C = 1 2 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2711.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 0 0 0 0 0 \\times \\frac { 1 } { 1 0 0 0 0 } = 2 0 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2713.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{3} \\cdot \\frac{1}{4} \\cdot \\frac{1}{5} \\cdot \\frac{1}{6} \\cdot \\frac{1}{7} \\cdot \\frac{1}{8} \\cdot \\frac{1}{9} \\cdot \\frac{1}{10} \\cdot \\frac{1}{11} \\cdot \\frac{1}{12} \\cdot \\frac{1}{13} \\cdot \\frac{1}{14} \\cdot \\frac{1}{15} \\cdot \\frac{1}{16} \\cdot \\frac{1}{17} \\cdot \\frac{1}{18} \\cdot \\frac{1}{19} \\cdot \\frac{1}{20} \\cdot \\frac{1}{21} \\cdot \\frac{1}{22} \\cdot \\frac{1}{23} \\cdot \\frac{1}{24} \\cdot \\frac{1}{25} \\cdot \\frac{1}{26} \\cdot \\frac{1}{27} \\cdot \\frac{1}{28} \\cdot \\frac{1}{29} \\cdot \\frac{1}{30} \\cdot \\frac{1}{31} \\cdot \\frac{1}{32} \\cdot \\frac{1}{33} \\cdot \\frac{1}{34} \\cdot \\frac{1}{35} \\cdot \\frac{1}{36} \\cdot \\frac{1}{37} \\cdot \\frac{1}{38} \\cdot \\frac{1}{39} \\cdot \\frac{1}{40} \\cdot \\frac{1}{41} \\cdot \\frac{1}{42} \\cdot \\frac{1}{43} \\cdot \\frac{1}{44} \\cdot \\frac{1}{45} \\cdot \\frac{1}{46} \\cdot \\frac{1}{47} \\cdot \\frac{1}{48} \\cdot \\frac{1}{49} \\cdot \\frac{1}{50} \\cdot \\frac{1}{51}",
|
|
"gt_answers": "\\tan \\angle C O D = \\frac { E D } { F O } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2714.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "t = \\frac { \\Delta s } { V } = 0 . 5 s\n",
|
|
"image_path": "./data/HME100K/test_images/test_2715.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 6 0 0 0 c m ^ { 3 } = 0 . 0 3 6 m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2716.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LHGE = 2LBGH.\"",
|
|
"gt_answers": "\\angle H G E = \\frac { 1 } { 2 } \\angle B G H\n",
|
|
"image_path": "./data/HME100K/test_images/test_2717.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(N = \\frac{M}{M + N}\\)\n\nThis formula represents the relationship between the number of moles (N) and the number of moles of a compound (M) plus the number of moles of another compound (N). The formula can be used to calculate the number of moles of a compound when given the number of moles of another compound and vice versa.",
|
|
"gt_answers": "\\frac { N } { N a } = n = \\frac { m } { M }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2718.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2\\pi i \\int_{0}^{2\\pi} \\frac{e^{i(x-y)}}{x-y} dxdy\\)\n\nThis is a complex integral, which can be evaluated using the residue theorem. The integral is equal to the sum of the residues of the function at the poles of the integrand, which are located at x = 0 and x = y. The residue at x = 0 is equal to 1, and the residue at x = y is equal to 0. Therefore, the integral is equal to 2\u03c0i.",
|
|
"gt_answers": "( x ^ { \\cdot } - \\frac { 1 } { 2 } ) ^ { 2 } + 2 - \\frac { 1 } { 4 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2719.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the Greek letter \"x\" as the variable, and the letter \"n\" is used to represent the number of terms in the series. The formula is written as follows:\n\nx^n + x^(n-1) + x^(n-2) + ... + x^2 + x + 1 = 0\n\nThis is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "4 \\times ( x - 2 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2720.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(7 \\times 21 + 48 = 169\\)",
|
|
"gt_answers": "\\frac { 7 } { 1 6 } = \\frac { 2 1 } { 4 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2723.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nKD(P,D) = 1/2(P + D) - 1/2(P - D)\n\nThis formula represents the kinetic energy of a particle with momentum P and displacement D. The kinetic energy is calculated as 1/2(P + D) - 1/2(P - D), where the first term represents the potential energy of the particle due to its position and the second term represents the kinetic energy due to its momentum.",
|
|
"gt_answers": "K D = \\frac { 1 } { 2 } \\cdot \\frac { 3 } { 2 } H D = \\frac { 3 } { 4 } H\n",
|
|
"image_path": "./data/HME100K/test_images/test_2724.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 3x + 2y = 10.",
|
|
"gt_answers": "\\sqrt { \\frac { 3 x - 2 } { x - 1 } } - 8 = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2725.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(r = \\sqrt{r_1^2 + r_2^2 + r_3^2 + r_4^2 + r_5^2 + r_6^2 + r_7^2 + r_8^2 + r_9^2 + r_{10}^2 + r_{11}^2 + r_{12}^2 + r_{13}^2 + r_{14}^2 + r_{15}^2 + r_{16}^2 + r_{17}^2 + r_{18}^2 + r_{19}^2 + r_{20}^2 + r_{21}^2 + r_{22}^2 + r_{23}^2 + r_{24}^2 + r_{25}^2 + r_{26}^2 + r_{27}^2 + r_{28}^2 + r_{29}^2 + r_{30}^2 + r_{31}^2 + r_{32}^2 + r_{33}^2 + r_{34}^2 + r_{35}^2 + r_{36}^2 + r_{37}^2 + r_{38}^2 + r_{39}^2 + r_{40}^2 + r_{41}^2 + r_{42}^2 + r_{43}^2 + r_{44}^2 + r_{45}^2 + r_{46}^2 + r_{47}^2 + r_{48}^2 + r_{49}^2 + r_{50}^2 + r_{51}^2 + r_{52}^2 + r_{53}^2 + r_{54}^2 + r_{55}^2 + r_{56}^2 + r_{57}^2 + r_{58}^2 + r_{59}^2 + r_{60}^2 + r_{61}^2 + r_{62}^2 + r_{63}^2 + r_{64}^2 + r_{65}^2 + r_{66}^2 + r_{67}^2 + r_{68}^2 + r_{69}^2 + r_{70}^2 + r_{71}^2 + r",
|
|
"gt_answers": "V ^ { 2 } = \\frac { 2 g } { 5 } \\cdot 5 R = 5 2 g R +\n",
|
|
"image_path": "./data/HME100K/test_images/test_2726.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x < \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2727.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2\\pi r^2 \\cos(2\\theta) = 4\\pi r^2\\)\n\nThis formula relates the area of a circle to its radius and the angle it subtends. The area of a circle is given by the formula `pi r^2`, where `pi` is the constant value equal to 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214843375948073725344629187537693176738700572932594812809679671766793818359375105527480771526875277853959433751054882097496738700572932594812809679671766793818359375105527480771526875277853959433751054882097496738700572932594812809679671766793818359375105527480771526875277853959433751054882097496738700572932594812809679671",
|
|
"gt_answers": "A D = 2 \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2728.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"S(A) = 1/2(A + B) + 1/2(A - B)\".",
|
|
"gt_answers": "S _ { \\Delta O A C } = \\frac { 1 } { 2 } O C \\cdot A D\n",
|
|
"image_path": "./data/HME100K/test_images/test_2729.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(ABEF + 100 = 1000\\)",
|
|
"gt_answers": "\\angle B E F = 1 5 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2730.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: LBOLDCOD = LBOLDCOD + LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * LBOLDCOD * L",
|
|
"gt_answers": "\\angle B O D = \\angle C O D = \\frac { 1 } { 2 } \\angle B O C = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2731.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{",
|
|
"gt_answers": "C _ { n } S O _ { 4 } + M g ( O H ) _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2732.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m \\cdot t^2 = m \\cdot 9.81 \\cdot 9.81 = 9.81^2 \\cdot m\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } m + 3 = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2733.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Je'edo'DB.B.\".",
|
|
"gt_answers": "D E ^ { 2 } = D O \\cdot D B .\n",
|
|
"image_path": "./data/HME100K/test_images/test_2734.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V_{UV} = \\frac{V_U - V_V}{U - V}\\)\n\nThis formula represents the voltage difference between two points in a circuit, where U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U and V are the voltages at the two points and U",
|
|
"gt_answers": "V ^ { \\prime } _ { 2 } = V - V _ { 1 } ^ { \\prime } = V - V _ { 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2735.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 180-155 = 25.",
|
|
"gt_answers": "1 8 0 ^ { \\circ } - 1 6 5 ^ { \\circ } = 1 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2736.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(N_2 + 2N_3 + 3N_4 = 10\\)\n\nThis is a simple algebraic equation that can be solved using the distributive property of multiplication. The distributive property states that when you multiply a number by a sum of numbers, the result is the sum of the products of each number with the other numbers in the sum. In this case, we have three numbers on the left side of the equation and four numbers on the right side. We can multiply each number on the left side by the corresponding number on the right side, and then add the products together to get the solution.\n\nThe distributive property can be applied as follows:\n\n\\(N_2 \\cdot (N_3 + N_4) + N_3 \\cdot (2N_4) + N_4 \\cdot (3N_3) = 10\\)\n\nSolving for each term on the left side:\n\n\\(N_2 \\cdot (N_3 + N_4) = 5N_3 + 5N_4\\)\n\n\\(N_3 \\cdot (2N_4) = 6N_4^2\\)\n\n\\(N_4 \\cdot (3N_3) = 12N_3^3\\)\n\nSubstituting these expressions into the original equation:\n\n\\(5N_3 + 5N_4 + 6N_4^2 + 12N_3^3 = 10\\)\n\nSolving for each term on the right side:\n\n\\(5N_3 + 5N_4 + 6N_4^2 + 12N_3^3 = 10\\)\n\n\\(5N_3 + 5N_4 + 6N_4^2 + 12N_3^3 = 10\\)\n\n\\(5N_3 + 5N_4 + 6N_4^2 + 12N_3^3 = 10\\)\n\n\\(5N_3 + 5N_4 + 6N_4^2 + 12N_3^3 = 10\\)\n\n\\(5N_3 + 5N_",
|
|
"gt_answers": "\\vert A B \\vert = \\frac { \\sqrt { 3 2 - 6 m ^ { 2 } } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2737.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: AD + BD = AB.",
|
|
"gt_answers": "A D ^ { 2 } + B D ^ { 2 } = A B ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2739.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x = 2 + 3\" using LaTeX format.",
|
|
"gt_answers": "x _ { 2 } = - \\frac { \\sqrt { m - 1 } } { m - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2740.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 16x + 3 = 0.\"",
|
|
"gt_answers": "- x = - \\frac { 1 6 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2741.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"C + BT + BD + AB + AD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + BD + BA + B",
|
|
"gt_answers": "\\angle B + \\angle A D B + \\angle B A D = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2742.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 2x - 1 = 0\\)",
|
|
"gt_answers": "\\sqrt { \\frac { 2 } { 3 } } = \\frac { \\sqrt { 6 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2743.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"5H2O + 4C2H5OH = 4C3H7OH + 2H2O.\"",
|
|
"gt_answers": "5 H _ { 2 } O + C u S O _ { 4 } = C u S O _ { 4 } \\cdot 5 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2745.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(a + b = 2\\pi\\)\n\nThis formula represents the relationship between the sum of two angles and the circumference of a circle. The angle a is the angle between the positive x-axis and the line segment connecting the center of the circle to the point on the circle with coordinates (a, 0). The angle b is the angle between the positive y-axis and the line segment connecting the center of the circle to the point on the circle with coordinates (0, b). The circumference of the circle is represented by the variable pi, which is equal to 3.141592653589793.",
|
|
"gt_answers": "A ^ { \\prime } C = M C - M A ^ { \\prime } = \\sqrt { 1 9 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2746.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 277 - 10 + 15x3 + 33.",
|
|
"gt_answers": "2 x - 1 0 = 1 5 x + 3 - 3 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2748.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x^2 + 4y^2 = 9.",
|
|
"gt_answers": "x ^ { 2 } + 4 x y + 4 y ^ { 2 } = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_2749.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LBod-LPDE = 28\\)",
|
|
"gt_answers": "\\angle B O D = \\angle D O E = 2 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_2751.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"cos(x) = sin(x) / (1 + cos(x))\".",
|
|
"gt_answers": "\\cos c = \\frac { \\sqrt { 5 } } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2752.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2\\ce{CaSO4} + 2\\ce{H2O} \\rightarrow Ca(OH)2 + 2\\ce{H2SO4}\\)",
|
|
"gt_answers": "2 C a S O _ { 4 } \\cdot 2 H _ { 2 } O \\xrightarrow { \\Delta } 2 C a S O _ { 4 } \\cdot H _ { 2 } O + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2753.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as tan(LACD) = AD/CD.",
|
|
"gt_answers": "\\tan \\angle A C D = \\frac { A D } { C D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2754.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\Delta A B C = D F E F - \\Delta B D C - \\Delta C E A , - \\Delta B F A\n",
|
|
"image_path": "./data/HME100K/test_images/test_2757.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "\\therefore 0 = - 3 k + 3 \\therefore k = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2758.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 3x + 2\\)",
|
|
"gt_answers": "x = \\frac { 4 } { 3 } \\cdot y = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2761.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(k(x) = \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + \\frac{1}{2} \\left(x^2 + 2x + 1\\right) + \\frac{1}{2} \\left",
|
|
"gt_answers": "x ^ { 2 } + k ( x + 1 ) = x ^ { 2 } + x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2763.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "7 2 c = D ^ { \\prime } B\n",
|
|
"image_path": "./data/HME100K/test_images/test_2764.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000",
|
|
"gt_answers": "2 0 k g \\times ( 1 m - 0 . 1 m / s t ) = 3 0 k g \\cdot 0 . 1 m / s . t\n",
|
|
"image_path": "./data/HME100K/test_images/test_2765.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AB + AL = A2 + B2.\"",
|
|
"gt_answers": "A B ^ { 2 } = A C \\cdot A E\n",
|
|
"image_path": "./data/HME100K/test_images/test_2767.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(ABD-160-LABC\\)",
|
|
"gt_answers": "\\angle A B D = 1 8 0 - \\angle A B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_2769.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4Al302 + 2Al2O3.",
|
|
"gt_answers": "4 A l + 3 O _ { 2 } = 2 A l _ { 2 } O _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2770.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to provide a LaTeX representation. However, the image shows a mathematical formula written in Japanese characters, which is likely a representation of a mathematical expression in Japanese.",
|
|
"gt_answers": "1 6 + 9 + 1 5 + 2 1 + 2 5 + 3 3 + 3 5 + 2 4 + 1 8 + 1 1 + 5 ) \\div 1 2 = 1 6 . 2 5 ( ^ { \\circ } C )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2772.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2} + 1\\)",
|
|
"gt_answers": "x _ { 1 } = - \\frac { 4 } { 7 } \\sqrt { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2773.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x - 5 = 0\\)",
|
|
"gt_answers": "( 2 - 7 + \\frac { 1 } { 2 } ) a\n",
|
|
"image_path": "./data/HME100K/test_images/test_2775.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 16/24 - 16/25 = 1/24 - 1/25.",
|
|
"gt_answers": "1 6 : 2 4 = \\frac { 1 6 } { 2 4 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2776.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "0 < \\frac { b } { a } < 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2777.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"p + 2p + 3p + 4p + 5p + 6p + 7p + 8p + 9p + 10p + 11p + 12p + 13p + 14p + 15p + 16p + 17p + 18p + 19p + 20p + 21p + 22p + 23p + 24p + 25p + 26p + 27p + 28p + 29p + 30p + 31p + 32p + 33p + 34p + 35p + 36p + 37p + 38p + 39p + 40p + 41p + 42p + 43p + 44p + 45p + 46p + 47p + 48p + 49p + 50p + 51p + 52p + 53p + 54p + 55p + 56p + 57p + 58p + 59p + 60p + 61p + 62p + 63p + 64p + 65p + 66p + 67p + 68p + 69p + 70p + 71p + 72p + 73p + 74p + 75p + 76p + 77p + 78p + 79p + 80p + 81p + 82p + 83p + 84p + 85p + 86p + 87p + 88p + 89p + 90p + 91p + 92p + 93p + 94p + 95p + 96p + 97p + 98p + 99p + 100p + 101p + 102p +",
|
|
"gt_answers": "P A + \\frac { 3 } { 5 } P M\n",
|
|
"image_path": "./data/HME100K/test_images/test_2778.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\angle B A E = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2779.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 4x + 5 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 4 x ^ { 2 } - 4 x y + y ^ { 2 } } { 2 x + y } \\div ( 4 x ^ { 2 } -\n",
|
|
"image_path": "./data/HME100K/test_images/test_2780.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Sn3 + Tg9 = 19.\"",
|
|
"gt_answers": "S _ { n } < \\frac { 3 } { 1 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2781.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 4x + 4 = 10\\)",
|
|
"gt_answers": "\\frac { 4 } { 3 } x - \\frac { 3 } { 4 } x = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2782.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x - x - 2 x + 2 x - \\frac { 1 } { 2 } x = \\frac { 1 } { 6 } - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2784.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1}{13} + \\frac{1",
|
|
"gt_answers": "\\therefore F O = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2785.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x5x7x10x11x12x13x14x15x16x17x18x19x20x21x22x23x24x25x26x27x28x29x30x31x32x33x34x35x36x37x38x39x40x41x42x43x44x45x46x47x48x49x50x51x52x53x54x55x56x57x58x59x60x61x62x63x64x65x66x67x68x69x70x71x72x73x74x75x76x77x78x79x80x81x82x83x84x85x86x87x88x89x90x91x92x93x94x95x96x97x98x99x100x101x102x103x104x105x106x107x108x109x110x111x112x113x114x115x116x117x118x119x120x121x122x123x124x125x126x127x128x129x130x131x132x133x134x135x136x137x138x139x140x141x142x143x144x145x146x147x148x149x150x151x152x153x154x155x15",
|
|
"gt_answers": "6 \\times 5 \\times 4 = 1 2 0 ( d m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2786.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\tan \\angle D A C = \\frac { \\sqrt { 3 } } { 3 } = \\frac { D C } { A D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2787.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2021 G + 2021 T + 2022 T + 2022 G + 2022 T + 2023 G + 2023 T + 2023 G + 2023 T + 2024 G + 2024 T + 2024 G + 2024 T + 2025 G + 2025 T + 2025 G + 2025 T + 2026 G + 2026 T + 2026 G + 2026 T + 2027 G + 2027 T + 2027 G + 2027 T + 2028 G + 2028 T + 2028 G + 2028 T + 2029 G + 2029 T + 2029 G + 2029 T + 2030 G + 2030 T + 2030 G + 2030 T + 2031 G + 2031 T + 2031 G + 2031 T + 2032 G + 2032 T + 2032 G + 2032 T + 2033 G + 2033 T + 2033 G + 2033 T + 2034 G + 2034 T + 2034 G + 2034 T + 2035 G + 2035 T + 2035 G + 2035 T + 2036 G + 2036 T + 2036 G + 2036 T + 2037 G + 2037 T + 2037 G + 2037 T + 2038 G + 2038 T + 2038 G + 2038 T + 2039 G + 2039 T + 2039 G",
|
|
"gt_answers": "2 0 2 1 ^ { 2 0 2 1 } a + 2 0 2 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2788.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "0 < x \\leq \\frac { x } { 2 } \\therefore \\frac { x } { 3 } \\leq 2 x + \\frac { \\pi } { 3 } \\leq \\frac { 4 } { 3 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_2789.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\" in LaTeX format.",
|
|
"gt_answers": "5 x ^ { 2 } + y ^ { 2 } = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2790.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x = - 2 \\pm 2 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2791.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { S _ { 1 } } { S _ { 2 } } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2793.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(F = \\frac{kx^2}{2m}\\)\n\nThis formula represents the force acting on an object due to its mass and the spring constant, k. The force is proportional to the square of the displacement, x, and inversely proportional to the mass, m.",
|
|
"gt_answers": "P = \\frac { F } { S } = \\frac { 2 0 1 x } { 0 . 8 \\times 1 0 ^ { - 4 } m ^ { 2 } } = 2 . 5 \\times 1 0 ^ { 5 } P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_2795.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 62 + 15 = 77.",
|
|
"gt_answers": "\\frac { 6 2 } { 1 5 } = 4 \\frac { 2 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2797.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "6 x = 6 ( 1 + 6 + 6 ^ { 2 } + 6 ^ { 3 } + \\cdots + 6 ^ { 1 0 0 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2798.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(LBAD = 90\u00b0 - 0.5(TG - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5(TA - TB) - 0.5(TB - TA) - 0.5",
|
|
"gt_answers": "\\angle B A D = 9 0 ^ { \\circ } - \\angle B = 9 0 ^ { \\circ } - 7 5 ^ { \\circ } = 1 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2799.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2 + 3 = 5\" in LaTeX format.",
|
|
"gt_answers": "y _ { 2 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2800.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"0.442 + 0.202 = 0.644.\"",
|
|
"gt_answers": "0 . 4 \\div 2 = 0 . 2 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2801.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"sin(60\u00b0) = 0.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\sin 6 0 ^ { \\circ } = 3 0 ( \\sqrt { 3 } - 1 ) c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2802.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2385-2353+2353-2385.",
|
|
"gt_answers": "3 8 5 - 3 2 5 1 \\div 3 = 2 0 ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_2803.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 480-216+24cdm3.",
|
|
"gt_answers": "4 8 0 - 2 1 6 = 2 6 4 ( d m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2804.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x + 4.",
|
|
"gt_answers": "x = \\frac { 1 7 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2805.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 15x + 16 = 40\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\nx^2 + 15x + 16 = 40\n\\end{equation}\n\nThe equation is written using the `\\(x^2 + 15x + 16 = 40\\)` syntax, where the `x^2` represents the square of the variable `x`, the `15x` represents the product of the variable `x` and the constant `15`, and the `16` represents the constant `16`.",
|
|
"gt_answers": "x = \\frac { 1 5 } { 4 0 } + \\frac { 1 6 } { 4 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2806.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AC + CE = 5555 + 1000 = 6555.\"",
|
|
"gt_answers": "A C = A E + C E = 5 + 5 = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2807.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 4y = 81.\"",
|
|
"gt_answers": "x ^ { 2 } = \\frac { 4 9 } { 8 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2810.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "O A = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2811.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"NaCl + CO2 = Na2CO3 + H2O.\"",
|
|
"gt_answers": "N a O H + C O _ { 2 } = N a _ { 2 } C O _ { 3 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2812.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A + B = 8.\"",
|
|
"gt_answers": "B A C = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_2814.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 2 = 12.\"",
|
|
"gt_answers": "\\frac { 1 - 2 m } { 5 } \\geq 3 m + 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2815.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 800/800 + 360/800 = 1.000.",
|
|
"gt_answers": "8 8 0 + 4 8 0 = 1 3 6 0 ( k g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2817.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "\\frac { x - 1 } { 2 } = \\frac { - x + 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2818.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x5 - 5x4 = 15x3.\"",
|
|
"gt_answers": "x = \\frac { 4 . 5 } { 7 . 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2819.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_2H_2O_2 + CO_2 \\rightarrow 2CO + H_2O\\)",
|
|
"gt_answers": "O B = C D \\cdot O C = O D\n",
|
|
"image_path": "./data/HME100K/test_images/test_2820.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\therefore B F = 1 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2822.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\vert a + \\frac { 1 } { a } \\vert = a + \\frac { 1 } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2825.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\sin(x) + 2\\sin(2x) + 2\\sin(3x) + 2\\sin(4x) + 2\\sin(5x) + 2\\sin(6x) + 2\\sin(7x) + 2\\sin(8x) + 2\\sin(9x) + 2\\sin(10x) + 2\\sin(11x) + 2\\sin(12x) + 2\\sin(13x) + 2\\sin(14x) + 2\\sin(15x) + 2\\sin(16x) + 2\\sin(17x) + 2\\sin(18x) + 2\\sin(19x) + 2\\sin(20x) + 2\\sin(21x) + 2\\sin(22x) + 2\\sin(23x) + 2\\sin(24x) + 2\\sin(25x) + 2\\sin(26x) + 2\\sin(27x) + 2\\sin(28x) + 2\\sin(29x) + 2\\sin(30x) + 2\\sin(31x) + 2\\sin(32x) + 2\\sin(33x) + 2\\sin(34x) + 2\\sin(35x) + 2\\sin(36x) + 2\\sin(37x) + 2\\sin(38x) + 2\\sin(39x) + 2\\sin(40x) + 2\\sin(41x) + 2\\sin(42x) + 2\\sin(43x) + 2\\sin(44x) + 2\\sin(45x) + 2\\sin(46x) + 2\\sin(47x) + 2\\sin(48x) + 2\\sin(49x) + 2\\sin(50x) + 2\\sin(",
|
|
"gt_answers": "1 - 2 \\sin ^ { 2 } c = - \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2826.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V = \\sqrt{F \\cdot r}\\)\n\nwhere V is the velocity, F is the force, and r is the distance.",
|
|
"gt_answers": "V = \\frac { s } { t } = \\frac { 1 3 5 0 } { 4 5 } = 3 0 0 k m / h\n",
|
|
"image_path": "./data/HME100K/test_images/test_2827.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `2019-01-01 00:00:00 + 365 days = 2020-01-01 00:00:00`. This formula calculates the date of the next year's New Year's Day based on the current date and the number of days in a year.",
|
|
"gt_answers": "1 . 3 5 t > 0 . 7 5 t > 0 . 3 5 t > 2 2 8 k g > 3 5 k g\n",
|
|
"image_path": "./data/HME100K/test_images/test_2828.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which are not supported by LaTeX. However, I can provide a rough translation of the characters into English: \"18.7 + 1.87 = 19.57.\"",
|
|
"gt_answers": "1 8 . 7 5 = 7 5 k + b\n",
|
|
"image_path": "./data/HME100K/test_images/test_2829.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a=b+c.",
|
|
"gt_answers": "a < b = c\n",
|
|
"image_path": "./data/HME100K/test_images/test_2830.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1}{10} \\cdot \\frac{1",
|
|
"gt_answers": "( 2 x - 3 y ) - ( 2 x - 6 y ) = - 7 + 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2831.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x _ { 1 } = 0 , x _ { 2 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2832.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 10x26.6.",
|
|
"gt_answers": "\\frac { 1 0 } { 3 } < x < 6 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_2833.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2m - 1 = 2m - 1\".",
|
|
"gt_answers": "2 m - 4 = 3 m - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2834.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(A + B + C + D = 40\\)\n\nThis formula represents the addition of four numbers, A, B, C, and D, which must equal 40.",
|
|
"gt_answers": "A Q = \\frac { A B } { \\cos A } = \\frac { 2 0 } { \\frac { 1 } { 2 } } = 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2835.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(355) = 3(355) + 3(355) + 3(35",
|
|
"gt_answers": "[ 3 2 8 - ( 3 5 4 - 3 1 ) ] \\times 7 2 0 = 3 6 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2836.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x + ",
|
|
"gt_answers": "4 x - 1 2 x + 3 x = 2 4 - 4 + 9 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2838.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which can be translated to \"the sum of the squares of the first n natural numbers.\"",
|
|
"gt_answers": "x = \\frac { 1 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2839.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\therefore x = \\frac { 1 2 + 2 G } { a - 3 . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2840.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 144-6+6=80.",
|
|
"gt_answers": "7 + 4 - 6 = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2842.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2}{2} + \\frac{y^2}{2} + \\frac{z^2}{2} = \\frac{1}{2} \\left(x^2 + y^2 + z^2\\right)\n\\end{equation}\n\nThis formula states that the sum of the squares of the distances between two points in a three-dimensional space is equal to the square of the distance between the two points divided by two.",
|
|
"gt_answers": "O E = x - \\sqrt { x ^ { 2 } - 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2843.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\" in LaTeX format.",
|
|
"gt_answers": "\\frac { \\pi } { 4 } + x ) = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2844.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(B = 15.5 - 2.5 \\cdot 0.5 = 12.5\\)",
|
|
"gt_answers": "B ^ { \\prime } = ( 5 , 2 \\sqrt { 2 } - 2 \\sqrt { 2 } ) = ( 5 , 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2845.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "1 0 0 0 0 \\times ( 1 + x ) ^ { 2 } = 1 2 1 0 0\n",
|
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"image_path": "./data/HME100K/test_images/test_2846.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
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{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(s_i = \\frac{g}{2} \\left( \\frac{1}{r_i} - \\frac{1}{r_{i+1}} \\right) \\left( \\frac{1}{r_i} + \\frac{1}{r_{i+1}} \\right) \\left( \\frac{1}{r_i} - \\frac{1}{r_{i+2}} \\right) \\left( \\frac{1}{r_i} + \\frac{1}{r_{i+2}} \\right) \\left( \\frac{1}{r_i} - \\frac{1}{r_{i+3}} \\right) \\left( \\frac{1}{r_i} + \\frac{1}{r_{i+3}} \\right) \\left( \\frac{1}{r_i} - \\frac{1}{r_{i+4}} \\right) \\left( \\frac{1}{r_i} + \\frac{1}{r_{i+4}} \\right) \\left( \\frac{1}{r_i} - \\frac{1}{r_{i+5}} \\right) \\left( \\frac{1}{r_i} + \\frac{1}{r_{i+5}} \\right) \\left( \\frac{1}{r_i} - \\frac{1}{r_{i+6}} \\right) \\left( \\frac{1}{r_i} + \\frac{1}{r_{i+6}} \\right) \\left( \\frac{1}{r_i} - \\frac{1}{r_{i+7}} \\right) \\left( \\frac{1}{r_i} + \\frac{1}{r_{i+7}} \\right) \\left( \\frac{1}{r_i} - \\frac{1}{r_{i+8}} \\right) \\left( \\frac{1}{r_i} + \\frac{1}{r_{i+8}} \\right) \\left( \\frac{1}{r_i} - \\frac{1}{r_{i+9}} \\right) \\left( \\frac{1}{r_i} + \\frac{1}{r_{i+9}}",
|
|
"gt_answers": "\\sin \\theta = \\frac { \\sqrt { 2 6 } } { 2 6 } ( 0 ^ { \\circ } < \\theta < 9 0 ^ { \\circ } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2847.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = \\frac{x^2}{2} + \\frac{x^3}{3} + \\frac{x^4}{4} + \\frac{x^5}{5} + \\frac{x^6}{6} + \\frac{x^7}{7} + \\frac{x^8}{8} + \\frac{x^9}{9} + \\frac{x^{10}}{10} + \\frac{x^{11}}{11} + \\frac{x^{12}}{12} + \\frac{x^{13}}{13} + \\frac{x^{14}}{14} + \\frac{x^{15}}{15} + \\frac{x^{16}}{16} + \\frac{x^{17}}{17} + \\frac{x^{18}}{18} + \\frac{x^{19}}{19} + \\frac{x^{20}}{20} + \\frac{x^{21}}{21} + \\frac{x^{22}}{22} + \\frac{x^{23}}{23} + \\frac{x^{24}}{24} + \\frac{x^{25}}{25} + \\frac{x^{26}}{26} + \\frac{x^{27}}{27} + \\frac{x^{28}}{28} + \\frac{x^{29}}{29} + \\frac{x^{30}}{30} + \\frac{x^{31}}{31} + \\frac{x^{32}}{32} + \\frac{x^{33}}{33} + \\frac{x^{34}}{34} + \\frac{x^{35}}{35} + \\frac{x^{36}}{36} + \\frac{x^{37}}{37} + \\frac{x^{38}}{38} + \\frac{x^{39}}{39} + \\frac{x^{40}}{40} + \\frac{x^{41}}{41} + \\frac{x^{42}}{42} + \\frac{x^{43}}{43} + \\",
|
|
"gt_answers": "y = k x + b ( k \\neq 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2848.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(10^{10} + 10^{10} = 10^{20}\\)",
|
|
"gt_answers": "\\sqrt { x + y } = \\sqrt { 6 + 1 0 } = \\sqrt { 1 6 } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2849.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x = 0 . 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_2850.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a2 - 25a + 44a - 5a = 0.",
|
|
"gt_answers": "a _ { 3 } + a _ { 7 } = 2 a _ { 5 } = 4 . = - \\frac { b } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2851.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{3}x^3 + \\frac{1}{4}x^4 + \\frac{1}{5}x^5 + \\frac{1}{6}x^6 + \\frac{1}{7}x^7 + \\frac{1}{8}x^8 + \\frac{1}{9}x^9 + \\frac{1}{10}x^{10} + \\frac{1}{11}x^{11} + \\frac{1}{12}x^{12} + \\frac{1}{13}x^{13} + \\frac{1}{14}x^{14} + \\frac{1}{15}x^{15} + \\frac{1}{16}x^{16} + \\frac{1}{17}x^{17} + \\frac{1}{18}x^{18} + \\frac{1}{19}x^{19} + \\frac{1}{20}x^{20} + \\frac{1}{21}x^{21} + \\frac{1}{22}x^{22} + \\frac{1}{23}x^{23} + \\frac{1}{24}x^{24} + \\frac{1}{25}x^{25} + \\frac{1}{26}x^{26} + \\frac{1}{27}x^{27} + \\frac{1}{28}x^{28} + \\frac{1}{29}x^{29} + \\frac{1}{30}x^{30} + \\frac{1}{31}x^{31} + \\frac{1}{32}x^{32} + \\frac{1}{33}x^{33} + \\frac{1}{34}x^{34} + \\frac{1}{35}x^{35} + \\frac{1}{36}x^{36} + \\frac{1}{37}x^{37} + \\frac{1}{38}x",
|
|
"gt_answers": "D F = \\frac { \\sqrt { 5 } } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2852.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{A + B + C}{A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z}\n\\end{aligned}\n\nThis formula is a combination of several terms, each of which is a product of two numbers. The total number of terms in the formula is 30.",
|
|
"gt_answers": "\\frac { A ^ { \\prime } B ^ { \\prime } } { A B } = \\frac { A ^ { \\prime } C ^ { \\prime } } { A C } = \\frac { B ^ { \\prime } C ^ { \\prime } } { B C } = k\n",
|
|
"image_path": "./data/HME100K/test_images/test_2853.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"4x - 4 = 0.\"",
|
|
"gt_answers": "4 x = - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_2854.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\cos(x) = \\frac{e^{ix} + e^{-ix}}{2}\n\\end{equation}\n\nThis formula represents the cosine function of the angle x, which is defined as the ratio of the sine of the angle to the cosine of the angle.",
|
|
"gt_answers": "\\cos B = \\frac { 1 } { 5 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2855.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3 = 5.",
|
|
"gt_answers": "x = \\frac { 5 } { 2 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2856.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"m2 = m1 + 4.\"",
|
|
"gt_answers": "m \\leq \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2857.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `Fx = 0.5 * (goon + 0.5 * goon^2 + 0.5 * goon^3 + 0.5 * goon^4 + 0.5 * goon^5 + 0.5 * goon^6 + 0.5 * goon^7 + 0.5 * goon^8 + 0.5 * goon^9 + 0.5 * goon^10 + 0.5 * goon^11 + 0.5 * goon^12 + 0.5 * goon^13 + 0.5 * goon^14 + 0.5 * goon^15 + 0.5 * goon^16 + 0.5 * goon^17 + 0.5 * goon^18 + 0.5 * goon^19 + 0.5 * goon^20 + 0.5 * goon^21 + 0.5 * goon^22 + 0.5 * goon^23 + 0.5 * goon^24 + 0.5 * goon^25 + 0.5 * goon^26 + 0.5 * goon^27 + 0.5 * goon^28 + 0.5 * goon^29 + 0.5 * goon^30 + 0.5 * goon^31 + 0.5 * goon^32 + 0.5 * goon^33 + 0.5 * goon^34 + 0.5 * goon^35 + 0.5 * goon^36 + 0.5 * goon^37 + 0.5 * goon^38 + 0.5 * goon^39 + 0.5 * goon^40 + 0.5 * goon^41 + 0.5 * goon^42 + 0.5 * goon^43 + 0.5 * goon^44 + 0.5 * goon^45 + 0.5 * goon^46 + 0.",
|
|
"gt_answers": "F \\times 1 0 0 c m = 9 0 0 N \\times 3 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2858.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2440.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "x = 2 4 3 0 \\div 1 . 0 S\n",
|
|
"image_path": "./data/HME100K/test_images/test_2859.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 26.834 x 11.304 = 316.088 cm.",
|
|
"gt_answers": "3 6 \\times 3 1 4 = 1 1 3 . 0 4 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2860.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(W_{1500} = 1500 \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\cdot 10^{-6} \\",
|
|
"gt_answers": "W = 1 5 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2861.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: y = 15x + 1.",
|
|
"gt_answers": "x = \\pm \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2863.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 3x - 2.",
|
|
"gt_answers": "y _ { 1 } = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2864.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(x + 1) - 3(x - 2) = 0.",
|
|
"gt_answers": "\\frac { 2 } { 3 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2865.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(A + B = C + D\\)\n\nThe formula is written in the form of an equation, with the variables A, B, C, and D representing the four terms.",
|
|
"gt_answers": "1 0 N \\cdot O A = F _ { 2 } \\cdot 2 O A\n",
|
|
"image_path": "./data/HME100K/test_images/test_2866.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LABD-60\u00b0\".",
|
|
"gt_answers": "\\angle A B D = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2867.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(s^2 + 2s \\cos(t) + 2t^2 = 2s^2 + 2s \\cos(t) + 2t^2 - 2s^2 \\cos(t) = 2t^2\\)\n\nThis is a quadratic equation in the variable \"t\" with a constant term of \"2s^2\" and a linear term of \"2s \\cos(t)\". The equation can be solved using the quadratic formula, which gives the solutions as:\n\n\\(t = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\)\n\nIn this case, the quadratic formula gives the solutions as:\n\n\\(t = \\frac{-2s^2 \\pm \\sqrt{(2s^2)^2 - 4(2s^2)(2s \\cos(t))}}{2(2s^2)} = \\frac{-2s^2 \\pm \\sqrt{4s^4 - 8s^2 \\cos(t)}}{2s^2} = \\frac{-2s^2 \\pm \\sqrt{4s^4 - 8s^2 \\cos(t)}}{2s^2 - 4s^2} = \\frac{-2s^2 \\pm \\sqrt{4s^4 - 8s^2 \\cos(t)}}{2s^2 - 4s^2 - 4s^2} = \\frac{-2s^2 \\pm \\sqrt{4s^4 - 8s^2 \\cos(t) - 16s^4}}{2s^2 - 4s^2 - 16s^4} = \\frac{-2s^2 \\pm \\sqrt{4s^4 - 16s^4}}{2s^2 - 16s^4} = \\frac{-2s^2 \\pm \\sqrt{4s^4 - 16s^4}}{2s^2 - 16s^4 - 16s^4} = \\frac{-2s^2 \\pm \\sqrt{4s^4 - 16s^4 - 16s^4}}{2s^2 - 16s^4",
|
|
"gt_answers": "2 \\sqrt { S _ { 2 } } = \\sqrt { S _ { 1 } } + \\sqrt { S _ { 3 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2868.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x^2 - 9x + 1 = 0`.",
|
|
"gt_answers": "\\frac { 2 } { 5 } x - 7 = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_2869.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 5y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, where the sum of x and y is equal to 10.",
|
|
"gt_answers": "\\frac { 2 } { 5 } + \\frac { 1 } { 2 } = \\frac { 4 } { 1 0 } + \\frac { 5 } { 1 0 } = \\frac { 9 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2870.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AC + AB = 20\".",
|
|
"gt_answers": "A C = 1 6 , A B = 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2871.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3n^2 + 1 = 11.",
|
|
"gt_answers": "x _ { 1 } = \\frac { 3 \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2872.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left( \\frac{1}{1 + \\left(",
|
|
"gt_answers": "\\frac { 4 \\sqrt { 3 } } { 3 } . - \\frac { \\sqrt { 3 } } { 6 } m ) , \\overrightarrow { F _ { 2 } k } = ( \\frac { \\sqrt { 3 } } { 3 } , \\frac { - \\sqrt { 3 } } { 3 } m ) . / / ( 1 , m ) / / \\overrightarrow { m } \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_2873.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "v = t + \\frac { 7 } { 6 } \\pi \\in ( \\frac { 7 } { 6 } \\pi , \\frac { 1 3 } { 6 } \\pi )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2874.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "A O \\bot B O\n",
|
|
"image_path": "./data/HME100K/test_images/test_2876.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4\\cdot m = 4\\cdot 10^{-3} \\cdot 10^{3} = 4 \\cdot 10^{-6} \\cdot 10^{6} = 4 \\cdot 10^{-9} \\cdot 10^{9} = 4 \\cdot 10^{-12} \\cdot 10^{12} = 4 \\cdot 10^{-15} \\cdot 10^{15} = 4 \\cdot 10^{-18} \\cdot 10^{18} = 4 \\cdot 10^{-21} \\cdot 10^{21} = 4 \\cdot 10^{-24} \\cdot 10^{24} = 4 \\cdot 10^{-27} \\cdot 10^{27} = 4 \\cdot 10^{-30} \\cdot 10^{30} = 4 \\cdot 10^{-33} \\cdot 10^{33} = 4 \\cdot 10^{-36} \\cdot 10^{36} = 4 \\cdot 10^{-39} \\cdot 10^{39} = 4 \\cdot 10^{-42} \\cdot 10^{42} = 4 \\cdot 10^{-45} \\cdot 10^{45} = 4 \\cdot 10^{-48} \\cdot 10^{48} = 4 \\cdot 10^{-51} \\cdot 10^{51} = 4 \\cdot 10^{-54} \\cdot 10^{54} = 4 \\cdot 10^{-57} \\cdot 10^{57} = 4 \\cdot 10^{-60} \\cdot 10^{60} = 4 \\cdot 10^{-63} \\cdot 10^{63} = 4 \\cdot 10^{-66} \\cdot 10^{66} = 4 \\cdot 10^{-69} \\cdot 10^{69} = 4 \\cdot 10^{-72} \\",
|
|
"gt_answers": ", x = 4 + m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2878.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 2x(8x8) + 6x(8x6) + 6x(6x8) + 6x(6x6) = 236x8 + 180x6 + 180x8 + 180x6 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x180 + 180x180 + 180x180 + 180x180 = 180x",
|
|
"gt_answers": "2 \\times ( 5 \\times 8 + 5 \\times 6 + 8 \\times 6 ) = 2 3 6 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2880.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"sppd = 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p + 2p",
|
|
"gt_answers": "S _ { \\Delta } A P D = \\frac { 1 } { 2 } P R\n",
|
|
"image_path": "./data/HME100K/test_images/test_2881.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(1000 - 3 \\times 3 \\times 5 \\times 7 = 1000 - 27 \\times 7 = 1000 - 194 = 806\\)",
|
|
"gt_answers": "1 0 0 \\div ( - 2 ) ^ { 2 } - 3 \\times [ ( - 2 ) ^ { 3 } + 5 ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_2882.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "3 = \\frac { 2 } { 8 } x - ( - \\frac { 4 } { 8 } x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2883.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 237.25-21x40.",
|
|
"gt_answers": "2 3 x - 2 1 x = 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2884.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1 m = 10^(-3) m.\"",
|
|
"gt_answers": "m = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2885.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a(x) = (x-4)(x-2)(x-0) + 4(x-2)(x-0) + 4(x-0)(x-2) + 2(x-0)(x-4) + 2(x-2)(x-4) + 2(x-4)(x-0) + 4(x-2)(x-0) + 4(x-0)(x-2) + 2(x-0)(x-4) + 2(x-2)(x-4) + 2(x-4)(x-0) + 4(x-2)(x-0) + 4(x-0)(x-2) + 2(x-0)(x-4) + 2(x-2)(x-4) + 2(x-4)(x-0) + 4(x-2)(x-0) + 4(x-0)(x-2) + 2(x-0)(x-4) + 2(x-2)(x-4) + 2(x-4)(x-0) + 4(x-2)(x-0) + 4(x-0)(x-2) + 2(x-0)(x-4) + 2(x-2)(x-4) + 2(x-4)(x-0) + 4(x-2)(x-0) + 4(x-0)(x-2) + 2(x-0)(x-4) + 2(x-2)(x-4) + 2(x-4)(x-0) + 4(x-2)(x-0) + 4(x-0)(x-2) + 2(x-0)(x-4) + 2(x-2)(x-4) + 2(x-4)(x-0) + 4(x-2)(x-0) + 4(x-0)(x-2) + 2(x-0)(x-4) + 2(x-2)(x-4) + 2(x-4)(",
|
|
"gt_answers": "( x - 2 0 ) ( x - 4 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2886.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1}\\)",
|
|
"gt_answers": "( 3 x + y ) ( 3 x - y ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2887.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\right) = \\frac{1}{4} \\)",
|
|
"gt_answers": "E A \\cong \\Delta O E A\n",
|
|
"image_path": "./data/HME100K/test_images/test_2888.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LCOD + LACD = LAD + LAD'.\"",
|
|
"gt_answers": "\\angle C O D + \\angle A O C = \\angle A O D = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2889.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\na^2 + b^2 = ab + c^2",
|
|
"gt_answers": "a ^ { 2 } + b ^ { 2 } \\geq 2 a b = \\frac { 2 } { c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2890.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(x^2 + y^2 = 4xy + 4x + 4y + 2xy^2 + 2x^2y + 2y^3\\)",
|
|
"gt_answers": "\\frac { 4 x - 1 } { 5 } - \\frac { 0 . 3 + 0 . 2 x } { 0 . 3 } = \\frac { 0 . 0 1 x + 0 . 0 4 } { 0 . 0 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2891.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3 = 7 - 2x.",
|
|
"gt_answers": "\\frac { 2 x } { 7 } + \\frac { x } { 3 } = - 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2892.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"305-14 9x100\".",
|
|
"gt_answers": "3 0 5 - 1 4 9 \\approx 2 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2893.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4x^{2}y^{2} + 4xy^{2} + 4x^{2}y + 4x^{2} + 4y^{2} + 4xy + 4y + 4 = 0\\)",
|
|
"gt_answers": "4 \\times 2 0 + 4 \\times 2 0 + 4 \\times 1 0 + 5 0 = 2 . 5 0 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2894.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"L(A + B) = L(A) + L(B) + 2AB\".",
|
|
"gt_answers": "\\angle F A C + \\angle A C E + \\angle E C F = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2895.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 5x + 10}{x^2 + 5x + 10} = 1\n\\end{equation}\n\nThis equation can be simplified to:\n\n\\begin{equation}\nx^2 + 5x + 10 = 10x^2 + 5x + 10\n\\end{equation}\n\nSolving for x, we get:\n\n\\begin{equation}\nx = \\frac{10}{10x^2 + 5x + 10}\n\\end{equation}\n\nTherefore, the solution to the equation is x = 10.",
|
|
"gt_answers": "x = - \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2896.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"7x8 = 56.\"",
|
|
"gt_answers": "x = \\frac { 4 } { 7 } \\times \\frac { 1 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2898.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\n\\(1000 \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{1000} \\cdot \\frac{1000}{100",
|
|
"gt_answers": "\\vert c m \\vert = \\sqrt { \\vert C P \\vert ^ { 2 } - \\vert P M \\vert ^ { 2 } } = \\sqrt { 4 - 3 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2899.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(V = \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left(",
|
|
"gt_answers": "V _ { 2 } ^ { \\prime \\prime } = V - V _ { 1 } ^ { \\prime } = V - 8 V _ { 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2900.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(27 - 31 + 27 - 21 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 27 - 27 + 2",
|
|
"gt_answers": "\\textcircled { 1 } \\div \\textcircled { 2 } = \\frac { 2 7 } { 3 6 } = \\frac { s - 2 7 } { s - 1 8 . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2901.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 4 - 2x - 4 = 0.",
|
|
"gt_answers": "\\frac { x + 1 } { 3 } - \\frac { x - 2 } { 2 } = \\frac { 4 + x } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2902.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) + \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) - \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right)^2\n\\end{aligned}\n\\end{equation}\n\nThis formula is a quadratic equation in the variable x, with the constant term being 1/2. The equation can be solved using the quadratic formula, which gives the solutions x = 1/2 (the root of the quadratic equation) and x = -1/2 (the negative root of the quadratic equation).",
|
|
"gt_answers": "- 2 x ^ { 4 } - x ^ { 2 } + 5 = ( - x ^ { 2 } + 1 ) ( 2 x ^ { 2 } + a ) + b .\n",
|
|
"image_path": "./data/HME100K/test_images/test_2903.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\ny = 4x^2 + 2x + 4",
|
|
"gt_answers": "y = \\frac { \\sqrt { 2 } \\alpha ^ { 2 } + 4 \\sqrt { 2 } \\alpha } { 2 \\alpha + 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2904.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LAEF = L3 - 70%.\"",
|
|
"gt_answers": "\\angle A E F = \\angle 3 = 7 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2906.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the chemical formula notation, which is a standard way to represent chemical compounds. The formula is written as NaCl + H2O = NaOH + HCl.",
|
|
"gt_answers": "N a _ { 2 } C O _ { 3 } + 2 H C l = N a C l + H _ { 2 } O + C O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_2907.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { y ^ { 2 } } { 2 } - \\frac { x ^ { 2 } } { 4 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2909.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `0.023 - 23 = 1000`.",
|
|
"gt_answers": "0 . 0 2 3 = \\frac { 2 3 } { 1 0 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2910.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 1000 - 400 + 36 = 3600.",
|
|
"gt_answers": "+ \\sqrt { x ^ { 2 } - y ^ { 2 } } = \\pm \\sqrt { 1 0 0 - 6 4 } = \\pm \\sqrt { 3 6 } = \\pm 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2911.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: P = UV/R + 0.71W.",
|
|
"gt_answers": "P = \\frac { U L ^ { 2 } } { R L } = \\frac { ( 1 V ) ^ { 2 } } { 6 \\Omega } \\approx 0 . 1 7 W\n",
|
|
"image_path": "./data/HME100K/test_images/test_2912.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: LDFB(x, y) = 900 - 100x + 10y.",
|
|
"gt_answers": "\\angle D F B + \\angle D B F = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2913.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 15 + 10 = 25.",
|
|
"gt_answers": "\\frac { 1 5 } { 5 0 } = \\frac { 3 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2915.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{2}x + 1\\)",
|
|
"gt_answers": "F _ { 1 } L _ { 1 } = F _ { 2 } L _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2916.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x + 0.6y = 0.06\\)\n\nThis formula represents the relationship between the variables x and y, where x is the first term and y is the second term. The equation states that the sum of the two terms is equal to 0.06.",
|
|
"gt_answers": "- \\frac { 3 } { 5 } = - 0 . 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2917.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 49\\)",
|
|
"gt_answers": "x _ { 1 } + x _ { 2 } = - \\frac { b } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2918.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2MgCl2 + 2HCl = MgCl2 + 2H2O.",
|
|
"gt_answers": "M g + 2 H C l = M g S O _ { 4 } + M g C l _ { 2 } + H\n",
|
|
"image_path": "./data/HME100K/test_images/test_2919.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(S_{AB} = \\frac{1}{2} \\left( \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "S _ { A B C P } = B C + E F = 2 L F = 2 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2920.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a negative sign in front of a number, which is a common representation of a negative number in mathematics.",
|
|
"gt_answers": "y = - \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2921.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle E H D = \\angle 1 = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2922.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 31.4 + 3.14 + 14 + 2.5 cm.",
|
|
"gt_answers": "3 1 . 4 \\div 3 . 1 4 \\div 2 = 5 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_2923.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"M = 2B + 2B.\"",
|
|
"gt_answers": "\\overrightarrow { C M } = 2 \\overrightarrow { M B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2924.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"dp-3-t\".",
|
|
"gt_answers": "D P = 3 - t\n",
|
|
"image_path": "./data/HME100K/test_images/test_2925.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3 = 5.",
|
|
"gt_answers": "O B = \\frac { 1 } { 2 } B D = \\frac { 1 } { 2 } \\times 6 = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_2926.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"u3v-1 = 1\".",
|
|
"gt_answers": "5 u - 3 v = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2927.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(t = \\frac{1}{2} \\left( \\sqrt{1 + \\left( \\frac{1}{2} \\right)^2} - 1 \\right) = \\frac{1}{2} \\left( \\sqrt{2} - 1 \\right)\\)",
|
|
"gt_answers": "\\tan ( \\frac { \\pi } { 4 } - \\alpha ) = \\frac { 1 - \\tan \\alpha } { 1 + \\tan \\alpha } = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2928.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 2 } { 3 } x + \\frac { 3 } { 4 } x - \\frac { 5 } { 6 } x = 1 + 2 + \\frac { 9 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2930.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 4 \\sqrt{a^2 + b^2} + 2ab\\)",
|
|
"gt_answers": "4 = 4 \\dot { a } ^ { 2 } + ^ { \\cdot } a ^ { 2 } - 4 \\dot { a } ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2931.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(L_A = 180 \\times L_B \\times \\frac{1}{2} \\times \\frac{1}{2} = 180 \\times 160 \\times \\frac{1}{4} \\times \\frac{1}{4} = 180 \\times 160 \\times \\frac{1}{8} = 180 \\times 160 \\times 0.125 = 22.5 \\text{ inches}\\)",
|
|
"gt_answers": ". \\angle A O B = 1 8 0 ^ { \\circ } - \\angle A B O - \\angle B A O = 1 5 0 ^ { \\circ } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_2932.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `a^2 + b^2 = c^2`.",
|
|
"gt_answers": "a + b + c = - 5 . 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2933.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(BDC = 1 + \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} = 1 + \\frac{1}{4} + \\frac{1}{4} + \\frac{1}{4} = 1 + \\frac{1}{8} = \\frac{3}{8}\\)",
|
|
"gt_answers": "\\angle B D C = \\frac { 1 8 0 - 6 1 } { 2 } = 5 9 . 5 ^ { \\circ } = \\angle B C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_2934.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "\\frac { x - 2 } { 2 } \\leq 1 = \\frac { 7 - \\pi } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2935.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(B_2 = \\frac{B_1^2}{2} + \\frac{B_1 \\cdot C_1}{2} + \\frac{C_1^2}{2}\\)\n\nThis formula calculates the bending moment of a beam with two supports and a point load at the center. The bending moment is calculated by multiplying the force applied at the center by the distance between the supports.",
|
|
"gt_answers": "\u3001 C Q = B C - B Q = 6 0 - 2 0 \\sqrt { 3 } ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2936.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(y = a + bx + c\\sqrt{x} + d\\sqrt{x^2 + 1}\\)\n\nThe formula is written in LaTeX format, which is a standard mathematical notation used for writing mathematical expressions.",
|
|
"gt_answers": "( 1 - a ) x ^ { 2 } - 4 x + 6 > 0 _ { \\cdot }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2939.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 35556666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666",
|
|
"gt_answers": "\\frac { 3 5 + 5 8 + 6 9 } { 1 0 0 } = \\frac { 9 3 + 6 9 } { 1 0 0 } = \\frac { 1 6 2 } { 1 0 0 } = 1 6 . 2 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_2940.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(P = \\frac{1}{2}mv^2 + Fg\\)\n\nwhere P is the pressure, m is the mass of the object, v is its velocity, and Fg is the gravitational force acting on the object.",
|
|
"gt_answers": "\\cdot \\frac { P M } { A N } = \\frac { C M } { C N . } = \\frac { 2 } { 3 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_2941.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 8(3+4) + 2(3+4) + 3(3+4) + 4(3+4) + 5(3+4) + 6(3+4) + 7(3+4) + 8(3+4) + 9(3+4) + 10(3+4) + 11(3+4) + 12(3+4) + 13(3+4) + 14(3+4) + 15(3+4) + 16(3+4) + 17(3+4) + 18(3+4) + 19(3+4) + 20(3+4) + 21(3+4) + 22(3+4) + 23(3+4) + 24(3+4) + 25(3+4) + 26(3+4) + 27(3+4) + 28(3+4) + 29(3+4) + 30(3+4) + 31(3+4) + 32(3+4) + 33(3+4) + 34(3+4) + 35(3+4) + 36(3+4) + 37(3+4) + 38(3+4) + 39(3+4) + 40(3+4) + 41(3+4) + 42(3+4) + 43(3+4) + 44(3+4) + 45(3+4) + 46(3+4) + 47(3+4) + 48(3+4) + 49(3+4) + 50(3+4) + 51(3+4) + 52(3+4) + 53(3+4) + 54(3+4) + 55(3+4) + 56(3+4) + 57(3+",
|
|
"gt_answers": "\\frac { 1 6 } { 3 } = \\frac { 1 } { \\cos ^ { 2 } \\alpha } \\cdot \\cos \\frac { 1 } { \\alpha } \\cdot ( - 4 m ^ { 2 } + 8 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2943.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "( x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2945.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "2 - 1 . 5 - \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2946.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2(2+1) = 4+2\".",
|
|
"gt_answers": "\\overrightarrow { a } + ( 2 - m ) \\overrightarrow { b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2947.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"y = 5/2x + 3.\"",
|
|
"gt_answers": "y = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2948.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{20} - 2^{19} + 2^{18} - 2^{17} + 2^{16} - 2^{15} + 2^{14} - 2^{13} + 2^{12} - 2^{11} + 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 10^{20} - 10^{19} + 10^{18} - 10^{17} + 10^{16} - 10^{15} + 10^{14} - 10^{13} + 10^{12} - 10^{11} + 10^{10} - 10^{9} + 10^{8} - 10^{7} + 10^{6} - 10^{5} + 10^{4} - 10^{3} + 10^{2} - 10^{1} + 10^{0} = 10^{20} - 10^{19} + 10^{18} - 10^{17} + 10^{16} - 10^{15} + 10^{14} - 10^{13} + 10^{12} - 10^{11} + 10^{10} - 10^{9} + 10^{8} - 10^{7} + 10^{6} - 10^{5} + 10^{4} - 10^{3} + 10^{2} - 10^{1} + 10^{0} = 10^{20} - 10^{19} + 10^{18} - 10^{17} + 10^{16} - 1",
|
|
"gt_answers": "\\frac { 1 } { 2 } a c c m 1 2 0 ^ { \\circ } = \\frac { 1 } { 2 } a s m 6 : + \\frac { 1 } { 2 } c s m 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2949.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(k_2 - 2k_1 + 3 = 12 - 2(2) + 3 = 12 - 4 + 3 = 9\\)",
|
|
"gt_answers": "k - 2 = - \\frac { 1 2 } { 7 } - 2 = 3 \\frac { 5 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2950.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nNaCl + H2O --> NaOH + HCl",
|
|
"gt_answers": "N a _ { 2 } C O _ { 3 } + 2 H C l = 2 N a C l + H _ { 2 } O + C O _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2951.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LDBE + LACED = 75\u00b0.\"",
|
|
"gt_answers": "\\angle D O B = \\angle D B E + \\angle A E D = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2952.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "x _ { 1 } = \\frac { \\sqrt { 5 } - 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2955.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"cos(B) = 3/2\".",
|
|
"gt_answers": "\\cos B = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2957.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\sqrt{x^2 + 2x + 1} + 1\\)",
|
|
"gt_answers": "( y + 2 ) ^ { 2 } + y ( y + 2 ) - y ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2958.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "\\sqrt { 3 } x = \\sqrt { 2 } x + 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2959.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few Chinese characters, which could be related to a Chinese mathematical expression or a Chinese character used in a mathematical context.",
|
|
"gt_answers": "\\sqrt { \\frac { 4 9 } { 2 5 } } = \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2960.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A2 + 3m.\"",
|
|
"gt_answers": "x = 3 m o l\n",
|
|
"image_path": "./data/HME100K/test_images/test_2961.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"pi squared = 4/3.\"",
|
|
"gt_answers": "x = \\sqrt [ 5 ] { \\frac { 1 6 } { 3 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2963.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x > 2 0 x < 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2964.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nA-2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1) = 2(R-1) + 2(R-1)",
|
|
"gt_answers": "A = [ ( O _ { 1 } + O 2 ) \\div 2 ] ^ { 2 } - R - r\n",
|
|
"image_path": "./data/HME100K/test_images/test_2965.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(BP = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\",
|
|
"gt_answers": "B P = \\sqrt { 3 ^ { 2 } + ( a - 1 ) ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2966.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "a x ^ { 2 } + ( 2 b - 9 ) x + c = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2967.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2 + d^2\\)\n\nThe formula is written in the form of an equation, with the variables a, b, c, and d representing the squares of the corresponding numbers.",
|
|
"gt_answers": "\\Delta A C D \\cong \\Delta A E B ( S . A . S )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2968.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LDO356-Leof L356.\"",
|
|
"gt_answers": "\\angle D O C = 3 6 0 ^ { \\circ } - \\angle E D F - \\angle E D C\n",
|
|
"image_path": "./data/HME100K/test_images/test_2969.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `x^2 + 6x + 6 = 0`.",
|
|
"gt_answers": "x = - \\frac { 5 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2970.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Bhagavad Gita\" in the handwriting style of a child.",
|
|
"gt_answers": "b < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2971.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nR1 + R2 + R3 + R4 = 4L\n\nThe formula represents the total resistance of four resistors connected in series, where R1, R2, R3, and R4 are the individual resistances. The total resistance is equal to the sum of the four resistors' resistances, which is 4L.",
|
|
"gt_answers": "R _ { B } = \\frac { V } { L } = \\frac { 2 V } { 0 . 5 A } = 4 \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_2972.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x^2 + 4x + 10 = 0.",
|
|
"gt_answers": "6 2 8 + 2 \\times 3 . 1 4 + 1 0 \\times 3 0 = 9 3 4 . 2 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_2973.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(3x^2 + 3x + 2 = 9x^2 + 3x + 2\\)",
|
|
"gt_answers": "x _ { 1 } = 3 , x _ { 2 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2975.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
|
|
"gt_answers": "- 3 + 1 = a - 1 , 4 + 0 = b + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_2976.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x384 + 341 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456",
|
|
"gt_answers": "6 4 \\times 6 = 3 8 4 3 8 4 + 1 2 = 3 9 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_2977.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x + 3y = 12\\)",
|
|
"gt_answers": "a = \\frac { 2 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2978.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4F-LACB9s\".",
|
|
"gt_answers": "\\angle F = \\angle A C B = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2982.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with the letters \"y\" and \"x\" in it, which could be a representation of a mathematical equation or a mathematical expression.",
|
|
"gt_answers": "y - \\frac { 1 } { 4 } = - \\frac { \\sqrt { 5 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2984.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x^2 + 8x + 15 = 500 + 100n, where n is an unknown integer.",
|
|
"gt_answers": "2 2 \\times 8 + 1 1 \\times 8 + 2 2 \\times 1 1 = 5 0 6 ( d m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2985.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Laplace's equation\" in LaTeX format.",
|
|
"gt_answers": "\\therefore \\angle P E C = \\angle A P E\n",
|
|
"image_path": "./data/HME100K/test_images/test_2987.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(A + B - C = D\\)\n\nThis formula represents the relationship between four variables: A, B, C, and D. The equation states that the sum of A and B is equal to D, and the difference between A and B is equal to C.",
|
|
"gt_answers": "\\frac { O B } { C D } = \\frac { A B } { A C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2988.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nZn(OH)2 + ZnSO4 + H2O \u2192 ZnSO4 + 2H2O + O2",
|
|
"gt_answers": "z _ { n } + H _ { 2 } S O _ { 4 } = H _ { 2 } \\uparrow + z n S O _ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2989.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(R_{ab} = \\frac{R_a R_b}{R_a + R_b}\\)\n\nThis formula represents the ratio of the resistances of two resistors connected in series. The resistors are labeled \"a\" and \"b\" in the image.",
|
|
"gt_answers": "\\therefore R t \\Delta A F C \\cong R t \\Delta A B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_2990.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(y = 0.5x^2 + 0.25x + 0.15\\)\n\nThis formula represents a quadratic function, where the variable \"y\" is the output and \"x\" is the input. The coefficients of the function are 0.5, 0.25, and 0.15.",
|
|
"gt_answers": "\\angle B O C = 9 0 ^ { \\circ } - 2 0 ^ { \\circ } = 7 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_2991.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "A D \\bot B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_2992.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "V _ { y } = a t\n",
|
|
"image_path": "./data/HME100K/test_images/test_2994.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A + B = C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z.\"",
|
|
"gt_answers": "A B ^ { 2 } = A E ^ { 2 } + B E ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_2995.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mathematical formula using the Greek letter \"pi\" (\u03c0) and the letter \"e\" (e). The formula is written in a way that it can be easily read and understood by those familiar with the subject.",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\leq m \\leq 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_2996.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "1 2 8 - 1 0 0 . 4 8 = 2 7 5 2 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_2997.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 39 = 50.",
|
|
"gt_answers": "x = 3 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_2998.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 64 - 4 = 60 - 4 = 56.",
|
|
"gt_answers": "6 4 \\div 4 ( < ) 6 4 \\div 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_2999.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "( x y = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3000.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle D M E = \\angle D M C = \\angle D N C = \\angle D N B = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3001.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"O(m^2)\".",
|
|
"gt_answers": "1 ^ { \\circ } m > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3002.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "2 k \\pi - \\frac { \\pi } { 2 } \\leq x - \\frac { x } { 6 } \\leq 2 k \\pi + \\frac { \\pi } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3003.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5/5 - 5/5 = 0.",
|
|
"gt_answers": "\\frac { 4 } { 5 } + \\frac { 1 } { 5 } - \\frac { 2 } { 5 } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3004.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^3 + 3x^2 - 5x + 12.\"",
|
|
"gt_answers": "x = 3 0 0 ( x - \\frac { 5 } { 1 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3005.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(2s + 3s) + 2(2s + 3s) = 4(2s + 3s) + 4(2s + 3s) = 8(2s + 3s) = 16(s) = 16.",
|
|
"gt_answers": "\\frac { 1 3 } { 3 6 } = 2 - 2 \\cos \\alpha \\cos \\beta - 2 \\sin \\alpha \\sin \\beta\n",
|
|
"image_path": "./data/HME100K/test_images/test_3006.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a negative sign, which is typically used to indicate a negative value.",
|
|
"gt_answers": "- 5 x = 3 \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3007.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(C_2H_4O_2 + 2H_2O \\rightarrow 2CO_2 + 4H_2O\\)",
|
|
"gt_answers": "P A = \\frac { C _ { 1 4 } } { C _ { 2 0 } ^ { 2 } } \\approx 0 . 4 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3008.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot",
|
|
"gt_answers": "\\frac { 2 - a - 1 } { 2 } = \\frac { \\sqrt { 2 } ( 1 - \\frac { 1 } { a } ) - \\sqrt { 2 } } { \\sqrt { 2 } ( 1 - \\frac { 1 } { a } ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3009.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3/8 + 2/8 = 5/8 + 1/8.\"",
|
|
"gt_answers": "8 3 / 8 a = 0 . 4 5 b\n",
|
|
"image_path": "./data/HME100K/test_images/test_3010.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 100\\)\n\nThis formula represents the relationship between the variables x and y, where x and y are real numbers and the result is an integer. The equation states that the square of the sum of x and y is equal to 100.",
|
|
"gt_answers": "\\frac { 1 } { x } = \\frac { 1 } { 0 . 1 } x = 0 . 1 m o l\n",
|
|
"image_path": "./data/HME100K/test_images/test_3012.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 4x - 10 = 0.",
|
|
"gt_answers": "x _ { 1 } = 5 0 x _ { 2 } = - 4 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3013.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(1.222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222",
|
|
"gt_answers": "1 2 : 1 . 2 = 1 2 \\div 1 . 2 = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3014.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(g = \\frac{1}{46} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\",
|
|
"gt_answers": "4 6 \\div ( 5 ) = 9 \\cdots 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3016.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "\\frac { 2 } { x + 1 } = a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3017.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{2}x^2 + \\frac{1}{",
|
|
"gt_answers": "F _ { ( S ) } = \\frac { 1 } { 3 } + \\frac { - \\frac { 1 } { 2 } - \\frac { 1 } { 2 } j } { 5 - 2 j } + \\frac { - \\frac { 1 } { 2 } + \\frac { 1 } { 2 } j } { 5 + 2 j }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3018.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5x2 + 7y2.",
|
|
"gt_answers": "\\frac { 5 } { 7 } = \\frac { 5 \\times 2 } { 7 \\times 2 } = \\frac { 1 0 } { 1 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3019.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20070522 - 20070523 = 20070522 - 20070524 = 20",
|
|
"gt_answers": "2 4 0 \\times 0 5 2 5 + ( 2 5 2 - 2 4 0 ) \\times 0 . 5 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_3020.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{3}x^2 + \\frac{2}{3}x + 1\\)",
|
|
"gt_answers": "y _ { 1 } = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3021.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\ny = 20 - 16x\n\nThe formula is written using the standard mathematical notation for subtracting two numbers and multiplying by a constant.",
|
|
"gt_answers": "\\frac { y ^ { 2 } } { 2 0 } - \\frac { x ^ { 2 } } { 1 6 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3022.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\pi r^2 + 2\\pi r^2 + 2\\pi r^2 + 2\\pi r^2 = 4\\pi r^2\\)",
|
|
"gt_answers": "\\angle B A E = \\cdot 3 0 ^ { \\circ } \\angle C A E = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3023.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"p = 36 - 1/L.\"",
|
|
"gt_answers": "P ( A ) = \\frac { 1 } { 3 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3024.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "y ^ { 2 } - 1 = 0 - y ^ { 2 } - 2 y + 5 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3025.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(t_n = \\frac{1}{2} \\left( t_{n-1} + t_{n+1} \\right) - \\frac{1}{2} \\left( t_{n-2} + t_{n+2} \\right) + \\frac{1}{2} \\left( t_{n-3} + t_{n+3} \\right) - \\frac{1}{2} \\left( t_{n-4} + t_{n+4} \\right) + \\cdots + \\frac{1}{2} \\left( t_{n-5} + t_{n+5} \\right) - \\frac{1}{2} \\left( t_{n-6} + t_{n+6} \\right) + \\cdots + \\frac{1}{2} \\left( t_{n-7} + t_{n+7} \\right) - \\frac{1}{2} \\left( t_{n-8} + t_{n+8} \\right) + \\cdots + \\frac{1}{2} \\left( t_{n-9} + t_{n+9} \\right) - \\frac{1}{2} \\left( t_{n-10} + t_{n+10} \\right) + \\cdots + \\frac{1}{2} \\left( t_{n-11} + t_{n+11} \\right) - \\frac{1}{2} \\left( t_{n-12} + t_{n+12} \\right) + \\cdots + \\frac{1}{2} \\left( t_{n-13} + t_{n+13} \\right) - \\frac{1}{2} \\left( t_{n-14} + t_{n+14} \\right) + \\cdots + \\frac{1}{2} \\left( t_{n-15} + t_{n+15} \\right) - \\frac{1}{2} \\left( t_{n-16} + t_{n+16} \\right) + \\cdots + \\frac{1}{2} \\left( t_{n-17} + t_{n+1",
|
|
"gt_answers": "\\frac { \\tan \\alpha - \\tan \\beta } { 1 + \\tan \\alpha \\tan \\beta } = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3026.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 4x + 180 = 0\\)",
|
|
"gt_answers": "\\angle 3 + \\angle 4 = 1 8 0 ^ { \\circ } - 9 0 ^ { \\circ } = 9 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3027.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(4x^2 + 7y^2 = 100\\)\n\nThis is a quadratic equation in the form of a quadratic formula.",
|
|
"gt_answers": "x _ { 3 } = \\frac { 4 \\sqrt { 7 } } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3028.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2\\sqrt{2} \\cdot 0.3 \\cdot 0.2 = 0.64\\)",
|
|
"gt_answers": "\\cot \\angle B C O = \\frac { C O } { D B } = \\frac { 2 } { 1 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3029.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{170} \\cdot 8^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20} \\cdot 2^{20}",
|
|
"gt_answers": "7 6 0 \\div 2 8 \\div 2 0 = 2 1 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3030.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "y _ { 4 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3032.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(AB + BE = 10\\)\n\nThis formula represents the addition of two numbers, A and B, and the result is 10.",
|
|
"gt_answers": "\\cos B = \\frac { B E } { A B } = \\frac { 4 } { 5 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3033.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `x^2 + 4x + 8 = 0`.",
|
|
"gt_answers": "( x - 3 ) ( x + 2 ) + 4 = 2 x ^ { 2 } - 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3034.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"20/100 = 0.2\" using a calculator.",
|
|
"gt_answers": "\\angle P F O = 1 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3035.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1117-18 ICMW.",
|
|
"gt_answers": "1 1 + 7 = 1 8 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3036.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(y = \\frac{1}{2} \\left(x^2 - 2x + 1\\right) + 1\\)",
|
|
"gt_answers": "\\frac { y } { 4 } - \\frac { 1 } { y } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3037.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a red circle around it, which indicates that it is likely a mathematical expression.",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3038.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as tan(d) = AB/BC.",
|
|
"gt_answers": "\\tan \\alpha = \\frac { B C } { A B } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3039.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 25 - 7 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20 + 10 - 15 + 25 - 10 + 20 - 15 + 10 - 25 + 15 - 20",
|
|
"gt_answers": "\\frac { 7 } { 2 5 } < \\frac { 9 } { 2 5 } < \\frac { 9 } { 2 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3041.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(A + B = B + A\\)",
|
|
"gt_answers": "A ^ { \\prime } B = B\n",
|
|
"image_path": "./data/HME100K/test_images/test_3042.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2.52125\\times 10^{10} = 2.52125\\times 10^{12} \\times 10^{-2} = 2.52125\\times 10^{12} \\times 0.000000252125\\)",
|
|
"gt_answers": "2 5 . 1 2 \\times 1 0 = 2 5 1 . 2 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3043.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 0 m = 3 0 0 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_3046.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 10x3=300.",
|
|
"gt_answers": "1 0 \\times 3 = 3 0 ( d m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3047.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "+ C _ { 6 } ^ { 0 } + C _ { 6 } ^ { 1 } ( - \\sqrt { x } ) + C _ { 6 } ^ { 2 } ( - \\sqrt { x } ) ^ { 2 } + C _ { 6 } ^ { 3 } ( - \\sqrt { x } ) ^ { 3 } + C _ { 6 } ^ { 4 } ( - \\sqrt { x } ) ^ { 4 } + C _ { 6 } ^ { 5 } ( - \\sqrt { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3048.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a negative sign, which is typically written as a minus sign (-) in LaTeX.",
|
|
"gt_answers": "x = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3050.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\Delta B D E \\sim \\Delta E D O\n",
|
|
"image_path": "./data/HME100K/test_images/test_3051.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(P(X_1 = 1, X_2 = 2, X_3 = 3, X_4 = 4, X_5 = 5, X_6 = 6, X_7 = 7, X_8 = 8, X_9 = 9) = 1/240\\)",
|
|
"gt_answers": "P ( Y = 2 ) = C _ { 3 } ^ { 2 } ( \\frac { 1 } { 4 } ) ^ { 2 } ( \\frac { 3 } { 4 } ) = \\frac { 9 } { 6 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3052.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\nV = 1800 \\times 300 \\times 1000 / 450 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\times 300 \\times 1000 / 450 \\times 1000 = 1800 \\",
|
|
"gt_answers": "v = \\frac { s } { t } = \\frac { 1 3 5 0 } { 4 . 5 } = 3 0 0 k m / h\n",
|
|
"image_path": "./data/HME100K/test_images/test_3053.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(LA = 2 \\times 5 + 4 \\times 3 = 15 + 12 = 27\\)",
|
|
"gt_answers": "\\tan \\angle A = \\frac { 2 } { 4 \\sqrt { 2 } } = \\frac { \\sqrt { 2 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3054.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LEO = 100\u00b0 + 45\u00b0 = 145\u00b0.\"",
|
|
"gt_answers": "\\angle E O D = 1 8 0 ^ { \\circ } \\div 4 = 4 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3055.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"143-277/444 = 0.325.\"",
|
|
"gt_answers": "( 4 3 - 2 7 ) \\div 4 = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3056.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(B_e = \\frac{B_c \\cdot C_e}{C_c + C_e}\\)\n\nwhere B_e is the efficiency of the electric motor, B_c is the efficiency of the cooling system, and C_e is the efficiency of the electricity generation system.",
|
|
"gt_answers": "\\frac { B E } { C F } = \\frac { B C } { C E }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3057.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `sin(x) = sin(90 + x/2) - sin(x/2)`.",
|
|
"gt_answers": "\\therefore A C = \\sin 7 0 ^ { \\circ } \\cdot A B \\approx 0 . 9 4 \\times 2 0 = 1 8 . 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3058.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "y _ { 3 } = - \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3059.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(x + 3) - 5(x - 2) = 10x - 15.",
|
|
"gt_answers": "\\frac { 2 } { 5 } = \\frac { 4 \\times 2 } { 4 \\times 5 } = \\frac { 8 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3060.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "a _ { m } = \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3063.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 3y^2 - 2xy = 0\\)",
|
|
"gt_answers": "\\textcircled { 1 } - 3 \\times \\textcircled { 4 } : 6 x = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3066.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2x^2 + 14x - 14.",
|
|
"gt_answers": "\\frac { 2 } { 1 5 } \\times 7 = \\frac { 2 \\times 7 } { 1 5 } = \\frac { 1 4 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3067.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 274000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 7 + 6 0 > 1 0 0 - 1 5 - 1 5 > 9 3 - 4 0 >\n",
|
|
"image_path": "./data/HME100K/test_images/test_3068.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 50x = 50b + 50c.",
|
|
"gt_answers": "5 0 \\times 3 0 = 1 5 0 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3069.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(y = 2x^2 + 3x + 4\\)\n\nThe formula is written in the form of an equation, with the variables x and y on the left side and the constants 2, 3, and 4 on the right side. The expression is enclosed in parentheses, and the equation is separated from the rest of the text by a line break.",
|
|
"gt_answers": "\\angle D E B = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3070.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(3x + 1) = 12.",
|
|
"gt_answers": "\\frac { 3 } { 6 } < \\frac { 2 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3071.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula is commonly known as the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "x = \\frac { a - 5 } { a - 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3072.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 8 0 - 4 5 - 4 5 = 9 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3073.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(H_2O + CO_2 + O_2 \\rightarrow 2H_2O + CO_2\\)\n\nThis formula represents the chemical reaction between water and carbon dioxide to produce two molecules of water and one molecule of carbon dioxide.",
|
|
"gt_answers": "1 + ( 2 - a ) ^ { 2 } + 1 7 = 9 + ( 1 - a ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3074.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 12x6 = 72.",
|
|
"gt_answers": "1 2 \\times 6 = 7 2 ( d m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3075.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x",
|
|
"gt_answers": "4 \\times 4 \\times 4 = 6 4 c m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3076.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(x + 3) - 3(x - 2) = 0.",
|
|
"gt_answers": "\\frac { 2 } { 3 } x \\div \\frac { 2 } { 3 } = \\frac { 8 } { 6 } x \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3077.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "\\times 5 \\times 6 0 s = 2 7 0 0 J\n",
|
|
"image_path": "./data/HME100K/test_images/test_3078.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "A E = 1 \\therefore A D = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3079.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = b^2\\)\n\nThis formula represents the equation of a circle with center (0, 0) and radius b.",
|
|
"gt_answers": "x _ { 1 } + x _ { 2 } = - \\frac { b } { a } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3080.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 0 0 0 0 c m = 1 k m\n",
|
|
"image_path": "./data/HME100K/test_images/test_3081.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBC = 120\u00b0\".",
|
|
"gt_answers": "\\angle B O C = 1 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3082.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle A C B = 9 0 ^ { \\circ } \\angle C D B ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_3083.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 3x + 4 = 10\\)\n\nThis is a quadratic equation in the variable x, and it can be solved using the quadratic formula.",
|
|
"gt_answers": "( x + 1 ) ^ { 2 } . = 4 8 \\div 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3084.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `4x + 5y = 1003`.",
|
|
"gt_answers": "x - \\frac { 4 } { 5 } x = 1 0 + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3085.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(80 \\times 80 = 6400\\)",
|
|
"gt_answers": "( x - 2 ) ( x + 2 ) + 2 ( x + 1 ) ( x + 2 ) = - 8 ( x + 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3086.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x^2 - 3x + 1 = 0.\"",
|
|
"gt_answers": "x _ { 2 } = \\sqrt { 3 } - \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3087.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2}",
|
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"gt_answers": "1 . 1 2 2 . 1 8 2 . 2 5 1 3 . 5 3 \u3001 < > < > 4 . \\frac { 1 } { 1 0 } \\frac { 3 } { 8 } 5 . 4 0\n",
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"image_path": "./data/HME100K/test_images/test_3088.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n(3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3) + (3 + 3)",
|
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"gt_answers": "( 3 - i ) ( t + 2 i ) \\in R\n",
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"image_path": "./data/HME100K/test_images/test_3089.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 0.667 - 0.00667 = 0.661433.",
|
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"gt_answers": "0 . 6 6 7 > \\frac { 2 } { 3 } > 6 . 6 \\% > \\frac { 4 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3091.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x _ { 2 } = 4 y ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3092.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 30/15 - 2.",
|
|
"gt_answers": "\\frac { 3 0 } { 1 5 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3093.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as `6x^2 - 2x - 1 = 0`.",
|
|
"gt_answers": "\\sqrt { ( 2 - x ) ^ { 2 } + ( 2 x + 1 - 3 ) ^ { 2 } } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3094.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(N_{A+B} = N_A + N_B + N_{AB}\\)\n\nThis formula represents the total number of atoms in a compound made up of two elements, A and B, as well as the number of atoms in the compound formed by combining A and B. The total number of atoms in the compound is calculated by adding the number of atoms in each element, followed by the number of atoms in the compound formed by combining the two elements.",
|
|
"gt_answers": "N a _ { 2 } S O _ { 4 } + B a C l _ { 2 } = B a S O _ { 4 } l + 2 N a C l\n",
|
|
"image_path": "./data/HME100K/test_images/test_3098.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 0.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666",
|
|
"gt_answers": "0 . 6 = \\frac { 6 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3099.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 20000 x 5000 = 1000000000.",
|
|
"gt_answers": "2 0 0 0 0 \\times \\frac { 1 } { 5 0 0 0 } = 4 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3100.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{3} + \\frac{1}{3} + \\frac{1}{3} = \\frac{3}{3}\n\\end{equation}\n\nThis equation is a simple algebraic expression that represents the sum of three terms, each of which is equal to one third. The equation is written using the standard mathematical notation for equations, including the use of the equal sign, the parentheses, and the fraction bar.",
|
|
"gt_answers": "x = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3101.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3x^2 + 2x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 3 } { 5 } : x = 2 5 \\% = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3102.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + 64 + 512 + ",
|
|
"gt_answers": "5 1 , 2 \\div 8 5 = 6 \\cdots 2 5 1 2 \\div 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3103.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as y = 2x + 1.",
|
|
"gt_answers": "y - \\frac { 2 } { y } - 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3104.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 8x - 16 = 0\\)",
|
|
"gt_answers": "( 8 9 - 2 5 ) \\div 8 = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3105.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4}\n\\end{equation}\n\nThis equation is a simple algebraic expression that represents the result of adding two fractions with a common denominator of 2.",
|
|
"gt_answers": "2 [ \\frac { 4 } { 3 } x - ( \\frac { 2 } { 3 } x - \\frac { 1 } { 2 } ) ] = \\frac { 3 } { 4 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3107.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 2 0 = 1 0 0 + 1 0 0 + 1 0 0 + 1 0 0 + 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3108.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(x^2 + 4x + 1 = 0\\)\n\nThis formula represents a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "k ^ { 2 } x ^ { 2 } + ( 2 k - 4 ) x + 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3109.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a negative sign, which can be represented in LaTeX as follows:\n\n\\(y = -x\\)",
|
|
"gt_answers": "x = - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3111.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"abctbc1x2\" using LaTeX format.",
|
|
"gt_answers": "a b + a c + b c ) \\times 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3112.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 + c^2 = (a + b + c)^2\\)",
|
|
"gt_answers": "a = - \\frac { 3 } { 2 } < - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3114.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x^2 + 4x + 5 = 0.",
|
|
"gt_answers": ": y = - 4 8 x + 2 4 0 ( 2 . 5 \\leq x < 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3116.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3a^3 - 3a^2b + 3ab^2 - 3b^3 = 0\\)",
|
|
"gt_answers": "( a - 3 ) x = 3 + a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3119.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "x ^ { 2 } - 9 = 4 x ^ { 2 } - 2 4 x + 3 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3120.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z + A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z + A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z + A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z + A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z + A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z + A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z + A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z + A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z + A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q +",
|
|
"gt_answers": "A P \\cdot C Q = A D \\cdot C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_3121.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(P(LEs) = P(LEs) + P(BOPA) - P(LEs \\cap BOPA)\\)\n\nThis formula calculates the probability of a person having both a left eye and a right eye, given that they have either a left eye or a right eye. The formula uses the addition, subtraction, and intersection operators to determine the probability of each event occurring separately and then combining them to calculate the overall probability.",
|
|
"gt_answers": "P ^ { \\prime } = \\frac { F _ { 1 } } { S } = 1 0 0 P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3122.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(46x^2 + 48y^2 = 1000\\)",
|
|
"gt_answers": "x _ { 1 } x _ { 2 } = \\frac { 4 b ^ { 2 } - 4 } { 4 k ^ { 2 } + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3123.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\textcircled { 3 } \\frac { 1 } { 6 } : \\frac { 1 } { 4 } = x : \\frac { 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3125.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n2 ABD + LABC = 180\u00b0\n\nThe formula uses the letters A, B, and C to represent angles, and the letter D represents the hypotenuse. The formula states that the sum of the angles A, B, and C is equal to 180\u00b0.",
|
|
"gt_answers": "\\angle A B D + \\angle A B C = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3126.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 3x + 2 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 6 } { 5 } \\div 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3127.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4/3 - 3/2.",
|
|
"gt_answers": "4 = \\frac { m } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3128.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(6x + 3y = 12\\)",
|
|
"gt_answers": "x = \\frac { 5 } { 6 } \\div \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3129.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x - 18 = 7.",
|
|
"gt_answers": "\\frac { 2 } { 3 } x = \\frac { 1 7 } { 1 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3130.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: \"2x + 3y = 10.\"",
|
|
"gt_answers": "5 \\frac { 3 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3131.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3rd-order polynomial.\"",
|
|
"gt_answers": "\\frac { \\sin \\alpha + \\cos \\alpha } { \\sin \\alpha - \\cos \\alpha }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3132.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SS000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 H _ { 2 } S O _ { 3 } + O _ { 2 } \\rightarrow 2 H _ { 2 } S O _ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3133.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3(2n-1) - 2n = 3n - 2n = 0.",
|
|
"gt_answers": "3 ^ { n + 1 } a _ { n + 1 } = 3 ^ { n } a _ { n } - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3134.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1/5 x 1/1.5 = 1/7.5.",
|
|
"gt_answers": "\\frac { x } { 1 5 } = \\frac { 1 . 5 } { 0 . 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3135.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x _ { 2 } = - \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3136.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{4} \\cdot 10^{6} \\cdot 10^{12} \\cdot 10^{18} \\cdot 10^{24} \\cdot 10^{30} \\cdot 10^{36} \\cdot 10^{42} \\cdot 10^{48} \\cdot 10^{54} \\cdot 10^{60} \\cdot 10^{66} \\cdot 10^{72} \\cdot 10^{78} \\cdot 10^{84} \\cdot 10^{90} \\cdot 10^{96} \\cdot 10^{102} \\cdot 10^{108} \\cdot 10^{114} \\cdot 10^{120} \\cdot 10^{126} \\cdot 10^{132} \\cdot 10^{138} \\cdot 10^{144} \\cdot 10^{150} \\cdot 10^{156} \\cdot 10^{162} \\cdot 10^{168} \\cdot 10^{174} \\cdot 10^{180} \\cdot 10^{186} \\cdot 10^{192} \\cdot 10^{198} \\cdot 10^{204} \\cdot 10^{210} \\cdot 10^{216} \\cdot 10^{222} \\cdot 10^{228} \\cdot 10^{234} \\cdot 10^{240} \\cdot 10^{246} \\cdot 10^{252} \\cdot 10^{258} \\cdot 10^{264} \\cdot 10^{270} \\cdot 10^{276} \\cdot 10^{282} \\cdot 10^{288} \\cdot 10^{294} \\cdot 10^{300} \\cdot 10^{3",
|
|
"gt_answers": "2 . 4 \\div 4 = 0 . 6 ( d m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3137.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = r^2\\)",
|
|
"gt_answers": "\\frac { 1 } { R } = \\frac { 1 } { R _ { 1 } } + \\frac { 1 } { R _ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3138.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 3(x + 1) + 4(x - 1) = 12x^2 + 12x - 4.",
|
|
"gt_answers": "\\sqrt { 7 x + 3 y } = \\pm \\sqrt { 7 \\times 1 + 3 \\times 1 4 } = \\pm 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3139.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6x4 + 144cm^2\".",
|
|
"gt_answers": "- 6 \\times 6 \\times 4 = 1 4 4 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3140.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nSina = d\n\nThis formula represents the relationship between the sine of an angle and its corresponding distance. The sine of an angle is the ratio of the length of the opposite side of a right triangle to the length of its hypotenuse. The distance is the length of the adjacent side of the triangle.",
|
|
"gt_answers": "\\sin \\theta = \\frac { d } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3141.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{m(x^2 + 2x + 3)}{(x^2 + 2x + 3)^2 + 4x^2 + 4x + 4}\\)\n\nThe formula is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "( x + y ) - 1 ) m - ( 2 x - 3 y + 6 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3142.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(B = \\frac{200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "B = 8 4 0 \\div 2 4 0 0 = 0 . 3 5 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3143.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LAED = 90\u00b0\".",
|
|
"gt_answers": "\\angle A E D = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3144.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in the Greek alphabet, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a Greek letter in it, which could be a symbol or a letter used in mathematics.",
|
|
"gt_answers": "f ^ { \\prime } ( x ) > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3146.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"OB/BD = CD/OC\" using LaTeX format.",
|
|
"gt_answers": "O B = B D = C D = O C\n",
|
|
"image_path": "./data/HME100K/test_images/test_3147.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2n + 1\" and is represented using the LaTeX code `\\(2n + 1\\)` in the image.",
|
|
"gt_answers": "2 N O + O _ { 2 } \\rightarrow 2 N O _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3148.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2sin(30\u00b0) = 2sin(15\u00b0) + 2sin(45\u00b0) + 2sin(60\u00b0) + 2sin(75\u00b0) + 2sin(90\u00b0) + 2sin(105\u00b0) + 2sin(120\u00b0) + 2sin(135\u00b0) + 2sin(150\u00b0) + 2sin(165\u00b0) + 2sin(180\u00b0) + 2sin(195\u00b0) + 2sin(210\u00b0) + 2sin(225\u00b0) + 2sin(240\u00b0) + 2sin(255\u00b0) + 2sin(270\u00b0) + 2sin(285\u00b0) + 2sin(300\u00b0) + 2sin(315\u00b0) + 2sin(330\u00b0) + 2sin(345\u00b0) + 2sin(360\u00b0) + 2sin(375\u00b0) + 2sin(390\u00b0) + 2sin(405\u00b0) + 2sin(420\u00b0) + 2sin(435\u00b0) + 2sin(450\u00b0) + 2sin(465\u00b0) + 2sin(480\u00b0) + 2sin(495\u00b0) + 2sin(510\u00b0) + 2sin(525\u00b0) + 2sin(540\u00b0) + 2sin(555\u00b0) + 2sin(570\u00b0) + 2sin(585\u00b0) + 2sin(600\u00b0) + 2sin(615\u00b0) + 2sin(630\u00b0) + 2sin(645\u00b0) + 2sin(660\u00b0) + 2sin(675\u00b0) + 2sin(690\u00b0) + 2sin(705\u00b0) + 2sin(720\u00b0) + 2sin(735\u00b0) + 2sin(750\u00b0) + ",
|
|
"gt_answers": "\\vert - 3 \\vert - ( 3 - \\pi ) ^ { \\circ } - 2 \\sin 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3149.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few words written in Japanese, which could be a mathematical expression or a formula in Japanese.",
|
|
"gt_answers": "+ \\frac { 1 } { 1 \\times 2 } _ { + 1 + } \\frac { 1 } { 2 \\times 3 } _ { + 1 + } \\frac { 1 } { 3 \\times 4 } + \\cdots +\n",
|
|
"image_path": "./data/HME100K/test_images/test_3151.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(V = IR \\cdot A\\)\n\nwhere V is the voltage, I is the current, and A is the area of the conductor.",
|
|
"gt_answers": "V = \\frac { P } { F } = \\frac { 4 \\times 1 0 ^ { 4 } N } { 1 . 6 \\times 1 0 ^ { 3 } N } = 2 5 m / s\n",
|
|
"image_path": "./data/HME100K/test_images/test_3152.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { I _ { 1 } } { I _ { 2 } } = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3153.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { \\frac { 2 0 0 0 } { 8 } - \\frac { 2 0 0 0 } { 8 0 } } { x } = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3155.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(J_0 = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x _ { 2 } = - \\frac { \\sqrt { 1 0 } \\cdot } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3157.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 8 = 0\\)",
|
|
"gt_answers": "\\frac { 6 0 } { 1 0 0 } x = 1 2 8 x = - \\frac { 6 4 0 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3159.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "\\frac { 1 } { x + y } = a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3160.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 - 4x + 1 = 0.\"",
|
|
"gt_answers": "- \\frac { 1 } { 2 } x + 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3161.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 12 + 467 - 539 = 467.",
|
|
"gt_answers": "( 5 3 9 ) - ( 4 6 7 ) = ( 7 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3162.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2r + 1 = 3b\" using LaTeX format.",
|
|
"gt_answers": "2 R = \\frac { b } { C M B } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3165.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(C_{16} + 4 = 23\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(C_{16} + 4 = 23\\)",
|
|
"gt_answers": "C = \\sqrt { 1 6 - 4 } = 2 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3166.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(B_1 + B_2 + B_3 + B_4 = 0\\)\n\nThis formula represents the fact that the sum of the four blue bars in the image is equal to zero.",
|
|
"gt_answers": "P C = B C - B P ^ { \\prime } = 1 6 -\n",
|
|
"image_path": "./data/HME100K/test_images/test_3167.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"67 mL to 100 mL.\"",
|
|
"gt_answers": "6 7 m L = \\frac { 6 7 } { 1 0 0 0 } L\n",
|
|
"image_path": "./data/HME100K/test_images/test_3168.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"t^2 + 6v^2 = 9.\"",
|
|
"gt_answers": "4 u + 6 v = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3169.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"5x + 3 = 10.\"",
|
|
"gt_answers": "x = - \\frac { 5 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3170.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 45 - 35 = 10.",
|
|
"gt_answers": "\\frac { 2 5 } { 3 5 } > \\frac { 2 4 } { 4 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3171.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CNMn2+ = Mn3+ + 2CN-.\"",
|
|
"gt_answers": "\\frac { C N } { M N } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3172.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `2x^2 + 3x + 4 = 0`.",
|
|
"gt_answers": "x = \\frac { 2 } { 3 } \\times \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3173.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 3x^2 + 2x + 1\\)",
|
|
"gt_answers": "y = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3174.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(n = \\frac{1}{2} \\left( \\sqrt{2 \\pi} \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^2 \\left( \\frac{1}{2} \\right)^",
|
|
"gt_answers": "F _ { m } = 1 0 0 0 N = F _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3175.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `a^2 + b^2 = c^2`.",
|
|
"gt_answers": "a + b = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3176.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "A D / / B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_3178.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x + 4 = 0.",
|
|
"gt_answers": "1 \\div 2 0 = \\frac { 1 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3179.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `Bc = 20 - 0.2`.",
|
|
"gt_answers": "B C = \\vert 2 - 0 \\vert = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3180.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, but it can be translated to English as \"The sum of the squares of the first 100 natural numbers is equal to the sum of the squares of the first 100 even numbers.\"",
|
|
"gt_answers": "- \\frac { a } { 2 } + 2 k \\pi < 2 x - \\frac { \\pi } { 3 } < \\frac { x } { 2 } + k \\pi ( k\n",
|
|
"image_path": "./data/HME100K/test_images/test_3181.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "1 - \\frac { 1 } { 4 } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3182.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"21 - 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 8 } { 1 4 } \\textcircled { > } \\frac { 9 } { 2 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3183.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 9\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(x^2 + 2x + 3 = 9\\)\n\nThe LaTeX code for the formula is:\n\n\\begin{equation}\nx^2 + 2x + 3 = 9\n\\end{equation}\n\nThe LaTeX code for the image is:\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=8cm]{image.png}\n\\end{figure}",
|
|
"gt_answers": "\\frac { 2 x } { 3 } = \\frac { 4 x - 8 } { 9 } - 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3184.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(sin(3x) + sin(3y) + sin(3z) = 3sin(x)sin(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)cos(z) + 3cos(x)sin(y)cos(z) + 3cos(x)cos(y)sin(z) + 3sin(x)cos(y)sin(z) + 3cos(x)sin(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)cos(z) + 3cos(x)sin(y)cos(z) + 3cos(x)cos(y)sin(z) + 3sin(x)cos(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)sin(z) + 3cos(x)cos(y)cos(z) + 3sin(x)cos(y)sin",
|
|
"gt_answers": "\\sin \\frac { \\pi } { 3 } \\neq \\sin ( \\frac { 2 \\pi } { 3 } + \\frac { \\pi } { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3185.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x = 2 \\sqrt{3} \\sqrt{2} \\sqrt{5} \\sqrt{7} \\sqrt{11} \\sqrt{13} \\sqrt{17} \\sqrt{19} \\sqrt{23} \\sqrt{25} \\sqrt{29} \\sqrt{31} \\sqrt{37} \\sqrt{41} \\sqrt{43} \\sqrt{47} \\sqrt{53} \\sqrt{59} \\sqrt{65} \\sqrt{71} \\sqrt{77} \\sqrt{83} \\sqrt{89} \\sqrt{95} \\sqrt{101} \\sqrt{107} \\sqrt{113} \\sqrt{119} \\sqrt{125} \\sqrt{131} \\sqrt{137} \\sqrt{143} \\sqrt{149} \\sqrt{155} \\sqrt{161} \\sqrt{167} \\sqrt{173} \\sqrt{179} \\sqrt{185} \\sqrt{191} \\sqrt{197} \\sqrt{203} \\sqrt{209} \\sqrt{215} \\sqrt{221} \\sqrt{227} \\sqrt{233} \\sqrt{239} \\sqrt{245} \\sqrt{251} \\sqrt{257} \\sqrt{263} \\sqrt{269} \\sqrt{275} \\sqrt{281} \\sqrt{287} \\sqrt{293} \\sqrt{299} \\sqrt{305} \\sqrt{311} \\sqrt{317} \\sqrt{323} \\sqrt{329} \\sqrt{335} \\sqrt{341} \\sqrt{347} \\sqrt{353} \\sqrt{359} \\sqrt{365} \\sqrt{371} \\sqrt{377} \\sqrt{383} \\sqrt{389} \\sqrt{395} \\sqrt{",
|
|
"gt_answers": "x = \\frac { 1 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3187.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 4x - 1 = 3.",
|
|
"gt_answers": "\\frac { 4 } { x ^ { 2 } - 4 } = 1 - \\frac { 1 } { x + 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3188.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(CE = \\frac{B}{C} \\cdot DO\\)\n\nwhere CE is the cost of the project, B is the budget, DO is the duration of the project, and C is the cost per day.",
|
|
"gt_answers": "\\frac { C D } { C E } = \\frac { D O } { B O . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3189.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{16} \\cdot 2^{12} \\cdot 2^{8} \\cdot 2^{4} \\cdot 2^{2} \\cdot 2^{1} \\cdot 2^{0} = 65536^2 = 4294967296\\)",
|
|
"gt_answers": "( 1 5 + 1 2 ) \\times 2 + 8 \\times 4 + 3 0 = 1 1 6 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3190.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "1 0 \\times 6 \\times 2 = 1 2 0 ( c m ^ { 2 } ) ( 1 0 \\times 6 + 1 0 \\times 1 2 + 6 \\times 1 2 ) \\times 2 = 5 2 4 ( c m ^ { 2 } ) 5 2 4 - 1 2 0 = 4 0 4 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3191.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A(A+B) + C(A+B) + D(A+B) + E(A+B) + F(A+B) + G(A+B) + H(A+B) + I(A+B) + J(A+B) + K(A+B) + L(A+B) + M(A+B) + N(A+B) + O(A+B) + P(A+B) + Q(A+B) + R(A+B) + S(A+B) + T(A+B) + U(A+B) + V(A+B) + W(A+B) + X(A+B) + Y(A+B) + Z(A+B)\".",
|
|
"gt_answers": "A _ { 4 } ^ { 4 } A _ { 2 } ^ { 2 } + C _ { 3 } ^ { 1 } A _ { 3 } ^ { 3 } A _ { 2 } ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3192.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, which are not supported by LaTeX. However, I can provide a rough translation of the formula into English:\n\n\"The sum of the squares of the first 100 natural numbers is equal to the sum of the squares of the first 100 even numbers.\"",
|
|
"gt_answers": "x = 3 \\pm 2 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3193.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2} + 1\\)",
|
|
"gt_answers": "\\lambda : y = k x - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3195.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(P = \\frac{0.0055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555",
|
|
"gt_answers": "\\rho = \\frac { m } { v } = \\frac { 0 . 0 5 5 k g } { 5 \\times 1 0 ^ { - 5 } m ^ { 3 } } = 1 . 1 \\times 1 0 ^ { 3 } k g / m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3196.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"arctan(x) = tan(x/2) + tan(x/4) + tan(x/8) + ... + tan(x/2^n)\" where n is an integer.",
|
|
"gt_answers": "a c c \\sin ( \\sin x ) = x , x \\in [ - \\frac { \\pi } { 2 } , \\frac { \\pi } { 2 } ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_3197.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 16 - 8 + 4 = 20.",
|
|
"gt_answers": "\\frac { 1 6 } { 6 8 } = \\frac { 4 } { 1 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3198.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(B_c = \\frac{BC}{2} \\sin 60\u00b0 + \\frac{AC}{2} \\sin 60\u00b0\\)",
|
|
"gt_answers": "\\sin 6 0 ^ { \\circ } = \\frac { B F } { B C } = \\frac { \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3201.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3(5+2) = 3(7) = 21.",
|
|
"gt_answers": "3 + 2 \\sqrt { 2 } P Q = 3 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3202.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"y = 4x + 3.\"",
|
|
"gt_answers": "y _ { 4 } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3204.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 200 - 200 = 0.",
|
|
"gt_answers": "0 : 2 0 0 = \\frac { 1 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3206.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 5(2x-1) = 9.",
|
|
"gt_answers": "P _ { ( A ) } = 1 - \\frac { 4 } { 5 } = \\frac { 5 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3207.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x + 3y = 6.",
|
|
"gt_answers": "\\frac { 2 } { 3 } : 8 = \\frac { 1 } { 2 } : 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3208.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SASY\" using the Greek alphabet.",
|
|
"gt_answers": "\\Delta B A D \\cong \\Delta C A E ( S . A . S . )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3209.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SADB = 3\".",
|
|
"gt_answers": "S _ { \\Delta A D B } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3210.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\".",
|
|
"gt_answers": "a = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3211.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2x + actb + catc + 1.",
|
|
"gt_answers": "2 x . \\frac { a c + a b c + c } { c a + c + 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3212.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(300 \\times 400 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times",
|
|
"gt_answers": "5 0 + 4 0 + 4 0 = 1 3 0 0 m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3214.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: \"F(x) = 2x^2 - 3x + 4.\"",
|
|
"gt_answers": "F e _ { 3 } O F e _ { 2 } O _ { 3 } + 2 H C l = F e C l _ { 2 } + O\n",
|
|
"image_path": "./data/HME100K/test_images/test_3216.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(F_{g,L} = \\frac{1}{2} \\left( \\frac{1}{R_g} + \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} - \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} + \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} - \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} + \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} - \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} + \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} - \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} + \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} - \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} + \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} - \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} + \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} - \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} + \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} - \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} + \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} - \\frac{1}{R_L} \\right) \\left( \\frac{1}{R_g} + \\frac{1}{R_L} \\right) \\left( \\frac",
|
|
"gt_answers": "F _ { 1 } = G _ { 1 } - \\frac { G _ { 2 } l _ { 2 } } { L _ { 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3217.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{3a^2 + 2b^2 - 3c^2}{2ab} = \\frac{3a^2 + 2b^2 - 3c^2}{2ab}\n\\end{equation}\n\nThis equation is a simple algebraic expression that involves the variables a, b, and c. The expression is written in the form of an equation, with the left side being the numerator and the right side being the denominator. The numerator is a quadratic expression, which is a polynomial of degree two. The denominator is a linear expression, which is a polynomial of degree one.",
|
|
"gt_answers": "- 3 a ^ { 2 } - \\frac { 4 8 } { 2 5 } + 3 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3218.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 1\".",
|
|
"gt_answers": "x + y = - 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3219.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"d = a + b\" using LaTeX format.",
|
|
"gt_answers": "r A = 1 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3220.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 20 cm = 40 cm / 2.",
|
|
"gt_answers": "A Q = \\frac { 2 0 } { \\frac { 1 } { 2 } } = 4 0 c m .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3221.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"DA HE 4400.\"",
|
|
"gt_answers": "D A H = 4 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3222.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 0\\)",
|
|
"gt_answers": "x - 2 y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3224.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 2x + 1 = 3x^2 + 2x + 1\\)\n\nThis formula can be rewritten as:\n\n\\(2x^2 + 2x + 1 = 3x^2 + 2x + 1 - 2x^2 - 2x - 1\\)\n\nThis can be further simplified to:\n\n\\(2x^2 + 2x + 1 = 3x^2 + 2x + 1 - 2x^2 - 2x - 1 - 2x^2 - 2x - 1\\)\n\nFinally, the expression can be written as:\n\n\\(2x^2 + 2x + 1 = 3x^2 + 2x + 1 - 2x^2 - 2x - 1 - 2x^2 - 2x - 1 - 2x^2 - 2x - 1\\)\n\nThis is the simplified expression of the formula in LaTeX format.",
|
|
"gt_answers": "\\frac { 3 } { x + 2 } - \\frac { x - 1 } { ( x + 2 ) ( x - 2 ) } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3225.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\ny = 1 + 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8 + 10x^9 + 11x^10 + 12x^11 + 13x^12 + 14x^13 + 15x^14 + 16x^15 + 17x^16 + 18x^17 + 19x^18 + 20x^19 + 21x^20 + 22x^21 + 23x^22 + 24x^23 + 25x^24 + 26x^25 + 27x^26 + 28x^27 + 29x^28 + 30x^29 + 31x^30 + 32x^31 + 33x^32 + 34x^33 + 35x^34 + 36x^35 + 37x^36 + 38x^37 + 39x^38 + 40x^39 + 41x^40 + 42x^41 + 43x^42 + 44x^43 + 45x^44 + 46x^45 + 47x^46 + 48x^47 + 49x^48 + 50x^49 + 51x^50 + 52x^51 + 53x^52 + 54x^53 + 55x^54 + 56x^55 + 57x^56 + 58x^57 + 59x^58 + 60x^59 + 61x^60 + 62x^61 + 63x^62 + 64x^63 + 65x^6",
|
|
"gt_answers": "y = \\frac { \\dot { 8 } + 2 y } { 4 } + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3226.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 3x - 2 = 0\\)\n\nThis formula represents a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "x _ { 3 } = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3228.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{4} \\right) = \\frac{1}{4}\n\\end{equation}\n\nThis equation can be simplified further to:\n\n\\begin{equation}\n\\frac{1}{2} + \\frac{1}{4} = \\frac{3}{8}\n\\end{equation}\n\nThe equation is written using the `\\left( \\right)` and `\\left( \\right)` symbols to indicate the parentheses and the `\\frac` symbol to indicate the fraction.",
|
|
"gt_answers": "\\frac { 3 x - 9 } { 1 2 } - \\frac { 2 0 x - 1 6 } { 1 2 } = \\frac { 1 8 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3229.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "y _ { 1 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3230.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(n \\cdot \\sin(n \\cdot \\theta) = \\sin(n \\cdot \\theta) \\cdot n\\)",
|
|
"gt_answers": "- n \\sqrt { \\frac { n } { n ^ { 2 } - 1 } } = \\sqrt { n + \\frac { n } { n ^ { 2 } - 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3232.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b = \\frac{a^2}{2}\\)",
|
|
"gt_answers": "\\frac { b } { a } < 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3234.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a mathematical expression or a formula related to physics or chemistry.",
|
|
"gt_answers": "3 \\times ( 5 x - 2 ) - 4 \\times ( 3 x - 1 ) = 4 \\times ( x + 1 ) - 8 \\times ( 1 - x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3235.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 4x + 6 = 12.",
|
|
"gt_answers": "\\angle 4 = \\angle 6 = \\angle B P\n",
|
|
"image_path": "./data/HME100K/test_images/test_3236.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\nAP2 + BP2 = AB2\n\nThis formula represents the relationship between the areas of two squares and the area of a third square. The letters A, B, and C represent the areas of the squares, and the letter P represents the area of the third square. The formula states that the area of the third square is equal to the sum of the areas of the two squares multiplied by the square of the difference between their perimeters.",
|
|
"gt_answers": "A P ^ { 2 } + B P ^ { 2 } = A B ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3237.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 6x6s = 15.",
|
|
"gt_answers": "A P _ { 5 } = \\frac { 6 \\times 5 } { 2 } = 1 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3238.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2\\pi r^2 \\cdot 0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
|
|
"gt_answers": "0 . 9 8 = \\frac { n ^ { 2 } } { n ^ { 2 } \\pm 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3240.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4} + \\frac{1}{4} = \\frac{3}{8} \\)",
|
|
"gt_answers": "C u + 2 A g N O _ { 3 } = C u ( N O _ { 3 } ) _ { 2 } + 2 A g\n",
|
|
"image_path": "./data/HME100K/test_images/test_3241.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4x^2 + 4x + 4 = 16\\)",
|
|
"gt_answers": "3 4 9 4 - 1 2 \\times 1 0 = 2 2 9 . 4 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3242.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\ny = 2x^2 + 3x - 4\n\nThe formula is written in LaTeX format using the `=` sign to indicate the start of the expression, the `y` variable, and the `=` sign to indicate the equality sign. The `2` and `3` are written as `2x^2` and `3x`, respectively, using the `^` operator to indicate exponentiation. The `-4` is written as `-4x` using the `x` operator to indicate multiplication.",
|
|
"gt_answers": "y ^ { 2 } - 6 y + ( 1 + 4 k ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3244.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "- \\frac { b } { a } = - \\frac { 5 } { a } = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3246.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"245 = 225 + 20.\"",
|
|
"gt_answers": "2 3 \\div 2 5 = \\frac { 2 3 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3247.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Na2SO4 + H2O = NaOH + H2SO4.\"",
|
|
"gt_answers": "S O _ { 2 } + 2 N a O H = N a _ { 2 } S O _ { 3 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_3248.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"arc(cos(x))^2 + sin(x)^2 = 1.\"",
|
|
"gt_answers": "\\arccos x ( - 1 0 , \\pi )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3249.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a few numbers and symbols, which can be represented in LaTeX using the appropriate symbols and formatting.",
|
|
"gt_answers": "x = \\frac { 5 } { 3 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3251.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 20x + 30y = 100.",
|
|
"gt_answers": "2 0 \\times \\frac { 7 x } { 2 0 } = 2 0 x ( \\frac { x } { 5 } + 3 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3252.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
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"gt_answers": "\\frac { 1 } { 2 0 0 1 } ( y - 1 ) + \\frac { 1 } { 2 0 0 2 } ( y - 1 ) + \\cdots + \\frac { 1 } { 2 0 1 0 } ( y - 1 ) = 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3253.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Euler's formula for the circle.\"",
|
|
"gt_answers": "\\angle E K G = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3254.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "\\frac { x ^ { 2 } } { 3 } + \\frac { y ^ { 2 } } { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3256.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4.555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555",
|
|
"gt_answers": "4 . 5 5 > 4 . 5 1 > 4 . 5 > 4 . 1 5 > 4 . 0 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3257.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "E a _ { 2 } t x ^ { 2 } = \\frac { 1 } { 2 } \\times 2 \\times 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3258.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3556644.",
|
|
"gt_answers": "3 + 5 + 6 = 1 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3259.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4FEC = 3 \\times 65\\)",
|
|
"gt_answers": "\\angle F E C = ( \\frac { 1 3 0 } { 2 } ) ^ { \\circ } = 6 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3260.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "B E = \\frac { 1 } { 2 } A B = \\frac { 1 } { 2 } \\times 2 a = a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3261.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(k = \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{",
|
|
"gt_answers": "x = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3262.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4} \\).",
|
|
"gt_answers": "x > \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3263.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{4x^2 + 4x + 1}{x^2 + 2x + 1} = \\frac{4x^2 + 4x + 1}{x^2 + 2x + 1}\n\\end{equation}\n\nThis is a simple algebraic expression that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "x + \\frac { 1 } { 4 } = \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3264.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\nB = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\",
|
|
"gt_answers": "\\frac { B E } { B F } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3265.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LB0A0G-220\u00b0.\"",
|
|
"gt_answers": "\\angle B O A + \\angle A O C = 2 4 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3266.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nx = 20 - 13/20\n\nThe formula uses the mathematical operations of subtraction and division to calculate the value of x.",
|
|
"gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3267.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 5/25 = 2/5.",
|
|
"gt_answers": "\\frac { 5 } { 8 } = \\frac { 2 5 } { 4 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3268.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 8 = 2(3 + 1).",
|
|
"gt_answers": "8 \\div 5 = \\frac { 8 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3270.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "\\frac { 5 } { 4 } > \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3271.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "y _ { 2 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3272.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"40mm/2mm = 20mm/1mm\".",
|
|
"gt_answers": "4 0 m m \\div 2 m m = \\frac { 4 0 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3273.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nP(C) = (B + C) * (B - C) / 4",
|
|
"gt_answers": "P ^ { \\prime } C = B C - B P ^ { \\prime } = 1 6 - 4 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3274.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 600x3 = 400x6.",
|
|
"gt_answers": "6 0 0 \\times \\frac { 2 } { 3 } = 4 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3275.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\frac { 1 } { a } < \\frac { 1 } { b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3277.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4} \\left( 1 + 1 \\right) = \\frac{1}{4} \\cdot 2 = \\frac{1}{2} \\cdot 2 = \\frac{1}{4} \\cdot 4 = \\frac{1}{8} \\cdot 2 = \\frac{1}{8} \\cdot 4 = \\frac{1}{16} \\cdot 2 = \\frac{1}{16} \\cdot 4 = \\frac{1}{32} \\cdot 2 = \\frac{1}{32} \\cdot 4 = \\frac{1}{64} \\cdot 2 = \\frac{1}{64} \\cdot 4 = \\frac{1}{128} \\cdot 2 = \\frac{1}{128} \\cdot 4 = \\frac{1}{256} \\cdot 2 = \\frac{1}{256} \\cdot 4 = \\frac{1}{512} \\cdot 2 = \\frac{1}{512} \\cdot 4 = \\frac{1}{1024} \\cdot 2 = \\frac{1}{1024} \\cdot 4 = \\frac{1}{2048} \\cdot 2 = \\frac{1}{2048} \\cdot 4 = \\frac{1}{4096} \\cdot 2 = \\frac{1}{4096} \\cdot 4 = \\frac{1}{8192} \\cdot 2 = \\frac{1}{8192} \\cdot 4 = \\frac{1}{16384} \\cdot 2 = \\frac{1}{16384} \\cdot 4 = \\frac{1}{32768} \\cdot 2 = \\frac{1}{32768} \\cdot 4 = \\frac{1}{65536} \\cdot 2 = \\frac{1}{65536} \\cdot 4 = \\frac{1}{131",
|
|
"gt_answers": "\\angle 1 + \\angle 3 = \\frac { 1 } { 2 } ( \\angle A B E + \\angle C D E )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3278.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(A = \\frac{F}{m} \\cdot \\sin \\theta\\)\n\nwhere:\n\n* A is the area of the triangle\n* F is the force acting on the triangle\n* m is the mass of the triangle\n* \u03b8 is the angle between the force and the base of the triangle.",
|
|
"gt_answers": "A F = \\frac { 2 0 } { \\sin 3 0 ^ { \\circ } } = \\frac { 2 0 } { \\frac { 1 } { 2 } } = 4 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_3279.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\ny = 3x + 2\n\nThis formula represents a linear equation in two variables, where y is the dependent variable and x is the independent variable. The constant 3 is the slope of the line, and 2 is the y-intercept.",
|
|
"gt_answers": "y = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3280.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 12 + 13 - 4 = 16.",
|
|
"gt_answers": "\\frac { 1 2 } { 1 6 } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3281.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-2000 = 5000-2000 = 3000-2000 = 1000-20",
|
|
"gt_answers": "( 1 0 0 0 - 2 5 0 ) \\div 2 5 = 3 0 m / m\n",
|
|
"image_path": "./data/HME100K/test_images/test_3282.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x _ { 2 } = \\frac { 1 + \\sqrt { 1 0 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3283.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3.155442 = 3.155442.",
|
|
"gt_answers": "3 : 1 . 5 = 4 : 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3285.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "2 ^ { - 1 } \\times 4 \\times 3 + ( 3 + 4 + 5 ) \\times 1 + \\pi = \\pi + 1 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3287.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"X = 12 + 7.\"",
|
|
"gt_answers": "x = - \\frac { 1 2 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3288.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(300 \\times (0.6 \\times 0.4) = 180\\)",
|
|
"gt_answers": "( 6 0 - 2 0 ) \\div \\frac { 4 } { 3 } = 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3289.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(y = 2x + 4\\)\n\nThis formula represents a linear equation in two variables, where y is the dependent variable and x is the independent variable. The constant 2 represents the slope of the line, and 4 represents the y-intercept.",
|
|
"gt_answers": "x ^ { 2 } + y ^ { 2 } \\geq \\frac { 4 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3290.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 . 2 5 = 1 0 0 = \\textcircled { 2 5 } = 0 . 0 0 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3291.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(BM = \\frac{AM}{Me} = \\frac{1}{1} = 1\\)\n\nThe formula is a simple equation that states that the ratio of the area of the blue and the red circles is equal to the ratio of the area of the blue circle to the area of the red circle.",
|
|
"gt_answers": "\\frac { B M } { M N } = \\frac { A M } { M E } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3292.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1/2(1+3) = 1/2(4).",
|
|
"gt_answers": "\\frac { 1 } { 2 } m + 3 = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3293.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 2.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3294.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the Greek alphabet, which is not a standard format for mathematical expressions. However, I can provide a similar expression in LaTeX format:\n\n\\(I_{r,s} = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2",
|
|
"gt_answers": "I _ { R } = I - I _ { L } = 0 . 6 A - 0 . 5 A = 0 . 1 A\n",
|
|
"image_path": "./data/HME100K/test_images/test_3295.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 3 = 0.\"",
|
|
"gt_answers": "x _ { 2 } = - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3296.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `3x + 2 = 10`.",
|
|
"gt_answers": "t _ { 1 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3298.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"B2Ld = 90.\"",
|
|
"gt_answers": "\\angle B = \\angle D = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3299.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 5\\)",
|
|
"gt_answers": "y _ { 1 } = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3300.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"va = matb + matb\".",
|
|
"gt_answers": "V A = \\frac { f t _ { 1 } } { m A + m B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3301.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = \\frac{1800 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times 10^3 \\times",
|
|
"gt_answers": "\\rho = \\frac { m } { V } = \\frac { 0 . 5 6 k g } { 2 \\times 1 0 ^ { - 4 } m ^ { 3 } } = 2 . 8 \\times 1 0 ^ { 3 } k g / m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3302.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x + 2y = 12\\)\n\nThis formula represents the relationship between the variables x and y, where 3x + 2y = 12.",
|
|
"gt_answers": "\\frac { 1 2 } { ( x + 3 ) ( x - 1 ) } + \\frac { 3 } { x + 3 } = - \\frac { 2 } { x - 1 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3303.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: Na+ + Ba2+ + 2H2O = NaOH + Ba(OH)2.",
|
|
"gt_answers": "N a _ { 2 } C O _ { 3 } + B a ( O H ) _ { 2 } = 2 N a O H + B a C O _ { 3 } \\downarrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_3304.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "( 1 - \\frac { 5 } { 9 } ) x = \\frac { 8 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3305.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\left( \\frac{1}{n} \\cdot \\",
|
|
"gt_answers": "y = \\frac { 1 } { 2 } M N \\cdot R N = \\frac { 1 } { 2 } \\times 6 x = 3 x .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3307.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "( x - t _ { 1 } 1 ^ { 2 } = \\frac { 5 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3308.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "R = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3309.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(f(x) = 4x^2 + 8x + 5\\)",
|
|
"gt_answers": "\\rho = - \\frac { 4 } { 3 } x - \\frac { 8 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3311.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "7 0 + 0 = 7 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3312.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A = \\frac{1}{2} \\left( \\sqrt{B^2 + C^2} + \\sqrt{D^2 + E^2} \\right)\\)",
|
|
"gt_answers": "\\angle A B C = \\angle A C B = \\angle A = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3313.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"HF = 3/2 * 2 * 2 = 12.\"",
|
|
"gt_answers": "H F = \\frac { \\sqrt { 3 } } { 3 } \\cdot 2 0 0 \\sqrt { 3 } \\cos ^ { 3 } \\theta\n",
|
|
"image_path": "./data/HME100K/test_images/test_3314.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"10x + 5 = 4x + 10.\"",
|
|
"gt_answers": "\\tan A = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3315.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 2 = 0\\)",
|
|
"gt_answers": "\\frac { 2 } { 3 } [ x - ( - 3 ) ] = \\frac { 2 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3316.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CDDE = 10x59-299.\"",
|
|
"gt_answers": "\\angle D O E = \\frac { 1 } { 2 } \\times 5 8 ^ { \\circ } = 2 9 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3317.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a(b-c)^2 + b(c-d)^2 + c(d-a)^2 + d(a-b)^2 = 0\\)",
|
|
"gt_answers": "1 0 ) - a + c - 2 b\n",
|
|
"image_path": "./data/HME100K/test_images/test_3318.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(W = W_0 + \\int_0^t \\left( \\frac{dW}{dt} \\right) dt\\)\n\nThis formula represents the work done by a force acting on an object over a period of time. The initial value of the work, W0, is the work done at time t = 0, and the integral represents the accumulated work done over the entire time period. The force acting on the object is denoted by F, and the derivative of the work with respect to time is given by the symbol dW/dt.",
|
|
"gt_answers": "W _ { a } : W _ { b } : W _ { c } = 1 : 2 : 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3319.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(5x + 7y = 80\\)\n\nThis formula represents the relationship between the variables x and y, where x is the first term and y is the second term. The result of the equation is 80, which is the sum of the two terms.",
|
|
"gt_answers": "x = - \\frac { 5 5 } { 1 6 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3320.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": ": 6 . 4 x + 3 . 2 \\times 4 . 3 . 2 x = 2 5 . 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3321.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"5x4 = 20.\"",
|
|
"gt_answers": "\\frac { 5 } { 8 } \\times 4 = \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3322.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 22x100 - 44000cm.",
|
|
"gt_answers": "2 2 2 \\times 2 0 0 = 4 4 4 0 0 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3323.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 1/7 + 1/10 = 1/10 + 1/7.",
|
|
"gt_answers": "\\vert - \\frac { 7 } { 1 0 } \\vert = \\frac { 7 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3324.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3(3+1) - 2(3+1) = 3(4) - 2(4) = 12 - 8 = 4.",
|
|
"gt_answers": "\\frac { 7 } { 3 } - \\frac { 1 } { 3 } = \\frac { 6 } { 3 } = \\frac { 7 } { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3325.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) + \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) - \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac",
|
|
"gt_answers": "8 x ^ { 2 } - x ^ { 3 } - 8 x + x ^ { 2 } = 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3326.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "a ^ { 2 } + 2 a - 3 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3327.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "( 0 = ) - \\frac { a } { 3 } < x\n",
|
|
"image_path": "./data/HME100K/test_images/test_3328.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(n^3 + 3n^2 + 3n + 1 = 10\\)\n\nThe formula is written using the LaTeX equation editor, which allows for easy formatting and readability.",
|
|
"gt_answers": "\\cdot x _ { 1 } = \\frac { \\sqrt { 3 a + 3 } } { a + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3329.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 19.5^2\\)",
|
|
"gt_answers": "5 ^ { 2 } \\times 3 . 1 4 = 7 8 . 5 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3330.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Boost + ClosB 2aCosA\".",
|
|
"gt_answers": "b \\cos C + c \\cos B = 2 a \\cos A\n",
|
|
"image_path": "./data/HME100K/test_images/test_3331.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "b _ { n + 1 } = \\frac { 6 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3333.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4\\times 10^{14} \\times 10^{14} = 4 \\times 10^{28}\\)",
|
|
"gt_answers": "( 4 n + 4 ) ^ { 2 } - 1 6 n ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3336.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "1 3 + x = \\frac { 4 7 } { 2 } + \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_3339.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 12.\"",
|
|
"gt_answers": "4 f + g + 5 g - 4 f = 1 2 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3340.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "D M = A M\n",
|
|
"image_path": "./data/HME100K/test_images/test_3341.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x = - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3342.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"400cm^2 = 400cm x 10cm = 4000cm^2.\"",
|
|
"gt_answers": "S = 4 0 0 c m ^ { 2 } = 4 \\times 1 0 ^ { - 2 } m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3343.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"wringsing-2 = wringsing-1 + wringsing-0\".",
|
|
"gt_answers": "\\arcsin \\frac { \\sqrt { 5 } } { 5 } = \\beta\n",
|
|
"image_path": "./data/HME100K/test_images/test_3344.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "f = \\frac { 5 } { 3 } n _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3345.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 5\\)",
|
|
"gt_answers": "y _ { 2 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3347.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 10x + 5 = 0\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = 1 0 - 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3348.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(x+3) - 3(x+4) + 4(x+5) - 5(x+6) + 6(x+7) - 7(x+8) + 8(x+9) - 9(x+10) + 10(x+11) - 11(x+12) + 12(x+13) - 13(x+14) + 14(x+15) - 15(x+16) + 16(x+17) - 17(x+18) + 18(x+19) - 19(x+20) + 20(x+21) - 21(x+22) + 22(x+23) - 23(x+24) + 24(x+25) - 25(x+26) + 26(x+27) - 27(x+28) + 28(x+29) - 29(x+30) + 30(x+31) - 31(x+32) + 32(x+33) - 33(x+34) + 34(x+35) - 35(x+36) + 36(x+37) - 37(x+38) + 38(x+39) - 39(x+40) + 40(x+41) - 41(x+42) + 42(x+43) - 43(x+44) + 44(x+45) - 45(x+46) + 46(x+47) - 47(x+48) + 48(x+49) - 49(x+50) + 50(x+51) - 51(x+52) + 52(x+53) - 53(x+5",
|
|
"gt_answers": "( 9 2 0 + 4 3 8 \\div 7 3 ) \\times 3 4 = 3 1 4 8 . 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3350.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"W = 10 red/loud.\"",
|
|
"gt_answers": "\\omega = 1 0 r a d \\cdot l s .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3351.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = a + bx + cx^2 + dx^3 + ex^4 + fx^5 + gx^6 + hx^7 + ix^8 + jx^9 + kx^{10} + lx^{11} + mx^{12} + nx^{13} + ox^{14} + px^{15} + qx^{16} + rx^{17} + sx^{18} + tx^{19} + ux^{20} + vx^{21} + wx^{22} + wy^{23} + x^{24} + y^{25} + z^{26} + x^{27} + y^{28} + z^{29} + x^{30} + y^{31} + z^{32} + x^{33} + y^{34} + z^{35} + x^{36} + y^{37} + z^{38} + x^{39} + y^{40} + z^{41} + x^{42} + y^{43} + z^{44} + x^{45} + y^{46} + z^{47} + x^{48} + y^{49} + z^{50} + x^{51} + y^{52} + z^{53} + x^{54} + y^{55} + z^{56} + x^{57} + y^{58} + z^{59} + x^{60} + y^{61} + z^{62} + x^{63} + y^{64} + z^{65} + x^{66} + y^{67} + z^{68} + x^{69} + y^{70} + z^{71} + x^{72} + y^{73} + z^{74} + x^{75} + y^{76} + z^{77} + x^{78} + y^{79} + z^{80} + x^{81} + y^{82",
|
|
"gt_answers": "\\frac { 1 } { x - y } = a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3353.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "m ( x + y - 3 ) + n ( 2 x - y ) + 3 x - 3 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3354.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula language. The formula is:\n\n\\(y = 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle B D E = \\angle B E D = \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } - 3 0 ^ { \\circ } ) = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3355.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)",
|
|
"gt_answers": "x - y = \\frac { 1 } { 2 } \\sqrt { 7 } + \\frac { 1 } { 2 } \\sqrt { 5 } - \\frac { 1 } { 2 } \\sqrt { 7 } + \\frac { 1 } { 2 } \\sqrt { 5 } . = \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3357.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 15x8 = 200.",
|
|
"gt_answers": "2 5 \\times 8 = 2 0 0 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3358.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x(3-1) + 1x(4-1) = 12.",
|
|
"gt_answers": "3 - \\frac { 2 x - 1 } { 5 } = \\frac { x + 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3359.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + y^2 = 4x^2 + 4y^2`.",
|
|
"gt_answers": "x ^ { 2 } - y ^ { 2 } - 4 x + 4 y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3360.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"X^2 + Y^2 = 3^2.\"",
|
|
"gt_answers": "\\times 8 \\times \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3361.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/2 + 1/3 = 1/6 + 1/9 = 1/12 + 1/15 = 1/18 + 1/21 = 1/24 + 1/27 = 1/30 + 1/33 = 1/36 + 1/39 = 1/42 + 1/45 = 1/48 + 1/51 = 1/54 + 1/57 = 1/60 + 1/63 = 1/66 + 1/69 = 1/72 + 1/75 = 1/78 + 1/81 = 1/84 + 1/87 = 1/90 + 1/93 = 1/96 + 1/99 = 1/102 + 1/105 = 1/108 + 1/111 = 1/114 + 1/117 = 1/120 + 1/123 = 1/126 + 1/129 = 1/132 + 1/135 = 1/138 + 1/141 = 1/144 + 1/147 = 1/150 + 1/153 = 1/156 + 1/159 = 1/162 + 1/165 = 1/168 + 1/171 = 1/174 + 1/177 = 1/180 + 1/183 = 1/186 + 1/189 = 1/192 + 1/195 = 1/198 + 1/201 = 1/204 + 1/207 = 1/210 + 1/213 = 1/216 + 1/219 = 1/222 + 1/225 = 1/228 + 1",
|
|
"gt_answers": "\\times \\frac { E C } { A B } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3363.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 . 3 3 m = 3 3 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_3364.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 4xy\\)",
|
|
"gt_answers": "\\frac { 2 } { a x } = \\frac { 2 - 3 x } { a x - 3 x } = \\frac { 6 x } { 3 a x ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3365.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "3 x - 2 = 1 2 x - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3367.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "F G = M h\n",
|
|
"image_path": "./data/HME100K/test_images/test_3368.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 2x - 3.",
|
|
"gt_answers": "y = \\frac { 2 x - 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3369.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x5 = 30 cm.",
|
|
"gt_answers": "3 6 \\times 5 = 1 8 0 c m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3370.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"HtRos(B) = Im(B) / (1 + Im(B) / Vt(B))\", where HtRos(B) represents the Hall resistance of the B-type semiconductor, Im(B) is the imaginary part of the B-type semiconductor, Vt(B) is the voltage across the B-type semiconductor, and the symbol \"/\" represents division.",
|
|
"gt_answers": "m g ( H + R \\cos \\theta + R ) = \\frac { 1 } { 2 } m V B ^ { 2 } - \\frac { 1 } { 2 } m V _ { 0 } ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3372.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(k_{t}b_{t-1}b_{t-2}b_{t-3}...b_{t-n}b_{t-n-1}b_{t-n-2}...b_{t-1}b_{t}=k_{t}b_{t-1}b_{t-2}b_{t-3}...b_{t-n}b_{t-n-1}b_{t-n-2}...b_{t-1}b_{t}b_{t-n-1}b_{t-n-2}...b_{t-n-3}b_{t-n-4}b_{t-n-5}b_{t-n-6}b_{t-n-7}b_{t-n-8}b_{t-n-9}b_{t-n-10}b_{t-n-11}b_{t-n-12}b_{t-n-13}b_{t-n-14}b_{t-n-15}b_{t-n-16}b_{t-n-17}b_{t-n-18}b_{t-n-19}b_{t-n-20}b_{t-n-21}b_{t-n-22}b_{t-n-23}b_{t-n-24}b_{t-n-25}b_{t-n-26}b_{t-n-27}b_{t-n-28}b_{t-n-29}b_{t-n-30}b_{t-n-31}b_{t-n-32}b_{t-n-33}b_{t-n-34}b_{t-n-35}b_{t-n-36}b_{t-n-37}b_{t-n-38}b_{t-n-39}b_{t-n-40}b_{t-n-41}b_{t-n-42}b_{t-n-43}b_{t",
|
|
"gt_answers": "k = 5 , b = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3373.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(5x + 4 = 10\\)",
|
|
"gt_answers": "\\frac { 5 } { 3 } x - 1 + \\frac { x } { 3 } = - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3376.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a number and a symbol, which could be a mathematical operator or a variable.",
|
|
"gt_answers": "\\frac { 2 } { 5 } x = \\frac { 3 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3377.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "9 0 + 9 0 x = 4 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3378.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1",
|
|
"gt_answers": "9 : 1 2 ) ( 1 2 \\times 9 ) : ( 1 4 \\times 1 ) : ( 1 5 \\times 1 ) = 1 0 8 : 1 4 : 1 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3379.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{3}x^3 + \\frac{1}{4}x^4 + \\frac{1}{5}x^5 + \\frac{1}{6}x^6 + \\frac{1}{7}x^7 + \\frac{1}{8}x^8 + \\frac{1}{9}x^9 + \\frac{1}{10}x^{10} + \\frac{1}{11}x^{11} + \\frac{1}{12}x^{12} + \\frac{1}{13}x^{13} + \\frac{1}{14}x^{14} + \\frac{1}{15}x^{15} + \\frac{1}{16}x^{16} + \\frac{1}{17}x^{17} + \\frac{1}{18}x^{18} + \\frac{1}{19}x^{19} + \\frac{1}{20}x^{20} + \\frac{1}{21}x^{21} + \\frac{1}{22}x^{22} + \\frac{1}{23}x^{23} + \\frac{1}{24}x^{24} + \\frac{1}{25}x^{25} + \\frac{1}{26}x^{26} + \\frac{1}{27}x^{27} + \\frac{1}{28}x^{28} + \\frac{1}{29}x^{29} + \\frac{1}{30}x^{30} + \\frac{1}{31}x^{31} + \\frac{1}{32}x^{32} + \\frac{1}{33}x^{33} + \\frac{1}{34}x^{34} + \\frac{1}{35}x^{35} + \\frac{1}{36}x^{36} + \\frac{1}{37}x^{37} + \\frac{1}{38}x",
|
|
"gt_answers": "\\frac { 1 } { 2 a } = ( \\frac { 1 } { 2 } ) ^ { 2 } + \\frac { 1 } { 2 ^ { 2 } } + \\frac { 1 } { 2 ^ { 4 } } + \\cdots + \\frac { 1 } { 2 ^ { 1 0 0 } } + \\frac { 1 } { 2 ^ { 1 0 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3380.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 4k-4p+1.",
|
|
"gt_answers": "= \\frac { 4 x - 4 k - 4 } { k + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3381.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "b ^ { 2 } + c ^ { 2 } \\geq 2 b c\n",
|
|
"image_path": "./data/HME100K/test_images/test_3382.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x \\in [ \\frac { \\pi } { 2 } , \\pi ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_3383.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 12 - 10 = 2.",
|
|
"gt_answers": "\\frac { 1 0 } { 1 2 } > \\frac { 9 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3386.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "x + 7 0 - ( \\frac { 3 } { 2 } x - 7 0 ) = \\frac { 3 } { 2 } x \\cdot \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3387.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\nL = 99 - 50 = 49\n\\end{equation}",
|
|
"gt_answers": "\\angle A B C = 9 0 ^ { \\circ } ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_3388.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LDA(X, Y) = 100 * (X' * Y' - X * Y)/(||X||^2 * ||Y||^2).\"",
|
|
"gt_answers": "\\angle D B A + \\angle B A D = \\angle B A D + \\angle A E = 1 8 0 ^ { \\circ } - a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3389.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 0 0 b - ( 1 6 0 0 - 1 4 5 0 ) = 3 0 0 a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3391.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mathematical formula using the LaTeX language. The formula is written in a black box, with the letters \"E\" and \"I\" written in white. The formula is surrounded by a black border, and the text is written in a bold font.",
|
|
"gt_answers": "\\vert x _ { 2 } = \\frac { 3 } { 2 } \\vert x _ { 3 } = - \\frac { 1 } { 3 } \\vert x _ { 4 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3392.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written as follows:\n\n\\(y = 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle A O D = 9 0 ^ { \\circ } - a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3393.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written in the form of a mathematical equation, with the letters \"B\" and \"E\" representing the variables and the \"+\" sign representing the addition operation. The formula is written in a black box, which is a common way to display mathematical equations in LaTeX.",
|
|
"gt_answers": "\\therefore \\Delta B D E \\sim \\Delta E D O\n",
|
|
"image_path": "./data/HME100K/test_images/test_3394.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 12\\)",
|
|
"gt_answers": "S = \\frac { ( 1 + 2 ) \\times 1 } { 2 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3395.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2} + 3x + 5\\)",
|
|
"gt_answers": "x _ { 2 } = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_3396.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 43 + 44 = 4x4 + 4x3 + 4x2 + 4x1 + 4x0.",
|
|
"gt_answers": "4 ^ { 3 } = 6 4 4 \\times 3 = 1 2 4 + 4 + 4 = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3397.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 20x + 5y^2 + 25y = 100\\)",
|
|
"gt_answers": "1 0 \\times \\frac { 1 } { 5 } x - 2 0 = \\frac { 8 } { 5 } x \\times 2 5 + \\frac { 3 } { 2 5 } \\times 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3398.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 20 = 4 + 4.",
|
|
"gt_answers": "2 y = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3399.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3400.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"y = 3x + 4.\"",
|
|
"gt_answers": "y = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3401.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 5x5 + 25x2 - 10x10.",
|
|
"gt_answers": "2 5 \\div 5 - 5 \\textcircled { < } 5 \\times 5 \\div 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3402.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x2 + 37.89375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.1415926535897932375x3.14",
|
|
"gt_answers": "3 . 1 4 \\times 2 ^ { 2 } \\times 3 = 3 7 . 6 8 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3403.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 2x + 3}{x^2 + 4x + 5}\n\\end{equation}\n\nThis formula can be simplified by factoring out the common factor of (x^2 + 4x + 5) from both the numerator and denominator. The simplified expression is:\n\n\\begin{equation}\n\\frac{x^2 + 2x + 3}{x^2 + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5 - (x^2 + 4x + 5)} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5 - (x^2 + 4x + 5 - x^2 - 4x - 5)} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5 - (x^2 + 4x + 5 - 2x - 4x - 5)} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5 - (x^2 + 4x + 5 - 2x - 4x - 5) - 2x - 4x - 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5 - (x^2 + 4x + 5 - 2x - 4x - 5) - 2x - 4x - 5 + 2x + 4x + 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5 - (x^2 + 4x + 5 - 2x - 4x - 5) - 2x - 4x - 5 + 2x + 4x + 5 - 2x - 4x - 5} = \\frac{x^2 + 2x + 3}{x^2 + 4x + 5 - (x^2 + 4",
|
|
"gt_answers": "2 x ^ { 2 } + x = 2 x ^ { 2 } + 4 x + 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3404.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"L4CAMO 906.\"",
|
|
"gt_answers": "\\angle A H B = \\angle G M O = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3405.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, which can be represented in LaTeX using the `siunitx` package. Here is the LaTeX code for the expression:\n```\n\\documentclass{article}\n\\usepackage{siunitx}\n\n\\begin{document}\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\",
|
|
"gt_answers": "x < \\frac { 1 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3406.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 - 3x + 1 = 0.",
|
|
"gt_answers": "\\frac { 3 } { x } = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3407.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x _ { 1 } = - \\frac { 1 } { 3 } x _ { 2 } =\n",
|
|
"image_path": "./data/HME100K/test_images/test_3408.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6b+2z = 0\" using LaTeX format.",
|
|
"gt_answers": "\\cos B = \\frac { a ^ { 2 } + c ^ { 2 } - } { 2 a c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3409.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mathematical formula using the Hebrew alphabet. The formula is written in a black font on a white background, and it is surrounded by a black border.",
|
|
"gt_answers": ": \\overline { x _ { 3 } } > \\overline { x _ { 2 } } > \\overline { x _ { 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3410.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 + h^2 + i^2 + j^2 + k^2 + l^2 + m^2 + n^2 + o^2 + p^2 + q^2 + r^2 + s^2 + t^2 + u^2 + v^2 + w^2 + x^2 + y^2 + z^2 = 100\\)",
|
|
"gt_answers": "( a + 2 ) ^ { 2 } + ( 1 - a ) ( 1 + a )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3411.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: (2(n+1) + 3n) - 14.",
|
|
"gt_answers": "2 ( 2 + n ) + 3 n = 1 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3412.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 13\\)\n\nThis is a quadratic equation in the variable x, with the coefficients 2, 3, and 4. The solution to this equation is x = 5.",
|
|
"gt_answers": "O B = \\sqrt { A B ^ { 2 } - A D ^ { 2 } } = \\sqrt { 1 3 ^ { 2 } - 1 2 ^ { 2 } } = 5 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3413.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "D O = \\frac { 1 } { 2 } B D\n",
|
|
"image_path": "./data/HME100K/test_images/test_3415.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888",
|
|
"gt_answers": "8 0 0 + 8 0 + 8 = 8 8 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3416.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 49\\)",
|
|
"gt_answers": "w = - x ^ { 2 } + 7 x + 4 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3417.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "\\Rightarrow y _ { 1 } ^ { 2 } = 3 x _ { 1 } ^ { 2 } - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3418.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\cos(90^\\circ - \\theta) = \\cos\\theta\n\\end{equation}\n\nThis formula states that the cosine of an angle of 90 degrees minus the angle \u03b8 is equal to the cosine of the angle \u03b8.",
|
|
"gt_answers": ", \\angle C = \\angle B A D = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3419.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: \"y = 2x + 3.\"",
|
|
"gt_answers": "y _ { 2 } = - \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3420.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"24/12 = 2\".",
|
|
"gt_answers": "\\frac { 2 4 } { 2 } = 1 2 1 2 = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3421.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "P B = \\frac { F } { S } = \\frac { G } { s } = \\frac { 2 5 0 N } { 5 \\times 1 0 ^ { - 2 } m ^ { 2 } } = 5 \\times 1 0 ^ { 3 } P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3422.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 1.79 x 10^(-0.88) = 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "H _ { 2 } O _ { 2 } \\% = \\frac { 1 . 7 g } { 2 0 g } \\times 1 0 0 \\% = 8 . 5 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_3423.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nCH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH3CH2OH + OH - CH",
|
|
"gt_answers": "( C H _ { 3 } ) _ { 2 } N C H + O H \\ast 2 H \\ast\n",
|
|
"image_path": "./data/HME100K/test_images/test_3424.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 . 5 < 0 . 5 0 1 < 0 . 5 1 < 0 . 5 1 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3425.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x - 14 = 0.",
|
|
"gt_answers": "2 \\times 7 = 1 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3426.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 2y^2 - 2xy = 2(2x^2 + y^2) - 2xy\\)\n\nThis formula can be rearranged to solve for x and y:\n\n\\(x^2 + y^2 = 2(x^2 + y^2) - 2xy\\)\n\nSolving for x:\n\n\\(x^2 + y^2 - 2xy = 0\\)\n\nSolving for y:\n\n\\(x^2 + y^2 = 2xy\\)\n\nThus, the formula can be written as:\n\n\\(x^2 + y^2 = 2xy\\)\n\nThis formula can be used to find the area of a square with side lengths x and y.",
|
|
"gt_answers": "b \\overrightarrow { a } ^ { 2 } - 2 \\vert \\overrightarrow { a } \\vert - 2 4 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3429.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"6 + 3 = 9.\"",
|
|
"gt_answers": "y \\frac { 1 } { 3 } \\div \\frac { 1 } { 3 } = 6 \\div \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3430.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "3 0 2 \\div 6 = 5 0 \\cdots 2 6 1 7 \\div 5 = 1 2 3 \\cdots\n",
|
|
"image_path": "./data/HME100K/test_images/test_3431.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\nP = 2.01 x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-10) x 10^(-",
|
|
"gt_answers": "P = \\frac { F } { S } = \\frac { 2 0 N } { 2 \\times 1 0 ^ { - 2 } m ^ { 2 } } = 1 \\times 1 0 ^ { 3 } P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3432.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LGOF(180, 180) = 2LGOF(90, 90) + LGOF(180, 90) + LGOF(90, 180)\".",
|
|
"gt_answers": "\\angle Q G F + \\angle Q F G + \\angle G Q F = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3433.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x _ { 2 } = \\frac { 7 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3434.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\",
|
|
"gt_answers": "\\frac { x ^ { 2 } } { \\frac { 1 } { 2 } } - \\frac { y ^ { 2 } } { 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3435.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x - 2 = 5\\)",
|
|
"gt_answers": "y _ { 3 } = - \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3437.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 4x + 5 = 0\\)\n\nThis formula represents a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 1 } { 4 } - 6 x + 2 = x - 2 x + \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3438.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 10x - 10 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 1 0 } = \\frac { 1 5 } { 2 } : \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3439.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 11.",
|
|
"gt_answers": "x ^ { 2 } - x = 2 x + 4 + x ^ { 2 } + 2 x - x - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3440.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 14.",
|
|
"gt_answers": "3 . 1 4 \\times ( 4 \\div 2 ^ { 2 } ) ^ { 2 } x \\times \\frac { 1 } { 3 } = 3 . 1 4 \\times ( 3 \\div 2 ) ^ { 2 } \\times 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3441.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x^2 + 8x - 8d = 0\\)\n\nThis formula can be solved using the quadratic formula, which is:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\)\n\nSubstituting the values for a, b, and c from the given equation, we get:\n\n\\(x = \\frac{-8 \\pm \\sqrt{8^2 - 4(3)(8)}}{2(3)} = \\frac{-8 \\pm \\sqrt{64 - 120}}{2(3)} = \\frac{-8 \\pm 12}{2(3)} = \\frac{-8 \\pm 6}{2(3)} = \\frac{-8 \\pm 3}{2(3)} = \\frac{-8 \\pm 1}{2(3)} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-8 \\pm 1}{2} = \\frac{-",
|
|
"gt_answers": "- 3 x - 2 x = - 8 - a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3442.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( 2 \\times 1 0 ^ { 1 0 } ) \\div ( 8 \\times 1 0 ^ { 6 } ) = ( 2 \\div 8 ) \\times ( 1 0 ^ { 1 0 } \\div 1 0 ^ { 6 } ) = 0 . 2 5 \\times 1 0 ^ { 4 } = 2 . 5 \\times 1 0 ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3443.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "a ^ { 2 } + b ^ { 2 } = 2 \\geq 2 a b\n",
|
|
"image_path": "./data/HME100K/test_images/test_3444.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"31/12/2021 = 1/1/2022 + 1/2/2022 + 1/3/2022 + 1/4/2022 + 1/5/2022 + 1/6/2022 + 1/7/2022 + 1/8/2022 + 1/9/2022 + 1/10/2022 + 1/11/2022 + 1/12/2022 + 1/13/2022 + 1/14/2022 + 1/15/2022 + 1/16/2022 + 1/17/2022 + 1/18/2022 + 1/19/2022 + 1/20/2022 + 1/21/2022 + 1/22/2022 + 1/23/2022 + 1/24/2022 + 1/25/2022 + 1/26/2022 + 1/27/2022 + 1/28/2022 + 1/29/2022 + 1/30/2022 + 1/31/2022.\"",
|
|
"gt_answers": "F e _ { 2 } C _ { 3 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_3445.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{2x} + e^{3x} + e^{4x} + e^{5x} + e^{6x} + e^{7x} + e^{8x} + e^{9x} + e^{10x} + e^{11x} + e^{12x} + e^{13x} + e^{14x} + e^{15x} + e^{16x} + e^{17x} + e^{18x} + e^{19x} + e^{20x} + e^{21x} + e^{22x} + e^{23x} + e^{24x} + e^{25x} + e^{26x} + e^{27x} + e^{28x} + e^{29x} + e^{30x} + e^{31x} + e^{32x} + e^{33x} + e^{34x} + e^{35x} + e^{36x} + e^{37x} + e^{38x} + e^{39x} + e^{40x} + e^{41x} + e^{42x} + e^{43x} + e^{44x} + e^{45x} + e^{46x} + e^{47x} + e^{48x} + e^{49x} + e^{50x} + e^{51x} + e^{52x} + e^{53x} + e^{54x} + e^{55x} + e^{56x} + e^{57x} + e^{58x} + e^{59x} + e^{60x} + e^{61x} + e^{62x} + e^{63x} + e^{64x} + e^{65x} + e^{66x} + e^{67x} + e^{68x} + e^{69x} + e^{70x} + e^{71x} + e^{72x} + e^{73x",
|
|
"gt_answers": "\\frac { 1 } { 2 } [ \\frac { 2 } { 3 } x + \\frac { 2 } { 3 } ] = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3446.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2}{2} + \\frac{y^2}{2} = \\frac{1}{2} (x^2 + y^2)\n\\end{equation}\n\nThis formula states that the square of the distance between two points on a line is equal to the sum of the squares of the distances between the two points and the origin.",
|
|
"gt_answers": "\\frac { 5 } { x } = \\frac { 2 } { 5 } - \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3447.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 0.09 + 1 = 44.",
|
|
"gt_answers": "O P = \\sqrt { 4 + 1 } = \\sqrt { 5 } < 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3448.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `x^2 + 3x + 2 = 0`.",
|
|
"gt_answers": "x = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3449.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 25\\)",
|
|
"gt_answers": "f ^ { \\prime } _ { ( x ) } = e x - 2 x - a\n",
|
|
"image_path": "./data/HME100K/test_images/test_3450.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4x + 3y + 2z + 4x^2 + 3y^2 + 2z^2 + 4x^3 + 3y^3 + 2z^3 + 4x^4 + 3y^4 + 2z^4 + 4x^5 + 3y^5 + 2z^5 + 4x^6 + 3y^6 + 2z^6 + 4x^7 + 3y^7 + 2z^7 + 4x^8 + 3y^8 + 2z^8 + 4x^9 + 3y^9 + 2z^9 + 4x^{10} + 3y^{10} + 2z^{10} + 4x^{11} + 3y^{11} + 2z^{11} + 4x^{12} + 3y^{12} + 2z^{12} + 4x^{13} + 3y^{13} + 2z^{13} + 4x^{14} + 3y^{14} + 2z^{14} + 4x^{15} + 3y^{15} + 2z^{15} + 4x^{16} + 3y^{16} + 2z^{16} + 4x^{17} + 3y^{17} + 2z^{17} + 4x^{18} + 3y^{18} + 2z^{18} + 4x^{19} + 3y^{19} + 2z^{19} + 4x^{20} + 3y^{20} + 2z^{20} + 4x^{21} + 3y^{21} + 2z^{21} + 4x^{22} + 3y^{22} + 2z^{22} + 4x^{23} + 3y^{23} + 2z^{23} + 4x",
|
|
"gt_answers": "4 x ^ { 2 } + ( 4 b - 9 ) x + b ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3451.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 16x + 16 = 0\\)",
|
|
"gt_answers": "2 6 n ^ { 2 } - 3 2 n + 1 6 - 1 6 > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3452.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `x^2 + 2x - 3 = 0`.",
|
|
"gt_answers": "\\frac { - 1 + x } { 2 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3453.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000 \\times 1000",
|
|
"gt_answers": "S O _ { 2 } + I _ { 2 } + 2 H _ { 2 } O \\xlongequal { 1 0 0 \\sim 1 2 0 ^ { \\circ } C } 2 H I + H _ { 2 } S O _ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3454.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LAFC-90\" using the LaTeX formula notation.",
|
|
"gt_answers": "\\angle A F C = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3455.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2^3 + 2^2 + 2^1 + 2^0 = 16.\"",
|
|
"gt_answers": "6 < 1 7 < 2 3 < 2 5 < 5 4 < 5 7 < 1 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3456.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A(F-G) = A(F-G) + A(F-G)\".",
|
|
"gt_answers": "A E \\cdot A F = 4 8 - \\frac { 1 } { 2 } A E - A F\n",
|
|
"image_path": "./data/HME100K/test_images/test_3457.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 44563698 + 59638496 + 638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9638496384 + 9",
|
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"gt_answers": "4 2 \\textcircled { < } 5 0 5 9 \\textcircled { < } 6 3\n",
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"image_path": "./data/HME100K/test_images/test_3458.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"or 44-44+44=44\".",
|
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"gt_answers": "O _ { 2 } + 4 e ^ { - } + 4 H ^ { + } = 2 H _ { 2 } O\n",
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"image_path": "./data/HME100K/test_images/test_3459.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Labo = 30\u00b0.\"",
|
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"gt_answers": "\\angle A B O = 3 0 ^ { \\circ }\n",
|
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"image_path": "./data/HME100K/test_images/test_3461.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
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{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LCb = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\",
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"gt_answers": "\\angle C O B = 8 0 ^ { \\circ }\n",
|
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"image_path": "./data/HME100K/test_images/test_3462.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2n + 1 = 3.",
|
|
"gt_answers": "2 n + \\frac { 4 } { 3 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3463.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, which can be translated to \"7.25 x 10^10.\"",
|
|
"gt_answers": "7 x = 4 2 x = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3464.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ta = 2.5 + 0.5(Tb - Ta)\".",
|
|
"gt_answers": "T _ { A } : T _ { B } : T _ { c } = 3 : 4 : 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3465.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, but it can be represented in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{4}{x} + 4x = 16\n\\end{aligned}\n\\end{equation}\n\nThis is a simple algebraic equation that can be solved using the method of substitution.",
|
|
"gt_answers": "\\frac { 4 } { x } + \\frac { x + 2 } { y } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3466.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 4x - 28y^2 - 7y + 14 = 0\\)",
|
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"gt_answers": "9 0 \\div 3 . 1 4 \\approx 2 8 . 7 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3467.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 4x + 5 = 0.\"",
|
|
"gt_answers": "x = 5 \\div \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3468.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1",
|
|
"gt_answers": "2 a + 6 b - 2 c - 9 a + 6 b - 3 c = - 7 a + 1 2 b - 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3469.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX format as follows:\n\n\\(C_2H_5OH + 2NaOH \\rightarrow 2NaC_2H_5O + H_2O\\)",
|
|
"gt_answers": "m ( N a O H ) = 1 0 0 g \\times 5 \\% = 5 g\n",
|
|
"image_path": "./data/HME100K/test_images/test_3471.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, which are not supported by LaTeX. However, I can provide a rough translation of the expression using English characters:\n\n\"The sum of the squares of the first 100 natural numbers is equal to the sum of the squares of the first 100 even numbers.\"",
|
|
"gt_answers": "x = \\frac { 1 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3472.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "1 x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3473.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"5-2 = 3\".",
|
|
"gt_answers": "\\sqrt { 5 } - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3475.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "( 2 ) f _ { A } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3476.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x4 + 5x6 = 15x12.",
|
|
"gt_answers": "3 6 \\div 4 = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_3477.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x _ { 3 } = - 2 + 2 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3478.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 18x + 18 = 0\\)\n\nThis formula can be solved using the quadratic formula:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\)\n\nSubstituting the values for a, b, and c from the given equation:\n\n\\(x = \\frac{-18 \\pm \\sqrt{18^2 - 4(18)(18)}}{2(18)} = \\frac{-18 \\pm 18 \\sqrt{36}}{2(18)} = \\frac{-18 \\pm 18 \\sqrt{6}}{2(18)} = \\frac{-18 \\pm 9}{2(18)} = \\frac{-18 \\pm 4}{2(18)} = \\frac{-18 \\pm 2}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-18 \\pm 1}{2(18)} = \\frac{-1",
|
|
"gt_answers": "x _ { 1 } = \\frac { 1 8 } { 1 1 } \\vert x _ { 2 } = - \\frac { 1 8 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3479.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `Ga-374 (wt) = 7.114 x 10^10 (atm)`.",
|
|
"gt_answers": "( 2 a - 3 ) + ( a + 1 ) > 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_3480.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Love-Gae\" using the LaTeX formula notation.",
|
|
"gt_answers": ". \\angle O A E = \\angle G A E\n",
|
|
"image_path": "./data/HME100K/test_images/test_3481.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"A + B = C\" using LaTeX format.",
|
|
"gt_answers": "A M = \\sqrt { 5 ^ { 2 } - 3 ^ { 2 } } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3482.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(6 \\sqrt{2} - 6 \\sqrt{3} = 6 \\left( \\sqrt{2} - \\sqrt{3} \\right) = 6 \\left( \\frac{2}{\\sqrt{2}} - \\frac{3}{\\sqrt{3}} \\right) = 6 \\left( \\frac{1}{\\sqrt{2}} - \\frac{1}{\\sqrt{3}} \\right) = 6 \\left( \\frac{1}{2} - \\frac{1}{3} \\right) = 6 \\left( \\frac{1}{6} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9} \\right) = 6 \\left( \\frac{1}{3} - \\frac{1}{9",
|
|
"gt_answers": "\\sqrt [ 3 ] { 6 \\frac { 6 } { 2 1 5 } } = 6 \\sqrt [ 3 ] { \\frac { 6 } { 2 1 5 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3483.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "( 4 a ^ { 3 } b - 2 a ^ { 2 } + a ) \\div 2 a = 2 a ^ { 2 } b - a + \\frac { 1 } { 2 \u3002 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3484.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(K_f = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { x } { 6 0 } - \\frac { x } { 7 2 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3485.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\ny = 2x + 3\n\\end{equation}\n\nThis formula represents a linear equation, where y is the dependent variable and x is the independent variable. The equation states that y is equal to 2x + 3, where the constant 2 represents the slope of the line and the constant 3 represents the y-intercept.",
|
|
"gt_answers": "x - \\frac { y - 2 } { 2 } = 1 - \\frac { x - 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3487.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 2y^2 = 4xy\\)",
|
|
"gt_answers": "3 x ^ { 2 } + 2 x y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3488.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a + b = c\\)\n\nThis is a basic algebraic equation that represents the addition of two numbers, a and b, to equal a third number, c.",
|
|
"gt_answers": "b = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3489.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(k_{b}T = \\frac{RT}{V} \\tag{1}\\label{eq:1}`\n\nThis formula relates the Boltzmann constant, kb, to the temperature, T, and the volume, V, of a system. The Boltzmann constant is a constant that describes the relationship between the energy of a particle and its temperature. It is denoted by the letter k, and its value is approximately 1.3806485(15)\u00d710-23 J/K. The temperature, T, is a measure of the average kinetic energy of the particles in a system, and it is measured in Kelvin (K). The volume, V, is a measure of the amount of space occupied by the particles in the system, and it is measured in cubic meters (m\u00b3).\n\nThe equation in the image combines these three variables to calculate the Boltzmann constant, kb, in terms of the temperature, T, and the volume, V, of the system. The equation can be used to determine the temperature of a system based on its volume and the known value of the Boltzmann constant.",
|
|
"gt_answers": "y = k x + b ( k = l 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3490.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + y^2 = 1 + 10x + 10y`.",
|
|
"gt_answers": "x + 1 = 1 + x - 2 \\sqrt { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3491.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2^{20} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot 10^{10} \\cdot ",
|
|
"gt_answers": "7 0 0 c m = ( 7 0 ) d m = ( 7 ) m\n",
|
|
"image_path": "./data/HME100K/test_images/test_3492.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a=b+1.",
|
|
"gt_answers": "a = 1 b = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3493.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x = \\frac { - 1 + 1 . 4 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3495.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(Vo = \\frac{1}{2} \\cdot \\sqrt{m \\cdot g \\cdot h}\\)\n\nwhere Vo is the velocity, m is the mass, g is the gravitational constant, and h is the height.",
|
|
"gt_answers": "V _ { 0 } = \\frac { 2 } { 3 } L \\sqrt { \\frac { g } { 2 h _ { 3 } } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3496.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as F = 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "F = P S = 2 0 0 0 P a \\times 5 \\times 1 0 ^ { - 2 } m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3497.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 12-4k70.",
|
|
"gt_answers": "1 2 - 4 k > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3499.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\ny = 2x^2 + 7x - 8\n\\end{equation}",
|
|
"gt_answers": "\\frac { y ^ { 2 } } { 6 4 } + \\frac { x ^ { 2 } } { 4 8 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3503.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Eff-Sab = 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1",
|
|
"gt_answers": "E F = \\frac { 1 } { 2 } A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_3505.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x3 + 2x2 - 12x + 12 = 0.\"",
|
|
"gt_answers": "A E = \\frac { 1 2 } { 1 3 } \\times 1 3 = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3506.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "( x - \\frac { 1 } { x } ) ^ { 2 } + 2 ( x - \\frac { 1 } { x } ) + 2 = 0 ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_3510.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as BD = 1.",
|
|
"gt_answers": "B D = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3511.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"N-20\" using LaTeX format.",
|
|
"gt_answers": "x = \\frac { - b \\pm \\sqrt { 0 } } { 2 a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3512.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "A M ^ { 2 } + B N ^ { 2 } = M N ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3513.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CADC = 30\u00b0\".",
|
|
"gt_answers": "\\angle A D C = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3514.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"E013 = 1/4(E003 + E004).\"",
|
|
"gt_answers": "E ( 0 , \\frac { 4 } { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3515.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LB/OF + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE/LB + AE/LA + AE",
|
|
"gt_answers": "\\angle B D F = \\angle A D E = 1 8 0 ^ { \\circ } - \\angle A D F\n",
|
|
"image_path": "./data/HME100K/test_images/test_3516.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\nP = 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "P : \\frac { w } { t } = \\frac { 6 0 0 J } { 1 0 s } = 6 0 w .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3517.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: A + B - C = 0.",
|
|
"gt_answers": "\\frac { a } { \\frac { \\sqrt { 7 } } { 4 } } = \\frac { c } { \\frac { 3 \\sqrt { 7 } } { 8 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3518.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten style using the Greek alphabet. The formula is written in a black box, and the letters are written in a cursive style. The formula is likely a mathematical equation or a chemical formula.",
|
|
"gt_answers": "a ^ { 2 } + b ^ { 2 } - a b - 3 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3519.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3520.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(B_2 - C_2 = E_2\\)\n\nwhere B, C, and E are the values of the three sides of a triangle.",
|
|
"gt_answers": "\\therefore B D = C E\n",
|
|
"image_path": "./data/HME100K/test_images/test_3521.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nb = 10 - 3",
|
|
"gt_answers": "b = \\frac { 1 0 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3522.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 3x3 + 3x3 + 3x3 = 3x3x3 + 3x3x3 + 3x3x3.",
|
|
"gt_answers": "1 ^ { 2 } \\times 3 . 1 4 \\times 3 \\times \\frac { 1 } { 3 } = 3 . 1 4 ( d m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3523.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(F(x) = \\frac{10x^2 - 10x + 1}{x^2 + 1}\\)",
|
|
"gt_answers": "C a C O _ { 3 } = C a O + C O L\n",
|
|
"image_path": "./data/HME100K/test_images/test_3524.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Leo + Lodfot = Lodfot + Leo.\"",
|
|
"gt_answers": "\\angle E O F = \\angle D O F + \\angle D O E\n",
|
|
"image_path": "./data/HME100K/test_images/test_3525.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x + 3 = 12 + 3x.\"",
|
|
"gt_answers": "2 x + 1 = \\frac { 1 } { 2 } x + 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3526.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\ce{Ar3+ + H2O -> Ar(OH)3 + H3O+}\n\\end{equation}\n\nThis formula represents the reaction of arsenic trioxide (As2O3) with water (H2O) to produce arsenic trisulfide (As2S3) and hydrogen peroxide (H2O2).",
|
|
"gt_answers": "A a N O _ { 3 } + H C l = A g C l \\downarrow + H N O _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3527.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3b + 3b + 3b) + 3(3",
|
|
"gt_answers": "\\frac { 3 + 3 6 } { 3 9 } \\textcircled { = } \\frac { 3 6 + 3 } { 3 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3528.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(s_{n} = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left",
|
|
"gt_answers": "L - \\sin C = \\frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { 2 a b } = \\cos c\n",
|
|
"image_path": "./data/HME100K/test_images/test_3529.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "a = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3530.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(L_{B_{2}B_{D_{6}}}=2L_{B_{2}}L_{B_{D_{6}}}-L_{B_{2}}L_{B_{D_{6}}}^{2}-L_{B_{D_{6}}}^{2}L_{B_{2}}}\\)",
|
|
"gt_answers": "\\angle B O D = 2 \\angle B A D = 6 0 ^ { \\circ } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3531.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 20x - 30 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 6 } { 2 0 } - \\frac { 5 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3532.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\arcsin x = \\frac { 1 - y } { 2 } x = \\sin \\frac { 1 - y } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3533.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(K_c = \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2} \\left( \\frac{1}{15} \\left( \\frac{1}{2}",
|
|
"gt_answers": "k = - \\frac { 8 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3534.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"y = 1/x + 1.\"",
|
|
"gt_answers": "a _ { 1 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3536.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(P_{F-D} = P_{F} - P_{D}\\)\n\nwhere P_{F} is the potential difference between the forward and the reverse directions of the current, and P_{D} is the potential difference between the two directions of the current when the device is in the depletion region.",
|
|
"gt_answers": "\\frac { B E } { D F } = \\frac { B C } { D C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3537.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2PQ = 180\u00b0 + LBP + PBQ.",
|
|
"gt_answers": "\\angle P B Q = 1 8 0 ^ { \\circ } - \\angle B P Q - \\angle P Q B\n",
|
|
"image_path": "./data/HME100K/test_images/test_3539.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as BD = DC.",
|
|
"gt_answers": "\\overline { B D } = \\overline { D C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3541.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "y = \\frac { 9 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3542.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A = 40 + 3b\".",
|
|
"gt_answers": "A E = A Q + E Q = 4 0 + 3 0 \\sqrt { 3 } \\approx 6 1 . 9 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_3543.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "x = 1 , x = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3544.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"n = 1 + 1\" using LaTeX format.",
|
|
"gt_answers": "1 5 n ^ { 2 } + 2 n - 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3545.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 5x + 6 = 10\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(2x^2 + 5x + 6 = 10\\)\n\nThe LaTeX code for the formula is:\n\n\\begin{equation}\n2x^2 + 5x + 6 = 10\n\\end{equation}\n\nThe equation is written using the `\\( ... \\)` and `\\( ... \\)` LaTeX commands to enclose the expression and its variables, respectively.",
|
|
"gt_answers": "\u3001 \\frac { 2 x + 5 } { 6 } + \\frac { x + 1 1 } { 4 } + x = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3546.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 360x1 + 2734x40 = 1.",
|
|
"gt_answers": "3 6 0 \\times \\frac { 1 } { 2 + 3 + 4 } = 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3547.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a Chinese character in the middle, which could be a representation of a mathematical expression in Chinese.",
|
|
"gt_answers": "y = \\frac { - 1 \\pm \\sqrt { 1 7 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3548.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LaOe2(OH)3(OH)2.9K\".",
|
|
"gt_answers": "\\angle A O C : \\angle A O B = 2 k = 9 k\n",
|
|
"image_path": "./data/HME100K/test_images/test_3549.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1504300-2=1504298.",
|
|
"gt_answers": "1 5 0 \\div 3 0 0 = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3550.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 3x + 1.",
|
|
"gt_answers": "y _ { 1 } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3551.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C = 9000 N\\)",
|
|
"gt_answers": "C _ { 7 } = 9 0 0 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_3553.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nCO2 + H2O + O2 --> CO2 + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2O + H2",
|
|
"gt_answers": "C O _ { 2 } + C a ( O H ) _ { 2 } = C a C O _ { 3 } \\downarrow + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_3554.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x + 3y = 10\\)",
|
|
"gt_answers": "\\frac { n } { 2 } ( n + 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3555.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Soo-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa-Sooa",
|
|
"gt_answers": "S _ { \\Delta O P Q } = S _ { \\Delta O P A } - S _ { \\Delta O A Q } = \\frac { 1 } { 2 } \\times 5 \\times 4 - \\frac { 1 } { 2 } \\times 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3556.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 90x135 = 12,450.",
|
|
"gt_answers": "\\frac { 9 0 } { x } = \\frac { 1 3 5 } { x + 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3557.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as `2x^2 - 3x + 1 = 0`.",
|
|
"gt_answers": "x ^ { 2 } - k _ { 1 } x - b _ { 1 } = 0 \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_3558.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x + 3 = 14.\"",
|
|
"gt_answers": "\\frac { 4 } { 5 } x = \\frac { 3 } { 1 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3560.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(A + B = C\\)\n\nThis is a simple algebraic equation that represents the addition of two numbers, A and B, to produce the result C.",
|
|
"gt_answers": "S _ { \\Delta } A P B = \\frac { 1 } { 2 } A B \\times P H = \\frac { 1 } { 2 } \\times 3 \\times 1 = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3561.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 15x + 10 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "- \\frac { 1 6 } { 3 } < b < - \\frac { 8 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3563.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as K(1-3) = 0.",
|
|
"gt_answers": "k = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3565.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis equation is a simple algebraic expression that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": ": y = \\frac { 1 } { 2 } x ^ { 2 } - 2 x - 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3566.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 13b - 11 = 0.",
|
|
"gt_answers": "1 3 b - 1 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3567.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\therefore S _ { \\Delta B E D } = \\frac { 1 } { 2 } E H \\cdot B D = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3569.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(1 + \\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} + \\frac{1}{32} + \\frac{1}{64} + \\frac{1}{128} + \\frac{1}{256} + \\frac{1}{512} + \\frac{1}{1024} + \\frac{1}{2048} + \\frac{1}{4096} + \\frac{1}{8192} + \\frac{1}{16384} + \\frac{1}{32768} + \\frac{1}{65536} + \\frac{1}{131072} + \\frac{1}{262144} + \\frac{1}{524288} + \\frac{1}{1048576} + \\frac{1}{2097152} + \\frac{1}{4194304} + \\frac{1}{8388608} + \\frac{1}{16777216} + \\frac{1}{33554432} + \\frac{1}{67108864} + \\frac{1}{134217728} + \\frac{1}{268435456} + \\frac{1}{536870912} + \\frac{1}{1073741824} + \\frac{1}{2147483648} + \\frac{1}{4294967296} + \\frac{1}{8589934592} + \\frac{1}{17179869184} + \\frac{1}{34359738368} + \\frac{1}{68719476736} + \\frac{1}{137438953472} + \\frac",
|
|
"gt_answers": "y - \\frac { 6 } { y } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3571.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LH_2 + 3C_4H_4 + 4C_2H_2 + 4C_3H_3 + 4C_4H_4 + 4C_5H_5 + 4C_6H_6 + 4C_7H_7 + 4C_8H_8 + 4C_9H_9 + 4C_{10}H_{10} + 4C_{11}H_{11} + 4C_{12}H_{12} + 4C_{13}H_{13} + 4C_{14}H_{14} + 4C_{15}H_{15} + 4C_{16}H_{16} + 4C_{17}H_{17} + 4C_{18}H_{18} + 4C_{19}H_{19} + 4C_{20}H_{20} + 4C_{21}H_{21} + 4C_{22}H_{22} + 4C_{23}H_{23} + 4C_{24}H_{24} + 4C_{25}H_{25} + 4C_{26}H_{26} + 4C_{27}H_{27} + 4C_{28}H_{28} + 4C_{29}H_{29} + 4C_{30}H_{30} + 4C_{31}H_{31} + 4C_{32}H_{32} + 4C_{33}H_{33} + 4C_{34}H_{34} + 4C_{35}H_{35} + 4C_{36}H_{36} + 4C_{37}H_{37} + 4C_{38}H_{38} + 4C_{39}H_{39} + 4C_{40}H_{40} + 4C_{4",
|
|
"gt_answers": "\\angle 1 + \\angle 3 = 4 5 ^ { \\circ } \\therefore \\angle 3 + \\angle 4 = 4 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3572.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = z^2\\)",
|
|
"gt_answers": "x = 7 \\div \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3573.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "x - 1 = \\frac { 2 } { 3 } x + \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3574.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ay-on\" using LaTeX format.",
|
|
"gt_answers": "1 - y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3575.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"E = mc^2,\" where \"E\" represents energy, \"m\" represents mass, and \"c\" represents the speed of light squared.",
|
|
"gt_answers": "\\lambda + m = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3576.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(CaCO_3 + 2H_2O \\rightarrow Ca(OH)_2 + CO_2\\)",
|
|
"gt_answers": "C a ( O H ) _ { 2 } + C O _ { 2 } = C a C O _ { 3 } \\downarrow + H _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3578.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\n\\(b^2 - 2ab + a^2 = 0\\)\n\nThis formula can be written in LaTeX as:\n\n\\(b^2 - 2ab + a^2 = 0\\)\n\nThe formula can also be written as:\n\n\\(b^2 - 2ab + a^2 = 0\\)\n\nThe formula is a quadratic equation in two variables, where a and b are the coefficients of the quadratic term and the constant term, respectively.",
|
|
"gt_answers": "\\frac { b c } { a ^ { 2 } } \\cdot \\frac { 2 a } { b ^ { 2 } c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3579.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5x + 41.5s.",
|
|
"gt_answers": "5 \\frac { 3 } { 8 } x = 4 7 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3581.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, so I cannot provide a LaTeX representation of it. However, the image shows a mathematical formula with a few numbers and letters, which could be a mathematical equation or a formula related to physics or chemistry.",
|
|
"gt_answers": "M _ { 3 } ( \\frac { \\sqrt { 3 } } { 3 } , 0 ) M _ { 4 } ( \\sqrt { 3 } + 2 , 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3582.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4.550000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3583.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 5x3 - 6x5 + 9x6 = 18x6.",
|
|
"gt_answers": "\\frac { 5 \\times 1 3 } { 7 \\times 1 3 } = \\frac { 6 5 } { 9 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3584.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible for me to accurately transcribe it into LaTeX format without knowing the exact Korean characters. However, I can provide a rough approximation of the formula using the Roman alphabet:\n\n[x] + [y] = [z]\n\nThis formula represents the addition of two numbers, where the result is the sum of the two numbers.",
|
|
"gt_answers": "x = \\frac { 2 8 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3586.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `sin(x) + cos(x) = 1`.",
|
|
"gt_answers": "2 - 2 ( \\cos \\alpha . \\cos \\beta + \\sin \\alpha . \\sin \\beta ) = \\frac { 1 } { 9 } +\n",
|
|
"image_path": "./data/HME100K/test_images/test_3587.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b^2 = 4ac\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is represented by the letter \"b\" and the other two sides are represented by the letters \"a\" and \"c\".",
|
|
"gt_answers": "O ^ { \\prime \\prime } B = O B = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3588.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "2 \\times 0 . 5 \\times 2 + 2 \\times 1 \\times 2 + 0 . 5 \\times 1 \\times 2 = 7 m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3592.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows: \"A = 2x + 3.\"",
|
|
"gt_answers": "A M = \\frac { 1 } { 2 } B C = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3593.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 1 0 } { 3 } y + \\frac { 1 0 } { 6 } = 1 0 - \\frac { 1 0 } { 3 } + \\frac { 2 0 } { 3 } y\n",
|
|
"image_path": "./data/HME100K/test_images/test_3594.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the half of the square of one-half, which is equal to one-fourth.",
|
|
"gt_answers": "- 2 x = 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_3595.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows: `3.375`.",
|
|
"gt_answers": "x = 3 . 3 7 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3596.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/3 + 1/5 = 2/7.",
|
|
"gt_answers": "+ \\frac { \\sqrt { 5 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3597.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{1}{1",
|
|
"gt_answers": "( x ^ { 2 } + 2 x ) ^ { 2 } - ( x ^ { 2 } + 2 \\times ) - 6 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3598.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `x^2 + 5x + 3 = 0`.",
|
|
"gt_answers": "x = \\frac { 1 } { 5 } \\div \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3599.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(sin(x) + sin(y) = 2\\cos(x)\\cos(y) - 2\\sin(x)\\sin(y)\\).",
|
|
"gt_answers": "\\sin ( - 4 \\pi + \\frac { \\pi } { 2 } ) + \\tan \\pi - 2 \\cos O\n",
|
|
"image_path": "./data/HME100K/test_images/test_3601.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A + M = Q\\)\n\nThis formula represents the relationship between the quantities A, M, and Q, where A is the amount of money, M is the amount of money needed, and Q is the amount of money available. The equation states that the total amount of money available (Q) is equal to the amount of money needed (M) plus the amount of money already available (A).",
|
|
"gt_answers": "A M = M Q\n",
|
|
"image_path": "./data/HME100K/test_images/test_3602.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a black background and a white border, which could be a representation of a mathematical expression in Japanese.",
|
|
"gt_answers": "4 ( y + 1 ) ^ { 2 } - y ^ { 2 } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3604.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 3x + 2 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\vert x - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3605.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3 - 2x + 1.",
|
|
"gt_answers": "\\vert x \\vert = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3606.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(S = \\frac{V^2}{R} + \\frac{I^2}{L} + \\frac{E^2}{C} + \\frac{G^2}{M} + \\frac{B^2}{N}\\)\n\nThis formula represents the total energy stored in a circuit, where S is the total energy, V is the voltage, I is the current, E is the electric field, G is the gravitational field, B is the magnetic field, and N is the number of turns in the circuit.",
|
|
"gt_answers": "s = v t = 1 8 0 k m / h \\cdot / \\min = 1 8 0 k m / h \\cdot \\frac { 1 } { 6 0 } h = 3 k m\n",
|
|
"image_path": "./data/HME100K/test_images/test_3607.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 4(k + 1) = 2k + 1.",
|
|
"gt_answers": "\\angle K H D = A K F\n",
|
|
"image_path": "./data/HME100K/test_images/test_3609.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "3 , x = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3610.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "y 2 = k 1 \\times ( k \\neq 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3611.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"y = 2x + 1.\"",
|
|
"gt_answers": "y = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3612.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 4x9 + 3d = 0.",
|
|
"gt_answers": "S _ { 9 } = 4 \\times 9 + 3 6 d = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3613.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "\\angle D O E = \\angle A O B = 9 0 ^ { \\circ } - 1 5 ^ { \\circ } = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3614.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 3x + 4 = 0.\"",
|
|
"gt_answers": "x = 6 . 3 \\div 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_3615.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3\\times 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10} + 10^{10",
|
|
"gt_answers": "\\frac { 3 k } { 5 k } = \\frac { C H } { 2 } = \\frac { O H } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3616.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "1 2 \\div \\frac { 6 } { 3 5 } = 7 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3617.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "S _ { \\Delta } A O D \\Rightarrow A\n",
|
|
"image_path": "./data/HME100K/test_images/test_3618.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with the letters \"X\" and \"Y\" and the numbers \"40\" and \"60.\"",
|
|
"gt_answers": "x + \\frac { 3 } { 5 } x = 6 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3619.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(1+2) = 3(1+2) = 3(3) = 9.",
|
|
"gt_answers": "1 8 0 \\div 1 6 0 = \\frac { 9 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3620.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: A = 122 - 121.",
|
|
"gt_answers": "a _ { 1 } = - 1 5 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3621.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 3x + 2\\)",
|
|
"gt_answers": "y = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3622.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(x^2 + y^2 = 4795 - 30\\text{N}\\)\n\nThe formula is written in the form of an equation, with the variables x and y on the left side, and the constant 4795 on the right side. The variable N is written as a subscript, indicating that it is a constant.",
|
|
"gt_answers": "4 7 ^ { \\circ } S - 3 0 ^ { \\circ } N\n",
|
|
"image_path": "./data/HME100K/test_images/test_3623.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"9.9-4\" using LaTeX format.",
|
|
"gt_answers": "a _ { 2 } = \\frac { 3 } { 4 } , 9 = - \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3624.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 1.\"",
|
|
"gt_answers": "\\therefore x ^ { 2 } - y ^ { 2 } = ( x + y ) ( x - y\n",
|
|
"image_path": "./data/HME100K/test_images/test_3625.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"5 = 2 + 3 + 4 + 5.\"",
|
|
"gt_answers": "\\frac { C H } { A H } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3626.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 3x + 2y = 10.",
|
|
"gt_answers": "- \\frac { 3 } { 2 } \\times 1 = \\frac { - \\frac { 3 } { 8 } } { 2 k }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3628.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 8x - 8 = 0`.",
|
|
"gt_answers": "x _ { 3 } = - \\frac { 8 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3629.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 4x + 1 = 0.\"",
|
|
"gt_answers": "x _ { 1 } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3630.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as NaOH + H2SO4 --> Na2SO4 + H2O.",
|
|
"gt_answers": "2 N a O H + H _ { 2 } S O _ { 4 } = N a _ { 2 } S O _ { 4 } + 2 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_3632.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 5.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3633.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x ^ { 2 } - 4 \\times ( x + 1 ) + 3 ( x + 1 ) ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3635.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. In this case, the variable is x, and the square of x is x^2. The variable y is also involved in the equation, and its square is y^2. The equation is written in the form of an identity, which means that the two sides of the equation are equal to each other.",
|
|
"gt_answers": "x ^ { 4 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3637.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Bd = CD\" and is crossed out.",
|
|
"gt_answers": "B D = C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_3638.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a negative sign, which can be represented in LaTeX as follows:\n\n\\(x^2 - 2x + 1\\)",
|
|
"gt_answers": "1 5 . \\frac { 1 } { 2 } \\overrightarrow { b } - \\frac { 1 } { 2 } \\overrightarrow { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3639.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LCDBA\" using LaTeX format.",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\angle C D A = \\angle \\frac { 1 } { 2 } C B A\n",
|
|
"image_path": "./data/HME100K/test_images/test_3642.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{a}{b} = \\frac{a_1}{b_1} + \\frac{a_2}{b_2} + \\cdots + \\frac{a_n}{b_n}\n\\end{equation}\n\nThis formula represents the general case of finding the quotient of two polynomials, where the numerator and denominator are both polynomials of the same degree. The variables a and b represent the coefficients of the polynomials, and the subscripts 1, 2, ..., n represent the powers of the variables in the polynomials.",
|
|
"gt_answers": "\\frac { 1 } { a } + \\frac { 3 } { b } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3643.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 1.43x28.66 + 1.43x28.66 = 1.43x57.32.",
|
|
"gt_answers": "3 . 1 4 \\times 3 ^ { 2 } = 2 8 . 2 6 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3644.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(U = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "\\frac { U _ { v } } { U } = \\frac { n } { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3645.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2(3+4) = 180.\"",
|
|
"gt_answers": "\\cdot \\angle 1 + \\frac { 1 } { 3 } \\angle 1 = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3647.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x = 10 \\times 0.09 + 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 . 1 5 x - 0 . 9 = 0 . 0 7 x + 0 . 3 1 x = - 6 \\div 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3648.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 4x + 4 = 0.\"",
|
|
"gt_answers": "x = \\pm \\sqrt [ 4 ] { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3649.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten style using the Greek letter \"omega\" (\u03c9) as the symbol for the derivative. The formula is written in a way that it can be easily read and understood by someone who is familiar with the notation.",
|
|
"gt_answers": "C E + E D _ { \\min } = \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3650.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in the form of a mathematical formula, which is a combination of letters and symbols. The formula is written in a black box, and the letters and symbols are written in red. The formula is likely a mathematical equation or a chemical formula.",
|
|
"gt_answers": "1 . 0 \\times 1 0 ^ { 3 } k g / m ^ { 3 } \\times 1 0 N / k g \\times 0 . 2 \\times 1 0 ^ { - 2 } m\n",
|
|
"image_path": "./data/HME100K/test_images/test_3651.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"21 = 2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + ",
|
|
"gt_answers": "\\angle 1 = \\frac { 1 } { 2 } \\angle E A C\n",
|
|
"image_path": "./data/HME100K/test_images/test_3653.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(U_{total} = U_{1} + U_{2} + U_{3} + U_{4} + U_{5} + U_{6} + U_{7} + U_{8} + U_{9} + U_{10} + U_{11} + U_{12} + U_{13} + U_{14} + U_{15} + U_{16} + U_{17} + U_{18} + U_{19} + U_{20} + U_{21} + U_{22} + U_{23} + U_{24} + U_{25} + U_{26} + U_{27} + U_{28} + U_{29} + U_{30} + U_{31} + U_{32} + U_{33} + U_{34} + U_{35} + U_{36} + U_{37} + U_{38} + U_{39} + U_{40} + U_{41} + U_{42} + U_{43} + U_{44} + U_{45} + U_{46} + U_{47} + U_{48} + U_{49} + U_{50} + U_{51} + U_{52} + U_{53} + U_{54} + U_{55} + U_{56} + U_{57} + U_{58} + U_{59} + U_{60} + U_{61} + U_{62} + U_{63} + U_{64} + U_{65} + U_{66} + U_{67} + U_{68} + U_{69} + U_{70} + U_{71} + U_{72} + U_{73} + U_{74} + U_{75} + U_{76} + U_{77} + U_{78} + U_{79} + U_{80} + U_{81} + U_{82} + U_{83} +",
|
|
"gt_answers": "u _ { 3 } = u - ( u _ { 1 } + u _ { 2 } ) = 4 v\n",
|
|
"image_path": "./data/HME100K/test_images/test_3654.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBEF = 2.11\".",
|
|
"gt_answers": "\\angle B E F = \\angle C + \\angle 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3655.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 5x(3x-4) = 24.",
|
|
"gt_answers": "( 2 ) \\frac { 5 x } { 2 4 } = \\frac { 3 x - 4 } { 8 } - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3656.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^{2} + 2x - 3 = 0\\)",
|
|
"gt_answers": "x \\in ( a _ { 0 } , + \\infty ) - g ( a ) < 0 . 9 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3658.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1 + 2x + 2y + 2x^2 + 2y^2\\)",
|
|
"gt_answers": "2 x - 4 x = - 2 + m + m .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3659.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x + 5 = 10\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } a x + 5 = \\frac { 7 x - 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3660.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 6x2.7700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "6 \\times 2 . 7 \\times 0 . 0 6 = 0 . 9 7 2 ( m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3661.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x _ { 2 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3662.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(x + 1) - 3(x - 2) = 0.",
|
|
"gt_answers": "x _ { 1 } = - \\frac { 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3663.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 6x + 3 = 12.",
|
|
"gt_answers": "\\frac { 1 } { 6 } : \\frac { 1 } { 1 8 } = 3 : 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3664.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(Mg^{2+} + Cl^{-} \\rightarrow MgCl_{2}\\)",
|
|
"gt_answers": "M G \\bot E F\n",
|
|
"image_path": "./data/HME100K/test_images/test_3665.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nNH3 + 2H2O \u2192 N2 + 3H2 + O2",
|
|
"gt_answers": "N H _ { 3 } + H _ { 2 } O \\rightleftharpoons N H _ { 3 } \\cdot H _ { 2 } O \\rightleftharpoons N H _ { 4 } ^ { + } + O H ^ { - }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3666.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{3}x + \\frac{1}{4}\\)",
|
|
"gt_answers": "y _ { 2 } = \\frac { - 1 - \\sqrt { 5 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3667.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a black background, which could be written in LaTeX as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\text{Formula}\n\\end{aligned}\n\nThis equation is written in a standard mathematical notation, with the formula itself being the main content and the surrounding text being the equation's title.",
|
|
"gt_answers": "= 2 \\sqrt { 3 } + \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3668.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} = 0\n\\end{equation}\n\nThis equation is a quadratic equation in two variables, and it can be solved using the quadratic formula.",
|
|
"gt_answers": "= [ 4 0 \\times 6 0 - ( 4 a ^ { 2 } - 2 0 0 a + 2 4 0 0 ) ] \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_3669.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\Delta A N D \\sim \\Delta A C M\n",
|
|
"image_path": "./data/HME100K/test_images/test_3671.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(C_b^2 = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\",
|
|
"gt_answers": "c = b : d\n",
|
|
"image_path": "./data/HME100K/test_images/test_3672.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x + 2y = 12\\)\n\nThis formula represents a linear equation in two variables, where the variables x and y are multiplied together and added to 12.",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\div \\frac { 1 } { 3 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3673.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 5x + 3 = 0\\)",
|
|
"gt_answers": "3 x ^ { 2 } - 2 x ^ { 2 } - 5 = 0 x _ { 1 } = 3 x _ { 2 } = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3675.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LDFCF = 30^{\\circ}\\)",
|
|
"gt_answers": "\\because \\angle D C F = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3677.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "= \\frac { 1 - \\frac { 1 } { 4 } } { 1 + \\frac { 1 } { 4 } } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3679.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{3} \\cdot \\frac{1}{2} \\cdot \\frac{1}{4} = \\frac{1}{12}\n\\end{equation}\n\nThis formula represents the multiplication of three fractions, each with a denominator of 1/3, 1/2, and 1/4. The result is a fraction with a denominator of 1/12.",
|
|
"gt_answers": "x = \\frac { 1 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3681.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"11x + 18 = 100.\"",
|
|
"gt_answers": "x = \\frac { 1 1 } { 4 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3682.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a number and a Chinese character, which could be a mathematical symbol or a Chinese character representing a number.",
|
|
"gt_answers": "\\frac { 9 } { 2 4 } + \\frac { 2 0 } { 2 4 } = \\frac { 2 9 } { 2 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3683.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "u > v\n",
|
|
"image_path": "./data/HME100K/test_images/test_3684.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
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"gt_answers": "\\therefore \\angle A H C = 9 0 ^ { \\circ }\n",
|
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"image_path": "./data/HME100K/test_images/test_3685.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x^2 + 6x + 2 = 10\\)\n\nThe formula is written in the form of an equation, where the variables x and y are multiplied together and then added to a constant. The constant is 10 in this case.",
|
|
"gt_answers": "\\frac { 2 } { 3 } = \\frac { 2 \\times 2 } { 3 \\times 2 } = \\frac { 4 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3686.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"H(t) = H(t-1) + H(t-2) + H(t-3) + H(t-4) + H(t-5) + H(t-6) + H(t-7) + H(t-8) + H(t-9) + H(t-10) + H(t-11) + H(t-12) + H(t-13) + H(t-14) + H(t-15) + H(t-16) + H(t-17) + H(t-18) + H(t-19) + H(t-20) + H(t-21) + H(t-22) + H(t-23) + H(t-24) + H(t-25) + H(t-26) + H(t-27) + H(t-28) + H(t-29) + H(t-30) + H(t-31) + H(t-32) + H(t-33) + H(t-34) + H(t-35) + H(t-36) + H(t-37) + H(t-38) + H(t-39) + H(t-40) + H(t-41) + H(t-42) + H(t-43) + H(t-44) + H(t-45) + H(t-46) + H(t-47) + H(t-48) + H(t-49) + H(t-50) + H(t-51) + H(t-52) + H(t-53) + H(t-54) + H(t-55) + H(t-56) + H(t-57) + H(t-58) + H(t-59) + H(t-60) + H(t-61) + H(t-62) + H(t-63) + H(",
|
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"gt_answers": "B H = C H = \\frac { 3 } { 2 }\n",
|
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"image_path": "./data/HME100K/test_images/test_3687.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"P(A or B) = P(A) + P(B) - P(A and B).\"",
|
|
"gt_answers": "\\{ x \\vert - b \\leq x \\leq 3 \\}\n",
|
|
"image_path": "./data/HME100K/test_images/test_3688.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{x^3 - 3x^2 + 2x - 1}{x^2 + 2x + 1}\\)",
|
|
"gt_answers": "f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_3689.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3 = 5.",
|
|
"gt_answers": "\\frac { a } { c } = \\frac { 2 } { 3 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3690.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to provide a LaTeX representation of it without knowing the exact Japanese characters used. However, the image shows a mathematical formula with a number and a Japanese character, which could be a mathematical symbol or a word.",
|
|
"gt_answers": "( 1 - \\frac { 1 } { 3 } - \\frac { 1 } { 4 } - \\frac { 1 } { 8 } ) x < 1 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3691.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x ^ { 2 } + 2 x + 1 = \\frac { 2 } { x ^ { 2 } + 2 x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3692.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": ": y = - \\frac { \\sqrt { 3 } } { 3 } x + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3693.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\nCaCO3 + 2H2O + 2NaOH --> Ca(OH)2 + Na2CO3 + H2",
|
|
"gt_answers": "C u O + 2 H N O _ { 3 } = C u ( N O _ { 3 } ) _ { 2 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_3694.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: y = 2x^2 + 3x + 4.",
|
|
"gt_answers": "y = k _ { 2 } x + b\n",
|
|
"image_path": "./data/HME100K/test_images/test_3695.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"10x + 10y = 100.\"",
|
|
"gt_answers": "B C = 1 0 \\times \\tan 6 0 ^ { \\circ } = 1 0 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3696.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(W = \\frac{1}{2} \\left( \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 \\right) + \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 + \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 + \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 + \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 + \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 + \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 + \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 + \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 + \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 + \\left( \\frac{x^2 + y^2}{2} \\right)^2 + \\left( \\frac{x^2 - y^2}{2} \\right)^2 + \\left( \\frac{x^2 + y^2}{2} \\",
|
|
"gt_answers": "W = - x ^ { 2 } + 7 x + 4 8 = - ( x - 3 . 5 ) ^ { 2 } + 6 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3697.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "\\frac { 2 } { 2 } x - \\frac { 1 } { 2 } x = ( - 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3698.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "e B h B ^ { \\prime } = \\frac { 1 } { 2 } e A h A\n",
|
|
"image_path": "./data/HME100K/test_images/test_3699.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2.654444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444",
|
|
"gt_answers": "1 2 . 5 6 \\times 2 . 5 = 3 1 . 4 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3700.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 4y^2 = 9\\)",
|
|
"gt_answers": "( 3 \\times 4 ) ^ { 2 } ( 2 ) = ( 3 ) ( a b ) ^ { n }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3703.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the image shows a formula with a line of text and a few numbers, which could be a mathematical equation or a chemical formula.",
|
|
"gt_answers": "\\pm \\sqrt { \\frac { x } { y } } = \\pm \\sqrt { 4 } = \\pm 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3704.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(k = \\frac{1}{2} \\pi r^2 \\rho g\\)\n\nwhere k is the spring constant, r is the radius of the spring, \u03c1 is the density of the material, and g is the acceleration due to gravity.",
|
|
"gt_answers": "- \\frac { 1 } { 1 0 } x ^ { 2 } + 1 0 x = 2 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3705.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(st(",
|
|
"gt_answers": "( 5 + 3 y + 3 y ) ( 5 + 3 y - 3 y ) = 1 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3709.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(N_2 + N_3 = N_1 + N_2 + N_3\\)",
|
|
"gt_answers": "\\sqrt { h B ^ { 2 } } = \\sqrt { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3711.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(W = \\frac{300 \\times 100}{2} = 600\\)\n\nThis formula calculates the weight of an object in kilograms (kg) by multiplying its length (in meters) by its width (in meters) and dividing the result by two.",
|
|
"gt_answers": "w = \\frac { s } { 1 t } = \\frac { 3 0 0 } { \\frac { 4 0 } { 2 \\pi } \\times 6 0 } = \\frac { \\pi } { 4 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3712.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: J = 1/2(k + j) + 1/2(k - j).",
|
|
"gt_answers": "\\sqrt { 2 } = - \\sqrt { 2 } k\n",
|
|
"image_path": "./data/HME100K/test_images/test_3713.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2} + 1\\)",
|
|
"gt_answers": "y _ { 2 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3714.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 2x + 4.",
|
|
"gt_answers": "\\frac { x - 3 } { 2 } + \\frac { y - 2 } { 3 } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3715.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as PB = 74.",
|
|
"gt_answers": "P _ { ( B ) } = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3716.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
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"gt_answers": "( 1 . 5 \\times 0 . 8 + 1 . 5 \\times 0 . 5 + 0 . 8 \\times 0 . 5 ) \\times 2 = 4 . 7 ( m ^ { 2 } )\n",
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"image_path": "./data/HME100K/test_images/test_3717.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as: 3x + 1 = 11.",
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"gt_answers": "3 \\times \\frac { 1 } { 3 } = 1\n",
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"image_path": "./data/HME100K/test_images/test_3718.jpg",
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"model_name": "mPLUG"
|
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
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"gt_answers": "\\sqrt { 4 } - 1\n",
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"image_path": "./data/HME100K/test_images/test_3719.jpg",
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"model_name": "mPLUG"
|
|
},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression of the formula in the image is written as follows:\n\n\\begin{equation}\n\\frac{x^2 + 2x + 3}{x + 2} = 2x + 3\n\\end{equation}\n\nThe equation is written in LaTeX format using the `equation` environment, which provides a clean and professional look to the equation.",
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"gt_answers": "\\frac { 2 x - 3 } { 4 } + 1 = \\frac { x + 2 } { 5 } + \\frac { 3 } { 4 }\n",
|
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"image_path": "./data/HME100K/test_images/test_3721.jpg",
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"model_name": "mPLUG"
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|
},
|
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{
|
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written as \"2(L + 1) = 2L + 2.\"",
|
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"gt_answers": "\\angle 2 = \\frac { 1 } { 2 } \\angle A C D = \\angle 1\n",
|
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"image_path": "./data/HME100K/test_images/test_3722.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x + 3} \\cdot \\frac{1}{x^2 + 2x + 3} = \\frac{1}{x^2 + 2x",
|
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"gt_answers": "x _ { 1 } = 0 , x _ { 2 } = - 3 , x _ { 3 } = 3\n",
|
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"image_path": "./data/HME100K/test_images/test_3723.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 5\\)",
|
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"gt_answers": "y _ { 2 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3724.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 24ft3 = 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2ft3 + 2",
|
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"gt_answers": "2 F C + 3 C l 2 = 2 F e C l 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3726.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "\\frac { 7 . 5 } { 2 . 5 } = \\frac { x } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3728.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, but it can be represented in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3} \\cdot \\frac{1}{3} \\cdot \\frac{1}{3} + \\frac{1}{3}",
|
|
"gt_answers": "= \\frac { \\sqrt { 1 8 } } { \\sqrt { 3 } + \\sqrt { 2 } } = \\frac { \\sqrt { 1 8 } ( \\sqrt { 3 } - \\sqrt { 2 } ) } { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3731.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the Japanese language, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a red line drawn through it, which indicates that it is an important or significant part of the equation.",
|
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"gt_answers": "x = 2 y = -\n",
|
|
"image_path": "./data/HME100K/test_images/test_3732.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O(O",
|
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"gt_answers": "O B = O D = \\frac { 1 } { 2 } B D\n",
|
|
"image_path": "./data/HME100K/test_images/test_3733.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(B_n = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\angle B D E = B E D = \\frac { 1 } { 2 } \\times ( 1 8 0 ^ { \\circ } - 3 0 ^ { \\circ } ) = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3734.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "y = - \\frac { 1 } { 3 } x ^ { 2 } + \\frac { 4 } { 3 } x + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3735.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "G . \\therefore \\angle F H E = \\angle F A G = 4 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3737.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"a^2 + b^2 = c^2.\"",
|
|
"gt_answers": "\\frac { 1 } { a _ { n + 1 } } - \\frac { 1 } { a _ { n } } = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3738.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LEKG = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\angle E K G = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3739.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x + 1} = \\frac{x^2 + 3x - 2}{x^2 - 2x +",
|
|
"gt_answers": "x _ { 3 } = - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3740.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: AC + 16b + 80 = 100.",
|
|
"gt_answers": "A C ^ { 2 } = 1 6 + 6 4 = 8 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3741.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: CD + CB = C3.",
|
|
"gt_answers": "\\frac { C D } { C A } = \\frac { C A } { C B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3742.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = 2x^2 - 2x + 1\\)",
|
|
"gt_answers": "2 x + ( x + 2 ) ^ { 4 } = 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3743.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows: `1.752411.12`.",
|
|
"gt_answers": "7 . 1 5 2 < 7 . 1 \\square 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3745.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 4x + 3t.",
|
|
"gt_answers": "y = 4 - \\sqrt { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3748.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which are not supported by LaTeX. However, the image shows a mathematical formula with a negative sign in front of the expression. The formula could be written as follows in LaTeX:\n\n\\(x^2 - 2x + 1\\)",
|
|
"gt_answers": "\\overrightarrow { A E } = \\frac { \\sqrt { 2 } } { 2 } \\overrightarrow { A D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3749.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(C_4 = \\frac{1}{4} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "C = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3750.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{4(x+3)}{(x+4)(x+3)} = \\frac{4x+12}{x^2+12x+4}\n\\end{aligned}\n\\end{equation}\n\nThis formula can be simplified further by factoring out the common denominator, which results in the following expression:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{4(x+3)}{(x+4)(x+3)} = \\frac{4x+12}{x^2+12x+4} = \\frac{4x+12}{x^2+4x+4} = \\frac{4x+12}{x^2+4x} = \\frac{4x+12}{x^2+4} = \\frac{4x+12}{x^2} = \\frac{4x+12}{x} = \\frac{4x+12}{1} = 4x+12\n\\end{aligned}\n\\end{equation}\n\nThis simplified expression shows that the original formula can be written as a simple multiplication of the numerator and denominator by 4.",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\times 4 ( y - z + 3 ) = \\frac { 1 } { 2 } ( 4 - z ) ( x + 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3751.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 180^2\\)",
|
|
"gt_answers": "x \\div 2 \\times 2 = 1 8 0 \\times 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3752.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 5x + 6 = 0.\"",
|
|
"gt_answers": "\\frac { 8 } { 9 } \\times \\frac { 7 } { 7 } \\textcircled { = } \\frac { 8 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3753.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(u = \\sqrt{2\\left(v^2 - 2\\left(v^2 - 2\\right)\\right)}\\)\n\nThis formula can be interpreted as follows:\n\nThe variable `u` is equal to the square root of the sum of the squares of the variables `v` and `v^2 - 2`.",
|
|
"gt_answers": "U _ { e } = U - U _ { P } = 4 . 5 V - 2 V = 2 . 5 V\n",
|
|
"image_path": "./data/HME100K/test_images/test_3754.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(P_{x} = \\frac{V_{x}}{G_{x}} + \\frac{V_{y}}{G_{y}} + \\frac{V_{z}}{G_{z}}\\)\n\nwhere Px is the pressure in the x-direction, Vx is the volume in the x-direction, Gy is the volume in the y-direction, and Gx is the gravitational acceleration in the x-direction.",
|
|
"gt_answers": "P ( x = 1 ) = \\frac { C _ { 3 } ^ { 2 } C _ { 4 } ^ { 1 } } { C _ { 7 } ^ { 3 } } = \\frac { 1 2 } { 3 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3755.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x} + \\frac{1}{x^2} + \\frac{1}{x^3} + \\frac{1}{x^4} + \\frac{1}{x^5} + \\frac{1}{x^6} + \\frac{1}{x^7} + \\frac{1}{x^8} + \\frac{1}{x^9} + \\frac{1}{x^{10}} + \\frac{1}{x^{11}} + \\frac{1}{x^{12}} + \\frac{1}{x^{13}} + \\frac{1}{x^{14}} + \\frac{1}{x^{15}} + \\frac{1}{x^{16}} + \\frac{1}{x^{17}} + \\frac{1}{x^{18}} + \\frac{1}{x^{19}} + \\frac{1}{x^{20}} + \\frac{1}{x^{21}} + \\frac{1}{x^{22}} + \\frac{1}{x^{23}} + \\frac{1}{x^{24}} + \\frac{1}{x^{25}} + \\frac{1}{x^{26}} + \\frac{1}{x^{27}} + \\frac{1}{x^{28}} + \\frac{1}{x^{29}} + \\frac{1}{x^{30}} + \\frac{1}{x^{31}} + \\frac{1}{x^{32}} + \\frac{1}{x^{33}} + \\frac{1}{x^{34}} + \\frac{1}{x^{35}} + \\frac{1}{x^{36}} + \\frac{1}{x^{37}} + \\frac{1}{x^{38}} + \\frac{1}{x^{39}} + \\frac{1}{x^{40}} + \\frac{1}{x^{41}} + \\frac{1}{x^{42}} + \\frac{1}{x^{43}} + \\frac{1}{x^{44}} + \\frac{1}{x^{45}} + \\frac{1}{x",
|
|
"gt_answers": "\\frac { 3 x - 1 } { 2 } - \\frac { 5 - 2 x } { 3 } = \\frac { 5 x + 3 } { 4 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3758.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Anti-Ann-N\" using LaTeX format.",
|
|
"gt_answers": "a _ { n + 1 } - a _ { n } = n = 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_3759.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 3x + 2 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\div 3 = \\frac { 1 } { 2 } \\times \\frac { 1 } { 3 } = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3760.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 5\\)",
|
|
"gt_answers": "x - 3 y = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3761.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(atl-a\\)",
|
|
"gt_answers": "a + ( - \\frac { 1 } { a } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3762.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 10x + 9 = 100.",
|
|
"gt_answers": "x = \\frac { 1 0 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3763.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\therefore \\angle A B F + \\angle A B E = \\angle F B E = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3767.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)",
|
|
"gt_answers": "h = \\frac { 1 } { 2 } + 0 . 2 1 \\approx 0 . 7 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_3768.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"L1-L2 = L2-L3 + L3-L4 + L4-L5 + L5-L6 + L6-L7 + L7-L8 + L8-L9 + L9-L10 + L10-L11 + L11-L12 + L12-L13 + L13-L14 + L14-L15 + L15-L16 + L16-L17 + L17-L18 + L18-L19 + L19-L20 + L20-L21 + L21-L22 + L22-L23 + L23-L24 + L24-L25 + L25-L26 + L26-L27 + L27-L28 + L28-L29 + L29-L30 + L30-L31 + L31-L32 + L32-L33 + L33-L34 + L34-L35 + L35-L36 + L36-L37 + L37-L38 + L38-L39 + L39-L40 + L40-L41 + L41-L42 + L42-L43 + L43-L44 + L44-L45 + L45-L46 + L46-L47 + L47-L48 + L48-L49 + L49-L50 + L50-L51 + L51-L52 + L52-L53 + L53-L54 + L54-L55 + L55-L56 + L56-L57 + L57-L58 + L58-L59 + L59-L60 + L60-L61 + L61-L62 + L62-L63 + L63-L64 + L64-L65 + L65-L66",
|
|
"gt_answers": "\\angle 1 = 3 0 ^ { \\circ } \\angle 2 = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3769.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2019-01-01 00:00:00 + 2020-01-01 00:00:00 = 2020-01-01 00:00:00\".",
|
|
"gt_answers": "2 0 \\times 5 x + 1 0 \\times 7 x + 5 \\times 6 x = 4 8 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3770.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left( \\left(",
|
|
"gt_answers": "D F = 2 , C E = 3 , A F = 8 , B E = 6 ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_3771.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a number written in Japanese characters, which could be a mathematical expression or a formula in Japanese.",
|
|
"gt_answers": "2 5 < x < 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3772.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 7x + 2y = 37.",
|
|
"gt_answers": "\\frac { 3 } { 7 } + \\frac { 1 } { 6 } = \\frac { 2 4 } { 5 6 } + \\frac { 7 } { 5 6 } \\leq \\frac { 3 1 } { 5 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3773.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4u + 36 = 36u\\)",
|
|
"gt_answers": "4 u = 3 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3774.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the formula is likely a mathematical equation or a mathematical expression.",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\times \\frac { t } { 4 } \\times ( t - \\frac { 1 } { 2 } t ) = \\frac { 3 t } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3775.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(y = 2x^2 + 3x + 4\\)\n\nThis is a quadratic equation in the form of a function, where y is the dependent variable and x is the independent variable. The expression represents a quadratic function with a constant term (2), a linear term (3x), and a quadratic term (4).",
|
|
"gt_answers": "5 = 4 a + b\n",
|
|
"image_path": "./data/HME100K/test_images/test_3776.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { b } { \\sin B } = \\frac { c } { \\sin C } \\Rightarrow \\sin c = \\frac { \\sin B } { b } \\times C = \\frac { \\frac { \\sqrt { 2 } } { 2 } } { 2 \\sqrt { 2 } } \\times 2 \\sqrt { 3 } = \\frac { \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3777.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n2x2 = fc(dmc)3\n\nwhere fc is the function constant, dmc is the distance between the centers of mass of the two objects, and x2 is the distance between the centers of mass of the two objects squared.",
|
|
"gt_answers": "2 \\times 2 \\times 2 = 8 ( d m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3778.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": ") U _ { 1 } = I _ { 1 } R _ { 1 } = 0 . 6 A \\times 1 0 \\Omega = 6 V\n",
|
|
"image_path": "./data/HME100K/test_images/test_3779.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Feb 2021 - Beat 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\Delta F E B \\sim \\Delta B E A\n",
|
|
"image_path": "./data/HME100K/test_images/test_3780.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "4 0 \\div 8 = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3781.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"12x2x3-3.\"",
|
|
"gt_answers": "( x _ { 1 } + x _ { 2 } ) + 2 x _ { 2 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3782.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(P = \\frac{nRT}{V} = \\frac{n \\times 8.3144625 \\times 10^{-5} \\times 1000 \\times 1000}{V} = 8.3144625 \\times 10^{-5} \\times 1000 \\times 1000 \\times V\\)",
|
|
"gt_answers": "m = \\frac { G } { g } = \\frac { 1 . 4 7 N } { 1 0 N / k g } = 0 . 1 4 . 7 k g\n",
|
|
"image_path": "./data/HME100K/test_images/test_3783.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x _ { 3 } = \\frac { 4 \\sqrt { 7 } } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3784.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A + B = 2(C + D) - 2(E + F)\".",
|
|
"gt_answers": "A = 1 2 - 2 - 4 = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3785.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times 10^{10} \\times",
|
|
"gt_answers": "1 . 8 \\div \\frac { 1 } { 5 0 0 0 0 0 } = 9 0 0 0 0 0 ( c m ) = 9 ( k )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3786.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Korean.",
|
|
"gt_answers": "\\frac { 1 5 } { 1 6 } \\div \\frac { 5 } { 2 } = \\frac { 3 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3787.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible for me to accurately transcribe it using LaTeX. However, I can provide a rough translation of the expression: \"The sum of the squares of the first 100 natural numbers.\"",
|
|
"gt_answers": "( x ^ { 2 } - 2 x + 1 ) = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3788.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x + 3 = 5\\)",
|
|
"gt_answers": "x = \\frac { 2 1 } { 2 } \\div \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3789.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1 cm = 1000 mm\".",
|
|
"gt_answers": "m > - \\frac { 1 } { 2 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3790.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "3 y + \\frac { 4 } { y } = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3791.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 + 100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 119 + 120 + 12",
|
|
"gt_answers": "\\frac { 3 a - 5 } { 4 } = \\frac { 1 - a } { 3 } + \\frac { 1 } { 6 } + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3792.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(6x^2 + 4x + 1 = 0\\)",
|
|
"gt_answers": "\\textcircled { 1 } A \\times \\frac { 6 } { t } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3794.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Hindi, and it is not possible for me to accurately transcribe it using LaTeX. However, I can provide a rough translation of the formula:\n\n\"3 \u00f7 2 = 1.5\"",
|
|
"gt_answers": "= \\frac { 3 } { \\sqrt { 2 } - 1 } = 3 \\sqrt { 2 } + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3795.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written in the form of a mathematical equation, with the letters \"a\" and \"b\" representing variables, and the letter \"e\" representing the base of the natural logarithm. The expression is written in the form of a function, with the function name \"log\" and the arguments \"a\" and \"b\". The function is defined as the natural logarithm of the product of the two arguments.",
|
|
"gt_answers": "+ \\angle A B E + \\angle B A E = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3796.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(4d + 2r + 3s = 10\\)",
|
|
"gt_answers": "4 d m ^ { 3 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3797.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is: `C + C + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D + D + F + P + P + B + D",
|
|
"gt_answers": "C A + C B + P D > P A + P B + P D )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3799.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 + 100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 119 + 120 + 12",
|
|
"gt_answers": "1 8 + 4 + a ^ { 2 } = a ^ { 2 } - 6 a + 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3800.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given by:\n\n\\(2\\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3} \\cdot \\sqrt{2} \\cdot \\sqrt{3",
|
|
"gt_answers": "\\frac { 2 } { 2 + \\sqrt { 3 } - 2 } = \\frac { 2 } { \\sqrt { 3 } } = \\frac { 2 } { 3 } \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3801.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\nb^2 + b^2 - 4ac = 0\n\nThis formula is used to solve quadratic equations.",
|
|
"gt_answers": "x = \\frac { - b \\pm \\sqrt { b ^ { 2 } - 4 a c } } { 2 a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3803.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBLAG = 6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle B = \\angle A O F = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3806.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"I20 = 1/2(I10 + I30).\"",
|
|
"gt_answers": "\\frac { 1 } { 4 } = 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3807.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mathematical formula using the Greek letter \"pi\" (\u03c0) as the symbol for the ratio of the circumference of a circle to its diameter. The formula is written in a way that it can be easily read and understood by anyone familiar with the language of mathematics.",
|
|
"gt_answers": "x = \\frac { 5 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3808.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"LDE = 4BOD.\"",
|
|
"gt_answers": "\\angle D E = \\frac { 1 } { 2 } \\angle B O D\n",
|
|
"image_path": "./data/HME100K/test_images/test_3809.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `468 - 6 J13`.",
|
|
"gt_answers": "y = \\frac { 4 6 8 } { x } - 6 \\sqrt { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3810.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3\\cdot 2^{2} + 2\\cdot 2^{1} + 1\\cdot 2^{0} = 10\\)",
|
|
"gt_answers": "\\frac { 1 } { a _ { n + 1 } } = \\frac { 3 a _ { n } + 1 } { . a _ { n } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3811.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the half of the half of a whole, which is equal to one fourth.",
|
|
"gt_answers": "\\widehat { B D } = \\widehat { C D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3812.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{13}{2} + \\frac{1",
|
|
"gt_answers": "\\frac { 3 - 4 x } { 9 } = 1 - \\frac { x - 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3813.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(T = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "x < \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3814.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(2x^2 + 3x + 4 = 5(x + 1)^2\\)\n\nThe formula can be rewritten as:\n\n\\(2x^2 + 3x + 4 = 5(x + 1)^2 = 5(x + 1)(x + 1) + 4 = 5x^2 + 5x + 4 + 4 = 5x^2 + 9x + 4\\)\n\nThe formula can also be written as:\n\n\\(2x^2 + 3x + 4 = 5(x + 1)^2 = 5(x + 1)(x + 1) = 5x^2 + 5x + 5 = 5x^2 + 10x + 5\\)\n\nThe formula can be further simplified as:\n\n\\(2x^2 + 3x + 4 = 5(x + 1)^2 = 5(x + 1)(x + 1) = 5x^2 + 5x + 5 = 5x^2 + 10x + 5 = 5x^2 + 15x + 5\\)\n\nThe formula can be written in the form of a quadratic equation:\n\n\\(2x^2 + 3x + 4 = 5x^2 + 15x + 5\\)\n\nSolving for x, we get:\n\n\\(x = \\frac{-3 \\pm \\sqrt{9 + 20}}{2} = \\frac{-3 \\pm \\sqrt{11}}{2} = \\frac{-3 \\pm \\sqrt{22}}{2} = \\frac{-3 \\pm \\sqrt{4}}{2} = \\frac{-3 \\pm 2}{2} = \\frac{-3 \\pm 1}{2} = \\frac{-3 \\pm 1}{2} = \\frac{-3 \\pm 1}{2} = \\frac{-3 \\pm 1}{2} = \\frac{-3 \\pm 1}{2} = \\frac{-3 \\pm 1}{2} = \\frac{-3 \\pm 1}{2} = \\frac{-3",
|
|
"gt_answers": "1 \\times \\frac { \\vert a \\vert + \\frac { 1 } { 2 } } { 2 } \\times 2 = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3815.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x = \\frac { 1 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3816.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 25 - 30 = 5.",
|
|
"gt_answers": "\\frac { 7 } { 1 2 } = \\frac { 3 5 } { 6 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3817.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 4x2 + 7x + 2 = 10.",
|
|
"gt_answers": "\\frac { 4 } { 7 } = \\frac { 4 \\times 2 } { 7 \\times 2 } = \\frac { 8 } { 1 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3818.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"lati = 2\" using LaTeX format.",
|
|
"gt_answers": "\\vert a \\vert + 1 = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3819.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^3 + 3x^2 - 4x - 3 = 0.\"",
|
|
"gt_answers": "x = \\frac { 4 } { 3 } \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3820.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 0.550000000000000550000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 . 5 < 0 . 5 0 1 < 0 . 5 1 0 < 0 . 5 1 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3822.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{15}{13} = \\frac{15}{13}\n\\end{equation}\n\nThis is a simple mathematical expression that represents the ratio of two numbers, 15 and 13.",
|
|
"gt_answers": "x : 3 = 5 : 7 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3823.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nFet + HSO4 + H2O = Feso + H3O + H2SO4\n\nThis formula represents the reaction of aqueous solutions of ferrous sulfate (FeSO4) and hydrogen peroxide (H2O2) to produce ferrous sulfate hexahydrate (Feso) and hydrogen sulfate (H2SO4).",
|
|
"gt_answers": "F e + H _ { 2 } S O _ { 4 } = F e S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_3824.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac",
|
|
"gt_answers": ": \\overrightarrow { A F } = \\overrightarrow { A E } + \\overrightarrow { E F } = \\frac { 3 } { 4 } \\overrightarrow { b } + \\overrightarrow { a } - \\frac { 1 } { 4 } \\overrightarrow { b } = \\overrightarrow { o } + \\frac { 1 } { 2 } \\overrightarrow { b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3825.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 5\\)",
|
|
"gt_answers": "\\frac { x ^ { 2 } + 1 } { x } - \\frac { 2 x } { x ^ { 2 } + 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3826.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2} + \\frac{x^3}{3} + \\frac{x^4}{4} + \\frac{x^5}{5} + \\frac{x^6}{6} + \\frac{x^7}{7} + \\frac{x^8}{8} + \\frac{x^9}{9} + \\frac{x^{10}}{10} + \\frac{x^{11}}{11} + \\frac{x^{12}}{12} + \\frac{x^{13}}{13} + \\frac{x^{14}}{14} + \\frac{x^{15}}{15} + \\frac{x^{16}}{16} + \\frac{x^{17}}{17} + \\frac{x^{18}}{18} + \\frac{x^{19}}{19} + \\frac{x^{20}}{20} + \\frac{x^{21}}{21} + \\frac{x^{22}}{22} + \\frac{x^{23}}{23} + \\frac{x^{24}}{24} + \\frac{x^{25}}{25} + \\frac{x^{26}}{26} + \\frac{x^{27}}{27} + \\frac{x^{28}}{28} + \\frac{x^{29}}{29} + \\frac{x^{30}}{30} + \\frac{x^{31}}{31} + \\frac{x^{32}}{32} + \\frac{x^{33}}{33} + \\frac{x^{34}}{34} + \\frac{x^{35}}{35} + \\frac{x^{36}}{36} + \\frac{x^{37}}{37} + \\frac{x^{38}}{38} + \\frac{x^{39}}{39} + \\frac{x^{40}}{40} + \\frac{x^{41}}{41} + \\frac{x^{42}}{42} + \\frac{x^{43}}{43} + \\frac{x",
|
|
"gt_answers": "\\therefore a ^ { 2 } = b ^ { 2 } + c ^ { 2 } - 2 b \\cos A\n",
|
|
"image_path": "./data/HME100K/test_images/test_3827.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: \"60 + 30 = 90.\"",
|
|
"gt_answers": "\\angle B A E = \\angle A E B = 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3831.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, and their sum. The equation states that the sum of x and y is equal to 10.",
|
|
"gt_answers": "1 - \\frac { 3 } { 8 } - \\frac { 1 } { 8 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3832.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x + 5y = 9.",
|
|
"gt_answers": "\\frac { 3 } { 5 } = \\frac { 3 \\times 9 } { 5 \\times 9 } = \\frac { 2 7 } { 4 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3833.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{5}{6} + \\frac{6}{5} = \\frac{11}{10}\n\\end{equation}",
|
|
"gt_answers": "5 \\div 6 = \\frac { 5 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3834.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3(100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 7 1 \\div \\frac { 3 } { 7 } = 1 0 9 9 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3836.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 4x^2 + 4x + 1 = 0.",
|
|
"gt_answers": "4 x + 4 - 9 6 = 1 2 x - 3 x + 2 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3837.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 15.",
|
|
"gt_answers": "x ^ { 2 } = 1 5 + \\frac { \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3839.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2H2O + 2HCl \u2192 2H3O+ + Cl2.",
|
|
"gt_answers": "( 5 ) C l _ { 2 } + H _ { 2 } O = H ^ { + } + C l ^ { - } + H C l O\n",
|
|
"image_path": "./data/HME100K/test_images/test_3842.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4x^2 + 4x + 1 = 0\\)",
|
|
"gt_answers": "3 ( x - 2 ) - ( x - 1 ) = x ^ { 2 } - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3843.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 16\\)",
|
|
"gt_answers": "1 6 x : 2 1 ( 5 1 - x ) = 5 : 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3844.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2s^2 + 2s + 1 = 3.",
|
|
"gt_answers": "2 S n - 1 = a _ { n - 1 } ^ { 2 } + a _ { n - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3845.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 2y^2 = 18x^2 + 18y^2\\)",
|
|
"gt_answers": "( 7 \\times 2 ) + ( 7 \\times 5 ) + ( 2 \\times 5 ) \\times 2 = 1 1 8 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3846.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 10 = 0\\)",
|
|
"gt_answers": "\\boxed { 4 0 x + } 0 . 6 ( 4 0 - 1 0 ) + 4 0 x = 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3847.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1.4314 x 0.5 x 0.3333 = 0.0777.",
|
|
"gt_answers": "1 ^ { 2 } \\times 3 . 1 4 \\times 0 . 5 \\times \\frac { 1 } { 3 } = \\frac { 1 5 7 } { 3 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3848.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "A F = \\frac { 1 } { 2 } B D \\Rightarrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_3849.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = z^2\\)",
|
|
"gt_answers": "x _ { 2 } = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3851.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as follows:\n\n\\(A + B \\cdot (1 - \\frac{A}{B})^{2} = 0\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\nA + B \\cdot (1 - \\frac{A}{B})^{2} = 0\n\\end{equation}\n\nThe equation is a quadratic equation in the variable A, with B as a constant.",
|
|
"gt_answers": "B O = A B \\tan A = 2 0 \\tan 6 0 ^ { \\circ } = 2 0 \\times \\frac { \\sqrt { 2 } } { 3 } = \\frac { 2 0 \\sqrt { 2 } } { 3 } ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3852.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "1 \\frac { 2 } { 5 } \\textcircled { > } \\frac { 3 } { 8 } \\textcircled { > } 0 . 3 4 > \\frac { 1 } { 3 } \\textcircled { > } 0 . 3 0 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3853.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 6 } { 5 8 } \\approx 1 0 \\% 3 6 0 \\times 1 0 \\% = 3 6 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3854.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"P(A or B) = P(A) + P(B) - P(A and B).\"",
|
|
"gt_answers": "P _ { 2 } = \\frac { 1 } { 3 } P _ { ( A C ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3855.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\right) = \\frac{1}{4} \\).",
|
|
"gt_answers": "a = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3856.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "1 2 \\times 1 2 = 1 4 4 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3857.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 8x + 3y = 22.",
|
|
"gt_answers": "6 + \\frac { x } { 3 } = \\frac { 8 - 2 x } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3861.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"sin(A) = sin(A) + sin(A)\".",
|
|
"gt_answers": "S i n A = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3862.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 111 = 333.",
|
|
"gt_answers": "1 1 y = 3 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3863.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nx = 10 - 9/x\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\nx = 10 - \\frac{9}{x}\n\\end{equation}\n\nThe equation is a linear equation in the variable x, with the constant 10 on the left side and the variable 9 on the right side. The division sign \"/\" is used to indicate the operation of division.",
|
|
"gt_answers": "x = \\frac { 9 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3864.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\n\\(m = \\frac{food \\cdot time}{food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time + food \\cdot time +",
|
|
"gt_answers": "\\rho = \\frac { m } { V } = \\frac { 2 k g } { 2 . 5 \\times 1 0 ^ { - 3 } m ^ { 3 } } = 8 0 0 k g / m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3866.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 3x + 2 = 0\\)",
|
|
"gt_answers": "x = \\pm 3 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3867.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ln(x) = 1/x + 1/x^2 + 1/x^3 + 1/x^4 + 1/x^5 + 1/x^6 + 1/x^7 + 1/x^8 + 1/x^9 + 1/x^10 + 1/x^11 + 1/x^12 + 1/x^13 + 1/x^14 + 1/x^15 + 1/x^16 + 1/x^17 + 1/x^18 + 1/x^19 + 1/x^20 + 1/x^21 + 1/x^22 + 1/x^23 + 1/x^24 + 1/x^25 + 1/x^26 + 1/x^27 + 1/x^28 + 1/x^29 + 1/x^30 + 1/x^31 + 1/x^32 + 1/x^33 + 1/x^34 + 1/x^35 + 1/x^36 + 1/x^37 + 1/x^38 + 1/x^39 + 1/x^40 + 1/x^41 + 1/x^42 + 1/x^43 + 1/x^44 + 1/x^45 + 1/x^46 + 1/x^47 + 1/x^48 + 1/x^49 + 1/x^50 + 1/x^51 + 1/x^52 + 1/x^53 + 1/x^54 + 1/x^55 + 1/x^56 + 1/x^57 + 1/x^58 + 1/x^59 + 1/x^60 + 1/x^61 + 1/x^62 + 1/x^63 + 1/",
|
|
"gt_answers": "( 5 . 5 - 2 . 5 ) x + 5 - 5 \\times 4 8 = 4 8 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3869.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x = \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3871.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\nx^2 + y^2 = 1",
|
|
"gt_answers": "x = 7 o r x = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3872.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 4d^2 = 343d^2\\)",
|
|
"gt_answers": "7 \\times 7 \\times 7 = 3 4 3 d m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3873.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A - PT = CD.\"",
|
|
"gt_answers": "\\frac { A B } { D F } = \\frac { A D } { C D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3875.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "( \\frac { 1 } { x - y } + \\frac { 2 } { x ^ { 2 } - x y } ) \\div \\frac { x + 2 } { 2 x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3876.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 3x + 2 = 0.\"",
|
|
"gt_answers": "x = - 1 \\frac { 1 } { 3 } - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3877.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(L = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "\\angle 1 = \\frac { 1 } { 2 } \\angle A B C , \\angle 2 = \\frac { 1 } { 2 } \\angle A C B\n",
|
|
"image_path": "./data/HME100K/test_images/test_3878.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"77+33=110\".",
|
|
"gt_answers": "6 0 = ( 7 ) + ( 3 3 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3879.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"7x7 = 49.\"",
|
|
"gt_answers": "\\frac { 1 } { 1 2 } x - \\frac { 1 } { 6 } + 1 = 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_3880.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 170 - 20x10 = 10x100.",
|
|
"gt_answers": "\\frac { 1 7 - 2 0 x } { 3 } = \\frac { 1 0 x } { 7 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3881.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = 4a^2 + 4b^2\\)",
|
|
"gt_answers": "- 2 a = - \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3882.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x - 4 = 0.",
|
|
"gt_answers": "\\Delta = a ^ { 2 } - 4 \\times 4 \\times 4 < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_3883.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "S _ { 1 } ^ { 2 } = \\frac { 1 } { 5 } [ ( 8 5 - 8 5 ) ^ { 2 } + ( 7 5 - 8 5 ) ^ { 2 } + ( 8 0 - 8 5 ) ^ { 2 } + ( 8 5 - 8 5 ) ^ { 2 } + ( 1 0 0 - 8 5 ) ^ { 2 } ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_3884.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LACE-60\u00b0\".",
|
|
"gt_answers": "\\angle A C E = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3885.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x^2 - 3x + 1 = 0.\"",
|
|
"gt_answers": "x _ { 1 } = 0 . x _ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3886.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as U.i9v3.5eV.v7.5eV.",
|
|
"gt_answers": "U _ { 1 } ^ { \\prime } = 9 V - 1 . 5 V = 7 . 5 V\n",
|
|
"image_path": "./data/HME100K/test_images/test_3888.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(F = \\frac{1}{2}mv^2\\)\n\nThis formula represents the relationship between force (F) and the mass (m) of an object and its velocity (v).",
|
|
"gt_answers": "F _ { 1 } L _ { 1 } = F _ { 2 } L _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3889.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x9 + 6 = 33.",
|
|
"gt_answers": "3 \\times 9 + 6 = 3 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3890.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Wm R2 + R1 R3 + R2 R4 + R3 R5 + R4 R6 + R5 R7 + R6 R8 + R7 R9 + R8 R10 + R9 R11 + R10 R12 + R11 R13 + R12 R14 + R13 R15 + R14 R16 + R15 R17 + R16 R18 + R17 R19 + R18 R20 + R19 R21 + R20 R22 + R21 R23 + R22 R24 + R23 R25 + R24 R26 + R25 R27 + R26 R28 + R27 R29 + R28 R30 + R29 R31 + R30 R32 + R31 R33 + R32 R34 + R33 R35 + R34 R36 + R35 R37 + R36 R38 + R37 R39 + R38 R40 + R39 R41 + R40 R42 + R41 R43 + R42 R44 + R43 R45 + R44 R46 + R45 R47 + R46 R48 + R47 R49 + R48 R50 + R49 R51 + R50 R52 + R51 R53 + R52 R54 + R53 R55 + R54 R56 + R55 R57 + R56 R58 + R57 R59 + R58 R60 + R59 R61 + R60 R62 + R61 R63 + R62 R64 + R63 R65 + R64 R66 + R65 R67 + R66 R68 + R67 R69 + R68 R70 + R69 R71 + R70 R72 + R71 R73 + R72 R74 + R73 R75 + R7",
|
|
"gt_answers": "\\frac { U _ { 1 } } { U _ { 2 } } = \\frac { R _ { 1 } } { R _ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3891.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 + h^2 + i^2 + j^2 + k^2 + l^2 + m^2 + n^2 + o^2 + p^2 + q^2 + r^2 + s^2 + t^2 + u^2 + v^2 + w^2 + x^2 + y^2 + z^2 = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 \\cdot \\frac { a _ { 1 } ( 1 - q ^ { 3 } ) } { 1 - q } = 5 a _ { 1 } + 3 \\cdot \\frac { a _ { 1 } ( 1 - q ^ { 2 } ) \\cdot } { 1 - q }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3892.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 7 + 90 = 91.",
|
|
"gt_answers": "7 \\times 9 0 = 9 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_3894.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(12 = 1 \\times 12 + 2 \\times 12\\)",
|
|
"gt_answers": "1 - \\frac { 5 } { 1 2 } = \\frac { 7 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3895.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. The variable x represents the x-coordinate of a point on a graph, and y represents the y-coordinate. The equation states that the sum of the squares of these two variables is equal to 1. This equation is commonly used in geometry and algebra to represent the distance between two points on a line or a circle.",
|
|
"gt_answers": "1 2 k ^ { 2 } = k ^ { 2 } + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3896.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6x4 = 24.\"",
|
|
"gt_answers": "x _ { 4 } = - \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3898.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 3 = 5x^2 + 3x + 4\\)",
|
|
"gt_answers": "( x + 1 4 x ) + ( 5 + 1 4 + 5 ) = 3 6 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_3899.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "W _ { 2 } = 9 ( 2 0 - x ) - \\cdot [ 1 2 + 3 ( 2 0 - x ) ] = 1 0 8 - 6 x \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_3900.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(5x^2 + 3x - 2 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x : \\frac { 2 5 } { 2 } = \\frac { 1 2 } { 5 } : 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_3901.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nP(A or B) = P(A) + P(B) - P(A and B)\n\nThis formula represents the probability of A or B occurring, where A and B are two events. The probability of A occurring is represented by P(A), the probability of B occurring is represented by P(B), and the probability of both A and B occurring is represented by P(A and B). The formula calculates the sum of these three probabilities and subtracts the probability of both A and B occurring from the sum to obtain the probability of A or B occurring.",
|
|
"gt_answers": "R = \\frac { R _ { 0 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3902.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\ce{NaCl + H2SO4 -> Na2SO4 + HCl}\n\\end{equation}\n\nThis equation represents the chemical reaction between sodium chloride (NaCl) and hydrogen sulfate (H2SO4) to form sodium sulfate (Na2SO4) and hydrochloric acid (HCl).",
|
|
"gt_answers": "\u3001 a _ { 1 } < a _ { 2 } < \\cdots \\angle a _ { 7 } < a _ { 8 } < a _ { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3904.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"LaoE = 360/180 = 2.\"",
|
|
"gt_answers": "\\angle D O E = 3 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3905.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(J_b = \\frac{1}{2} \\left( \\frac{1}{3} \\left( \\frac{1}{4} \\left( \\frac{1}{5} \\left( \\frac{1}{6} \\left( \\frac{1}{7} \\left( \\frac{1}{8} \\left( \\frac{1}{9} \\left( \\frac{1}{10} \\left( \\frac{1}{11} \\left( \\frac{1}{12} \\left( \\frac{1}{13} \\left( \\frac{1}{14} \\left( \\frac{1}{15} \\left( \\frac{1}{16} \\left( \\frac{1}{17} \\left( \\frac{1}{18} \\left( \\frac{1}{19} \\left( \\frac{1}{20} \\left( \\frac{1}{21} \\left( \\frac{1}{22} \\left( \\frac{1}{23} \\left( \\frac{1}{24} \\left( \\frac{1}{25} \\left( \\frac{1}{26} \\left( \\frac{1}{27} \\left( \\frac{1}{28} \\left( \\frac{1}{29} \\left( \\frac{1}{30} \\left( \\frac{1}{31} \\left( \\frac{1}{32} \\left( \\frac{1}{33} \\left( \\frac{1}{34} \\left( \\frac{1}{35} \\left( \\frac{1}{36} \\left( \\frac{1}{37} \\left( \\frac{1}{38} \\left( \\frac{1}{39} \\left( \\frac{1}{40} \\left( \\frac{1}{41} \\left( \\frac{1}{42} \\left( \\frac{1}{43} \\left( \\frac{1}{44} \\left( \\frac{1}{45} \\left( \\frac{1}{46} \\left( \\frac{",
|
|
"gt_answers": "\\sqrt { ( \\sqrt { 3 } - 1 ) ^ { 2 } } = \\vert \\sqrt { 3 } - 1 \\vert = \\sqrt { 3 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3906.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 800^2\\)",
|
|
"gt_answers": "8 . 5 \\div \\frac { 1 } { 1 0 0 } = 8 5 0 ( c m ) = 8 . 5 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3907.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with three variables and an equal sign, which is a common type of equation in mathematics.",
|
|
"gt_answers": "3 \\div 4 = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3908.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(v_1 = v_2 + v_3 + v_4 + v_5 + v_6 + v_7\\)",
|
|
"gt_answers": "2 u - v = 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_3909.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(b_1^2 + b_2^2 + b_3^2 + b_4^2 = b_1^2 + b_2^2 + b_3^2 + b_4^2 + b_5^2 + b_6^2 + b_7^2 + b_8^2 + b_9^2 + b_{10}^2 + b_{11}^2 + b_{12}^2 + b_{13}^2 + b_{14}^2 + b_{15}^2 + b_{16}^2 + b_{17}^2 + b_{18}^2 + b_{19}^2 + b_{20}^2 + b_{21}^2 + b_{22}^2 + b_{23}^2 + b_{24}^2 + b_{25}^2 + b_{26}^2 + b_{27}^2 + b_{28}^2 + b_{29}^2 + b_{30}^2 + b_{31}^2 + b_{32}^2 + b_{33}^2 + b_{34}^2 + b_{35}^2 + b_{36}^2 + b_{37}^2 + b_{38}^2 + b_{39}^2 + b_{40}^2 + b_{41}^2 + b_{42}^2 + b_{43}^2 + b_{44}^2 + b_{45}^2 + b_{46}^2 + b_{47}^2 + b_{48}^2 + b_{49}^2 + b_{50}^2 + b_{51}^2 + b_{52}^2 + b_{53}^2 + b_{54}^2 + b_{55}^2 + b_{56}^2 + b_{57}^2 + b_{58}^2 + b_{59}^2 + b_{60}^2 + b_{61}^2 + b_{62}^2 + b_{63}^2 + b_{64}^2 + b_{65}^2 + b_{66}^2 + b_{67}^2 + b_{68}^2 + b_{6",
|
|
"gt_answers": "_ { \\cdot } s = \\frac { b ^ { 2 } + c ^ { 2 } - 2 b c \\cos A - b ^ { 2 } - c ^ { 2 } } { 4 } = - \\frac { b c \\cos A } { 2 } = \\frac { 1 } { 2 } b c \\sin A\n",
|
|
"image_path": "./data/HME100K/test_images/test_3911.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(8\\text{BCP} = 3\\text{BCP} + 5\\text{BCP} + 4\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} + 3\\text{BCP} + 2\\text{BCP} +",
|
|
"gt_answers": "S \\Delta B C P = - 3 y \\times \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3912.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: R = 1/2(V^2/R + V^2/2R + V^2/3R + V^2/4R + V^2/5R + V^2/6R + V^2/7R + V^2/8R + V^2/9R + V^2/10R + V^2/11R + V^2/12R + V^2/13R + V^2/14R + V^2/15R + V^2/16R + V^2/17R + V^2/18R + V^2/19R + V^2/20R + V^2/21R + V^2/22R + V^2/23R + V^2/24R + V^2/25R + V^2/26R + V^2/27R + V^2/28R + V^2/29R + V^2/30R + V^2/31R + V^2/32R + V^2/33R + V^2/34R + V^2/35R + V^2/36R + V^2/37R + V^2/38R + V^2/39R + V^2/40R + V^2/41R + V^2/42R + V^2/43R + V^2/44R + V^2/45R + V^2/46R + V^2/47R + V^2/48R + V^2/49R + V^2/50R + V^2/51R + V^2/52R + V^2/53R + V^2/54R + V^2/55R + V^2/56R + V^2/57R + V^2/58R + V^2/59R + V^2/60R + V^2/61R + V^2/62R + V^2/63R +",
|
|
"gt_answers": "R = \\frac { U } { I } = \\frac { 3 V } { 0 . 2 2 A } = 1 3 . 6 \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_3915.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is represented by the letter \"c,\" the side opposite the right angle is represented by \"a,\" and the side adjacent to the right angle is represented by \"b.\"",
|
|
"gt_answers": "( a + b ) ^ { 3 } = a ^ { 3 } + b ^ { 3 } + 3 a ^ { 2 } b + 3 b ^ { 2 } a = 2 + 3 a b\n",
|
|
"image_path": "./data/HME100K/test_images/test_3916.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/2(x + 1) - 1/2(x - 1) = 1/4(x^2 - 1)",
|
|
"gt_answers": "\\frac { A M } { D M } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3919.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(x^2 + 1000x + 1500 = 0\\)\n\nThis formula can be written in LaTeX as:\n\n\\(x^2 + 1000x + 1500 = 0\\)",
|
|
"gt_answers": "\\frac { 1 5 0 0 } { x } = \\frac { 1 5 0 0 } { x + 2 0 } + 2 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_3921.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 5x + 15 = 0\\)",
|
|
"gt_answers": "5 x = 1 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_3923.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(17^{2} - 9^{2} = 10^{2} - 9^{2} = 100 - 81 = 9\\)",
|
|
"gt_answers": "1 7 - 9 = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3924.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x^2 + 3x - 5 = 0.",
|
|
"gt_answers": "\\frac { 2 x - 1 } { 3 } \\leq 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_3925.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"MN:DN=23\".",
|
|
"gt_answers": "M N : D N = 2 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3926.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 4 = 16\\)",
|
|
"gt_answers": "x _ { 1 } = \\frac { - \\sqrt { 6 } + 3 \\sqrt { 6 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3928.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(A + B \\cdot x^2 + C \\cdot x^3 + D \\cdot x^4 + E \\cdot x^5 + F \\cdot x^6 + G \\cdot x^7 + H \\cdot x^8 + I \\cdot x^9 + J \\cdot x^{10} + K \\cdot x^{11} + L \\cdot x^{12} + M \\cdot x^{13} + N \\cdot x^{14} + O \\cdot x^{15} + P \\cdot x^{16} + Q \\cdot x^{17} + R \\cdot x^{18} + S \\cdot x^{19} + T \\cdot x^{20} + U \\cdot x^{21} + V \\cdot x^{22} + W \\cdot x^{23} + X \\cdot x^{24} + Y \\cdot x^{25} + Z \\cdot x^{26} = 27x^{27} + 28x^{28} + 29x^{29} + 30x^{30} + 31x^{31} + 32x^{32} + 33x^{33} + 34x^{34} + 35x^{35} + 36x^{36} + 37x^{37} + 38x^{38} + 39x^{39} + 40x^{40} + 41x^{41} + 42x^{42} + 43x^{43} + 44x^{44} + 45x^{45} + 46x^{46} + 47x^{47} + 48x^{48} + 49x^{49} + 50x^{50} + 51x^{51} + 52x^{52} + 53x^{53} + 54x^{54} + 55x^{55} + 56x^{56} + 57x^{57} + 58x",
|
|
"gt_answers": "A B ^ { 2 } = x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_3929.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `3x + 2 = 5`.",
|
|
"gt_answers": "x _ { 3 } = - \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3930.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"MgCl2 + 2HCl = MgCl4 + 2H2O.\"",
|
|
"gt_answers": "M g + 2 H C l = M g C l _ { 2 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_3931.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(k_1 = 2 + 4k_2\\)",
|
|
"gt_answers": "k ^ { 2 } = 2 ^ { 2 } + ( 4 - k ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3932.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\sqrt{2} \\right)^2 = \\frac{1}{4} \\left( \\sqrt{4} \\right)^2 = \\frac{1}{4} \\left( \\sqrt{8} \\right)^2 = \\frac{1}{8} \\left( \\sqrt{16} \\right)^2 = \\frac{1}{16} \\left( \\sqrt{32} \\right)^2 = \\frac{1}{32} \\left( \\sqrt{64} \\right)^2 = \\frac{1}{64} \\left( \\sqrt{128} \\right)^2 = \\frac{1}{128} \\left( \\sqrt{256} \\right)^2 = \\frac{1}{256} \\left( \\sqrt{512} \\right)^2 = \\frac{1}{512} \\left( \\sqrt{1024} \\right)^2 = \\frac{1}{1024} \\left( \\sqrt{2048} \\right)^2 = \\frac{1}{2048} \\left( \\sqrt{4096} \\right)^2 = \\frac{1}{4096} \\left( \\sqrt{8192} \\right)^2 = \\frac{1}{8192} \\left( \\sqrt{16384} \\right)^2 = \\frac{1}{16384} \\left( \\sqrt{32768} \\right)^2 = \\frac{1}{32768} \\left( \\sqrt{65536} \\right)^2 = \\frac{1}{65536} \\left( \\sqrt{131072} \\right)^2 = \\frac{1}{131072} \\left( \\sqrt{262144} \\right)^2 = \\frac{1}{262144} \\left( \\sqrt{524288} \\right)^2 = \\frac{1}{524288} \\left( \\sqrt{10485",
|
|
"gt_answers": "v = \\sqrt { g R \\tan \\theta }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3933.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6 = 3 + 3 + 2 + 1.\"",
|
|
"gt_answers": "\\frac { 3 } { x _ { 1 } } + \\frac { 3 } { x _ { 2 } } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_3934.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(15 \\times 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 3 } { 4 } < 0 . 7 6 < 1 . 5 < 1 \\frac { 3 } { 5 } < \\frac { 1 5 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3935.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 4\\)",
|
|
"gt_answers": "y _ { 1 } = \\frac { \\sqrt { 1 0 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3936.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(AB = \\sqrt{A^2 + B^2}\\)",
|
|
"gt_answers": "A B = \\sqrt { 4 ^ { 2 } + 3 ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3937.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x^2 + 3x + 4.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_3938.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(K_c = \\frac{1}{1 + \\left( \\frac{RT}{P_o} \\right)^2}\\)\n\nwhere K_c is the equilibrium constant for the reaction, R is the universal gas constant, T is the temperature in Kelvin, P_o is the partial pressure of oxygen, and K_c is the equilibrium constant for the reaction.",
|
|
"gt_answers": "k = 0 \\Rightarrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_3939.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{",
|
|
"gt_answers": "\\Delta F E C \\sim \\Delta F B A .\n",
|
|
"image_path": "./data/HME100K/test_images/test_3941.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 4x + 3 = 10\\)\n\nThis formula can be represented using the LaTeX code:\n\n\\(x^2 + 4x + 3 = 10\\)\n\nThe LaTeX code uses the `\\( ... \\)` and `\\( ... \\)` symbols to denote the beginning and end of the formula, respectively. The `\\( ... \\)` symbol is used to enclose the entire formula, while the `\\( ... \\)` symbol is used to enclose the individual terms within the formula.",
|
|
"gt_answers": "\\frac { 3 } { 4 } x - 1 + 2 = - \\frac { 4 } { 3 } ( x - \\frac { 1 } { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3943.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is: ABU DHB PHB.",
|
|
"gt_answers": "A B = C D D H = B F D G = B E\n",
|
|
"image_path": "./data/HME100K/test_images/test_3944.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 233099999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
|
|
"gt_answers": "2 3 : 0 0 - 9 : 0 0 = 1 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_3945.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(E_{i,j} = \\frac{1}{2} \\left( \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\overrightarrow { D E } = - \\overrightarrow { E D } = - \\overrightarrow { C F } = - \\overrightarrow { F A }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3946.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{2x^2 - 3x + 1}{x^2 + 2x + 1}\\)",
|
|
"gt_answers": "p ( x , - \\frac { 1 } { 2 } x ^ { 2 } - x + 4 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3947.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2019 \\times 2020 \\times 2021 \\times 2022 \\times 2023 \\times 2024 \\times 2025 \\times 2026 \\times 2027 \\times 2028 \\times 2029 \\times 2030 \\times 2031 \\times 2032 \\times 2033 \\times 2034 \\times 2035 \\times 2036 \\times 2037 \\times 2038 \\times 2039 \\times 2040 \\times 2041 \\times 2042 \\times 2043 \\times 2044 \\times 2045 \\times 2046 \\times 2047 \\times 2048 \\times 2049 \\times 2050 \\times 2051 \\times 2052 \\times 2053 \\times 2054 \\times 2055 \\times 2056 \\times 2057 \\times 2058 \\times 2059 \\times 2060 \\times 2061 \\times 2062 \\times 2063 \\times 2064 \\times 2065 \\times 2066 \\times 2067 \\times 2068 \\times 2069 \\times 2070 \\times 2071 \\times 2072 \\times 2073 \\times 2074 \\times 2075 \\times 2076 \\times 2077 \\times 2078 \\times 2079 \\times 2080 \\times 2081 \\times 2082 \\times 2083 \\times 2084 \\times 2085 \\times 2086 \\times 2087 \\times 2088 \\times 2089",
|
|
"gt_answers": "1 2 0 \\div 1 2 = 1 0 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3949.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 + 100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 119 + 120 + 12",
|
|
"gt_answers": "5 1 2 \\div 6 7 = 7 \\cdots\n",
|
|
"image_path": "./data/HME100K/test_images/test_3950.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a line of Chinese characters, which could be a representation of a mathematical expression in Chinese.",
|
|
"gt_answers": "x = - \\frac { C } { A }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3952.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, which are not supported by LaTeX. However, the image shows a mathematical formula with the letters \"E\" and \"B\" in it. The formula could be written in LaTeX as follows:\n\nE + B = C",
|
|
"gt_answers": "1 0 + \\sqrt { 3 } = x +\n",
|
|
"image_path": "./data/HME100K/test_images/test_3953.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a = \\frac{b \\times c}{180^{\\circ}}\\)",
|
|
"gt_answers": "\\cdot \\angle O B D + \\angle B O C = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3954.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a2 + b2 = c2.",
|
|
"gt_answers": "a = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3955.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 1 = 3x + 1.",
|
|
"gt_answers": "\\frac { 2 x } { ( x + 3 ) ( y - 1 ) } + \\frac { 1 } { x + 3 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3957.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(E = h \\cdot f \\cdot c\\)\n\nwhere E is the energy, h is the Planck's constant, f is the frequency, and c is the speed of light.",
|
|
"gt_answers": "\\frac { \\sqrt { 3 } } { 3 } = \\frac { \\sqrt { 1 5 } } { 6 } h\n",
|
|
"image_path": "./data/HME100K/test_images/test_3958.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"f(x) = 2x^2 - 3x + 1.\"",
|
|
"gt_answers": "x = \\frac { 3 } { a + 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3959.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + 2x + 3 = 10\n\\end{aligned}\n\\end{equation}",
|
|
"gt_answers": "\\frac { 1 } { 4 } x - \\frac { 1 } { 2 } - 3 + 4 = x\n",
|
|
"image_path": "./data/HME100K/test_images/test_3960.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 = c^2\\)\n\nwhere a, b, and c are real numbers.",
|
|
"gt_answers": "g ( 1 - \\frac { 3 } { 5 } s ) = \\frac { 1 } { 2 } ( 2 a 5 + V _ { p } ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3961.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 10x10x6000cm^2.",
|
|
"gt_answers": "1 0 \\times 1 0 \\times 6 = 6 0 0 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3962.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x + 1 = 5.",
|
|
"gt_answers": "\\frac { x } { x + 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3963.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x1",
|
|
"gt_answers": "1 0 \\times 8 \\times 2 = 1 6 0 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3964.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 2x - 1 = 0`.",
|
|
"gt_answers": "5 \\frac { 1 } { 2 } - 3 \\times 1 = a + \\frac { 1 } { 4 } \\times 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3965.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(P(T = 16) = \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\cdot \\frac{1}{6} \\",
|
|
"gt_answers": "\\sqrt { 2 5 + x ^ { 2 } } = \\sqrt { 9 + ( 1 6 - x ) ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3967.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + 1) - 2x(2x + ",
|
|
"gt_answers": "\\frac { 3 } { 1 6 } \\times \\frac { 8 } { 2 7 } = \\frac { 1 } { 1 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3968.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x = 2 + 3\" using LaTeX format.",
|
|
"gt_answers": "\\cos x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3969.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x = \\frac { 2 } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3970.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the image shows a mathematical formula with a negative sign, which could be written as:\n\n-x + y = z\n\nwhere x, y, and z are unknown variables.",
|
|
"gt_answers": "x _ { 1 } = \\frac { - 3 + \\sqrt { 1 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3971.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": ": \\frac { h ( n + 1 ) } { 2 } < s < \\frac { h ( n + i ) } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3972.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a number and a symbol, which could be a mathematical operator or a variable.",
|
|
"gt_answers": "\\frac { 1 } { 3 } x = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3973.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x100x",
|
|
"gt_answers": "\\frac { 1 0 0 x - 1 0 0 } { 2 5 } - \\frac { 1 0 0 x } { 1 2 5 } = \\frac { 6 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3974.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{1}{1",
|
|
"gt_answers": "y = \\frac { 1 } { 4 } x + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3976.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 4 = 10\\)",
|
|
"gt_answers": "( 1 2 \\times 4 ) + ( 1 2 \\times 5 ) + ( 4 \\times 5 ) \\times 2 = 2 5 6 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3978.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{25}{6} + \\frac{62}{12} + \\frac{66}{18} + \\frac{69}{24} + \\frac{72}{30} + \\frac{75}{36} + \\frac{78}{42} + \\frac{81}{48} + \\frac{84}{54} + \\frac{87}{60} + \\frac{90}{66} + \\frac{93}{72} + \\frac{96}{78} + \\frac{99}{84} + \\frac{102}{90} + \\frac{105}{96} + \\frac{108}{102} + \\frac{111}{105} + \\frac{114}{108} + \\frac{117}{111} + \\frac{120}{114} + \\frac{123}{117} + \\frac{126}{120} + \\frac{129}{123} + \\frac{132}{126} + \\frac{135}{132} + \\frac{138}{135} + \\frac{141}{138} + \\frac{144}{141} + \\frac{147}{144} + \\frac{150}{147} + \\frac{153}{150} + \\frac{156}{153} + \\frac{159}{156} + \\frac{162}{159} + \\frac{165}{162} + \\frac{168}{165} + \\frac{171}{168} + \\frac{174}{171} + \\frac{177}{174} + \\frac{180}{177} + \\frac{183}{180} + \\frac{186}{183}",
|
|
"gt_answers": "( 2 5 ) < ( 5 2 ) < ( 6 3 ) < ( 6 5 ) < ( 7 2 ) < ( 9 4 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3979.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\overrightarrow { B E } \\bot \\overrightarrow { O S }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3980.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x + 2y = 13\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 3 - 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3981.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5x2 - 16.",
|
|
"gt_answers": "4 0 \\times \\frac { 5 } { 1 6 } = \\frac { 2 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3984.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nNa+ + AgNO3 + H2O \u2192 Ag+ + NaNO3 + H2O",
|
|
"gt_answers": "A a N O _ { 3 } + N a C l = A g C l \\downarrow + N a N O _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3985.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/4\" using LaTeX format.",
|
|
"gt_answers": "x _ { 1 } = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3986.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(2\\pi r^2 + 2\\pi r\\cdot r' + r^2\\cdot r'^2 = 4\\pi r^2\\)\n\nThis formula can be rearranged to solve for the radius of the circle:\n\n\\(r^2 = \\frac{4\\pi r^2 - 2\\pi r\\cdot r' - r^2\\cdot r'^2}{2\\pi r^2}\\)\n\nSolving for r, we get:\n\n\\(r = \\sqrt{\\frac{4\\pi r^2 - 2\\pi r\\cdot r' - r^2\\cdot r'^2}{2\\pi r^2}}\\)\n\nThis formula can be used to find the area of a circle by multiplying the radius squared by the constant \u03c0.",
|
|
"gt_answers": "\\frac { \\sqrt { 3 } } { \\sin A } = \\frac { \\sqrt { 3 } } { \\frac { \\sqrt { 3 } } { 2 } . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3987.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "\\frac { 1 } { a _ { n + 1 } - 1 } - \\frac { 1 } { a _ { n } - 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_3988.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{10} - 2^{9} + 2^{8} - 2^{7} + 2^{6} - 2^{5} + 2^{4} - 2^{3} + 2^{2} - 2^{1} + 2^{0} = 2^{10} - 2^{9} + 2^{8} - 2^{7} + ",
|
|
"gt_answers": "\\vert - \\frac { 2 0 1 5 } { 2 0 1 6 } \\vert < - ( - \\frac { 2 0 1 6 } { 2 0 1 7 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3989.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the image shows a mathematical formula with two numbers and a sign, which could be a simple addition or subtraction problem.",
|
|
"gt_answers": "2 a + \\frac { 2 } { 3 } \\pi = \\frac { 3 } { 2 } \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_3990.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(Zn^{2+}(aq) + Mg^{2+}(aq) + 2Cl^{-}(aq) \\rightarrow Zn^{2+}(aq) + Mg^{2+}(aq) + 2Cl^{2-}(aq)\\)\n\nThe formula represents the chemical reaction between zinc ions (Zn^{2+}(aq)) and magnesium ions (Mg^{2+}(aq)) in aqueous solution, along with the formation of two chloride ions (Cl^{-}(aq)).",
|
|
"gt_answers": "Z n + M g C l _ { 2 } = M g + Z n C l _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3991.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(A + B) - (A - B) = 2(A + B) - (A - B) = 2A + 2B - 2(A - B) = 2A + 2B - 2A + 2B = 4A + 4B.",
|
|
"gt_answers": "\\frac { A G } { E G } = \\frac { G H } { C G }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3994.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a negative sign, which is likely a representation of a negative number or a negative exponent.",
|
|
"gt_answers": "x _ { 2 } = - \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3996.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"0.088 = 100.\"",
|
|
"gt_answers": "0 . 0 8 = \\frac { 8 } { 1 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3997.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 230 - 150 = 80 - 80 = 0.",
|
|
"gt_answers": "2 3 0 - 1 5 0 = 8 0 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_3998.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 60:41 = 1.5.",
|
|
"gt_answers": "6 0 : 5 4 = \\frac { 1 0 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_3999.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 5\\)\n\nThe formula is written in the form of an equation, where the variables x and y are multiplied together and then added to the constant 5.",
|
|
"gt_answers": "\\frac { 2 } { 3 } + \\frac { 2 } { 5 } = \\frac { 2 } { 5 } x - \\frac { 1 } { 3 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4000.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(BCLAC = \\frac{1}{2} \\cdot \\sin(48^\\circ) \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) \\cdot \\sin(48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) \\cdot \\cos(48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) \\cdot \\cos(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) \\cdot \\cos(180^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2} \\cdot \\sin(180^\\circ - 48^\\circ) = \\frac{1}{2}",
|
|
"gt_answers": "B C \\bot A C , \\angle 1 = 4 8 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4001.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 7 = 0\\)",
|
|
"gt_answers": "x = ( 3 . 7 5 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4002.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(P_{A} + P_{B} + P_{C} = P_{AB} + P_{BC} + P_{CA}\\)\n\nThis formula represents the law of conservation of momentum, which states that the total momentum of a system remains constant, regardless of the changes in the momentum of its individual parts. The letters A, B, and C represent the three parts of the system, and the subscripts indicate the momentum of each part. The equation is written in the form of an equation of addition, where the total momentum is the sum of the momenta of the three parts.",
|
|
"gt_answers": "\\frac { y A } { b F } = \\frac { P D } { P B } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4003.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(5x + 3y = 15\\)\n\nThis formula represents a linear equation in two variables, where the variables x and y are related by the constant 5. The equation can be solved by substituting values for x and y to find the values of x and y that make the equation true.",
|
|
"gt_answers": "x = \\frac { 5 } { 2 } \\div \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4004.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(x + 1) - 3(x - 2) = 10.",
|
|
"gt_answers": "1 - \\frac { 4 } { 2 0 } - \\frac { 1 } { 5 } - \\frac { 1 } { 4 } = \\frac { 2 1 } { 2 0 1 0 } = \\frac { 1 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4005.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1}{15} + \\frac{1",
|
|
"gt_answers": "\\frac { 6 } { 5 } = 1 \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4006.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 1 = 10\".",
|
|
"gt_answers": "8 x = \\frac { 4 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4007.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"soom = 4.4488888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888",
|
|
"gt_answers": "S _ { \\Delta O M N } = \\frac { 1 } { 2 } \\cdot 4 \\cdot 4 = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_4008.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(x + 1) - 2x - 1.",
|
|
"gt_answers": "2 H _ { 2 } O _ { 2 } \\rightarrow . 2 H _ { 2 } O + O _ { 2 \\uparrow }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4009.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}",
|
|
"gt_answers": "D F \\bot A C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4010.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 36 - 3 = 48 - 4.",
|
|
"gt_answers": "\\frac { 3 6 } { 4 8 } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4012.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: HCl + AgNO3 = AgCl + HNO3.",
|
|
"gt_answers": "H C l + A g N O _ { 3 } = A g C l \\downarrow + H N O _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4013.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2a^2 + b^2 + 4a^3 + 4b^3 = 16a^2 + 16b^2 + 16a^3 + 16b^3.",
|
|
"gt_answers": "2 a ^ { 3 } + 8 a ^ { 2 } - 6 a + a ^ { 2 } + 4 a - 3 + a + 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4014.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x^2 + 4y^2 = 16.\"",
|
|
"gt_answers": "\\sqrt { 2 x - 4 } = 1 + \\sqrt { x + 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4015.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"X^2 + Y^2 = 100.\"",
|
|
"gt_answers": "x + y = 3 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4016.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 217 + 27 = 244.",
|
|
"gt_answers": "2 1 + \\frac { 7 } { y }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4017.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 8/6 + 8/6 = 16/6.",
|
|
"gt_answers": "\\frac { 7 } { 8 } = \\frac { 7 2 } { 6 3 } \\frac { 6 3 } { 7 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4019.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a number of symbols and characters, which could be related to a scientific or engineering context.",
|
|
"gt_answers": "- 2 \\overrightarrow { a } + 4 \\overrightarrow { b } = ( 1 0 , 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4021.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(N = n \\times \\frac{n}{2} \\times \\frac{n}{3} \\times \\frac{n}{4} \\times \\frac{n}{5} \\times \\frac{n}{6} \\times \\frac{n}{7} \\times \\frac{n}{8} \\times \\frac{n}{9} \\times \\frac{n}{10} \\times \\frac{n}{11} \\times \\frac{n}{12} \\times \\frac{n}{13} \\times \\frac{n}{14} \\times \\frac{n}{15} \\times \\frac{n}{16} \\times \\frac{n}{17} \\times \\frac{n}{18} \\times \\frac{n}{19} \\times \\frac{n}{20} \\times \\frac{n}{21} \\times \\frac{n}{22} \\times \\frac{n}{23} \\times \\frac{n}{24} \\times \\frac{n}{25} \\times \\frac{n}{26} \\times \\frac{n}{27} \\times \\frac{n}{28} \\times \\frac{n}{29} \\times \\frac{n}{30} \\times \\frac{n}{31} \\times \\frac{n}{32} \\times \\frac{n}{33} \\times \\frac{n}{34} \\times \\frac{n}{35} \\times \\frac{n}{36} \\times \\frac{n}{37} \\times \\frac{n}{38} \\times \\frac{n}{39} \\times \\frac{n}{40} \\times \\frac{n}{41} \\times \\frac{n}{42} \\times \\frac{n}{43} \\times \\frac{n}{44} \\times \\frac{n}{45} \\times \\frac{n}{46} \\times \\frac{n}{47} \\times \\frac{n}{48} \\times \\frac{n}{49} \\times \\frac{n}{50} \\times \\frac{n}{51",
|
|
"gt_answers": "u = u _ { 1 } + u _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4022.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "z = \\frac { 1 + i } { 2 } + 2 = - i ( 1 + i ) + 2 = - i + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4023.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { x _ { i } } { x _ { i - 1 } } = \\frac { - a _ { i } + 1 ^ { 2 } } { - a _ { i ^ { 2 } } } = ( \\frac { a _ { i + 1 } } { a _ { i } } ) ^ { 2 } = q\n",
|
|
"image_path": "./data/HME100K/test_images/test_4024.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x^2 + 3x + 5\\)",
|
|
"gt_answers": "l _ { 1 } : y = 2 x - 2 ) = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4025.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(W = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "W = - b ^ { 2 } + 1 6 x + 2 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4026.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CADE = BAE 10\u00b0\".",
|
|
"gt_answers": "\\angle A O E = \\angle B A E = 9 0 ^ { \\circ } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4027.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(MN = 4mL\\)",
|
|
"gt_answers": "M N = M l = \\frac { 1 } { 4 } m ^ { 2 } + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4029.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2k^2 - 2k + 1 = 0\\)",
|
|
"gt_answers": "x _ { 1 } + x _ { 2 } = \\frac { - 2 k } { 1 - k ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4030.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "( 1 - a , 2 a - 5 ) = ( 1 - 2 , 2 \\times 2 - 5 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4033.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4034.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(1387-2(1387-1386)=1387-1385=2\\)",
|
|
"gt_answers": "( 3 8 5 - 3 2 5 ) \\div 3 = 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4035.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1/3 + 2/3 = 1.",
|
|
"gt_answers": "y _ { 3 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4036.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LA\\text{-}AD = 180^{\\circ} - 70^{\\circ} - 16^{\\circ} = 104^{\\circ}\\)",
|
|
"gt_answers": "\\angle A G D = 1 8 0 ^ { \\circ } - 7 0 ^ { \\circ } = 1 1 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4037.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LE = LBFC 90\u00b0\".",
|
|
"gt_answers": "\\angle E = \\angle B F C = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4038.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "\\frac { a } { \\cos A } = \\frac { b } { \\cos B } = \\frac { c } { \\sin C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4039.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mixture of English and Hindi, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few letters and numbers, which could be written in LaTeX as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\text{Sn} & = \\text{Sn-1} + \\text{Sn-2} + \\text{Sn-3} + \\text{Sn-4} + \\text{Sn-5} + \\text{Sn-6} + \\text{Sn-7} + \\text{Sn-8} + \\text{Sn-9} + \\text{Sn-10} + \\text{Sn-11} + \\text{Sn-12} + \\text{Sn-13} + \\text{Sn-14} + \\text{Sn-15} + \\text{Sn-16} + \\text{Sn-17} + \\text{Sn-18} + \\text{Sn-19} + \\text{Sn-20} + \\text{Sn-21} + \\text{Sn-22} + \\text{Sn-23} + \\text{Sn-24} + \\text{Sn-25} + \\text{Sn-26} + \\text{Sn-27} + \\text{Sn-28} + \\text{Sn-29} + \\text{Sn-30} + \\text{Sn-31} + \\text{Sn-32} + \\text{Sn-33} + \\text{Sn-34} + \\text{Sn-35} + \\text{Sn-36} + \\text{Sn-37} + \\text{Sn-38} + \\text{Sn-39} + \\text{Sn-40} + \\text{Sn-41} + \\text{Sn-42} + \\text{Sn-43} + \\text{Sn-44} + \\text{S",
|
|
"gt_answers": "S _ { n } = \\frac { 1 } { 3 ^ { n } } + \\frac { - 1 } { 3 ^ { 2 } } + \\frac { - 3 } { 3 ^ { 3 } } + \\cdots + \\frac { 3 - 2 n } { 3 n }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4040.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x - 3 = 0\\)",
|
|
"gt_answers": "\\frac { 3 x - 2 } { 5 } \\geq \\frac { 2 x + 1 } { 3 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4042.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 12 = 12 - 12.",
|
|
"gt_answers": "\\times 1 8 = \\frac { 1 2 } { 5 } ( k m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4043.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\",
|
|
"gt_answers": "= ( x + \\sqrt { 5 } y i ) ( x - \\sqrt { 5 } y i )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4045.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows: 0.515000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 . 5 1 1 < 0 . 5 0 1 < 0 . 5 1 < 0 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4046.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 9x + 3y = 18.",
|
|
"gt_answers": "x = \\frac { 3 5 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4047.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"daa'd'a\" using LaTeX format.",
|
|
"gt_answers": "D A = D ^ { \\prime } A\n",
|
|
"image_path": "./data/HME100K/test_images/test_4048.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"50x10x30-600000cm^2\".",
|
|
"gt_answers": "5 0 \\times 4 0 \\times 3 0 = 6 0 0 0 0 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4049.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x^2 + 4x^3 + 4x^4 + 4x^5 + 4x^6 + 4x^7 + 4x^8 + 4x^9 + 4x^10 + 4x^11 + 4x^12 + 4x^13 + 4x^14 + 4x^15 + 4x^16 + 4x^17 + 4x^18 + 4x^19 + 4x^20 + 4x^21 + 4x^22 + 4x^23 + 4x^24 + 4x^25 + 4x^26 + 4x^27 + 4x^28 + 4x^29 + 4x^30 + 4x^31 + 4x^32 + 4x^33 + 4x^34 + 4x^35 + 4x^36 + 4x^37 + 4x^38 + 4x^39 + 4x^40 + 4x^41 + 4x^42 + 4x^43 + 4x^44 + 4x^45 + 4x^46 + 4x^47 + 4x^48 + 4x^49 + 4x^50 + 4x^51 + 4x^52 + 4x^53 + 4x^54 + 4x^55 + 4x^56 + 4x^57 + 4x^58 + 4x^59 + 4x^60 + 4x^61 + 4x^62 + 4x^63 + 4x^64 + 4x^65 + 4x^66 + 4x^67 + 4x^68 + 4x^69 + 4x^70 + 4x^71 + 4x^72 + 4x^73 + 4x^74 +",
|
|
"gt_answers": "4 x ^ { 2 } . + 4 ( n - 1 ) x + n ^ { 2 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4050.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(3x + 5) - 3(x - 5) = 12 - 3x + 3x - 5 = 12 - 3x - 8 = 4.",
|
|
"gt_answers": "( 2 ) \\frac { 1 + 1 } { 2 } = 3 - \\frac { 3 y - 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4051.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"m = 4/3 x 10^2.\"",
|
|
"gt_answers": "m \\geq - \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4052.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/A + 1/B = 5/5.",
|
|
"gt_answers": ": O B = \\frac { 1 } { 2 } A B = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4053.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nH2O + 2HCL \u2192 2H2O + Cl2",
|
|
"gt_answers": "C u O + 2 H C l = C u C l _ { 2 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_4055.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 3x + 1\\)",
|
|
"gt_answers": "y = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4056.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(K_c = \\frac{D_4^{4+x} \\cdot D_4^{4-x}}{D_4^{2+x} \\cdot D_4^{2-x}}\\)\n\nThe formula is a quadratic equation in the variable x, where Kc is the concentration of the cation (cationic dye) and D4 is the concentration of the anion (divalent dye). The equation is used to determine the equilibrium constant for the reaction between the cation and anion.",
|
|
"gt_answers": "1 . k = \\frac { C ^ { 2 } _ { ( N O _ { 2 } ) } } { C _ { ( N _ { 2 } O _ { 4 } ) } } = \\frac { 0 . 4 \\times 0 . 4 } { 0 . 2 } = 0 . 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_4058.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A + B = C\" using the Greek letter \"A\" for \"alpha\" and \"B\" for \"beta.\" The letter \"C\" represents the unknown variable.",
|
|
"gt_answers": "A F = A D = B C = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4059.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 7 = 10.",
|
|
"gt_answers": "x = - \\frac { 1 2 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4061.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ladis+ABC\" using the LaTeX formula notation.",
|
|
"gt_answers": "\\angle A D B = \\angle D B C .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4062.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, but it can be translated to English as follows: \"4x4 = 16.\"",
|
|
"gt_answers": "\\frac { 3 } { 4 } ( x - 2 . 7 ) = 4 ^ { \\cdot } 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4063.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4064.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5.15 - 50 = 0.15 x 1.5 kg.",
|
|
"gt_answers": "5 1 . 5 - 5 0 = 1 . 5 ( k g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4065.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(H_2O + O_2 \\rightarrow 2H_2O_2\\)",
|
|
"gt_answers": "- 1 ^ { 2 } + H D ^ { 2 } = D E \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_4067.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, which are not supported by LaTeX. However, I can provide a rough translation of the formula into English:\n\n\"The sum of the squares of the first 100 natural numbers is equal to the sum of the squares of the first 100 even numbers.\"",
|
|
"gt_answers": "( x + 5 ) ( x - 1 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4068.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(F = \\frac{1}{2} \\pi r^2\\)\n\nThis formula represents the area of a circle with a radius of r.",
|
|
"gt_answers": "F _ { 1 } l _ { 1 } = F _ { 2 } l 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4070.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "\\frac { 3 } { 8 } + \\frac { 4 } { 8 } = \\frac { 7 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4071.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/x + 1/y = 1/z.",
|
|
"gt_answers": "x _ { 2 } = \\frac { - 1 - \\sqrt { 5 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4072.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(x - 1) = 3x - 2.",
|
|
"gt_answers": "\\frac { 3 } { 4 } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4073.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is the famous equation of energy, which states that the energy (E) of an object is equal to its mass (m) multiplied by the speed of light squared (c^2).",
|
|
"gt_answers": "[ ( - m ) ^ { 3 } ] ^ { 2 } = m ^ { 3 \\times 2 } = m ^ { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4074.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4075.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis formula represents a linear equation in two variables, where the variables x and y are related to each other by the constant 2. The equation states that the sum of the two variables is equal to 10.",
|
|
"gt_answers": "\\frac { 8 0 - 3 5 } { 8 0 } = \\frac { 4 5 } { 8 0 } = \\frac { 9 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4076.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 4 = 12.\"",
|
|
"gt_answers": "3 \\div 4 = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4078.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1552\\)",
|
|
"gt_answers": "\\frac { ( 1 . 5 \\times 1 . 5 ) \\times 6 } { 2 5 2 } = 1 5 . 1 2 ( d m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4079.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5x + 6.\"",
|
|
"gt_answers": "3 5 \\times 9 = 8 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4080.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{4x^2 + 4x + 4}{x^2 + 4x + 4} = \\frac{4x^2 + 4x + 4}{x^2 + 4x + 4}\n\\end{aligned}\n\\end{equation}\n\nThis is a simple algebraic expression that can be evaluated using the formula for the quotient of two polynomials.",
|
|
"gt_answers": "( 4 k ^ { 2 } + 1 ) x ^ { 2 } + 8 \\sqrt { 3 } k ^ { 2 } x + 1 2 k ^ { 2 } - 4 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4081.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ADDI BUSSI\" using a handwritten style.",
|
|
"gt_answers": "A D / / B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4083.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ABCD\" using LaTeX format.",
|
|
"gt_answers": "A Q \\bot C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_4084.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A = 2(B + C)\" using LaTeX format.",
|
|
"gt_answers": "B A : 5 \\sqrt { 5 } = \\frac { 1 } { 2 } 5 \\sqrt { 5 } = \\frac { 5 } { 2 } \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4085.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 5\\)\n\nThis formula represents the relationship between two variables, x and y, where the sum of their products is equal to 5.",
|
|
"gt_answers": "\\frac { 5 } { 1 2 } + \\frac { 4 } { 1 2 } = \\frac { 9 } { 1 2 } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4086.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\n\\(E = \\frac{1}{2}mv^2\\)\n\nwhere E is the energy, m is the mass, and v is the velocity.",
|
|
"gt_answers": "V = \\frac { s } { t } = \\frac { 1 4 k m } { 1 0 s } = 1 . 4 k m / s = 1 4 0 0 m / s\n",
|
|
"image_path": "./data/HME100K/test_images/test_4087.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"AH + 3 = 3AH.\"",
|
|
"gt_answers": "A H = \\frac { 8 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4088.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: `1/x^2 + 1/x + 1 = 0`.",
|
|
"gt_answers": "D K = \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4089.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x",
|
|
"gt_answers": ", 2 x + y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4090.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2^{20} + 2^{19} + 2^{18} + 2^{17} + 2^{16} + 2^{15} + 2^{14} + 2^{13} + 2^{12} + 2^{11} + 2^{10} + 2^{9} + 2^{8} + 2^{7} + 2^{6} + 2^{5} + 2^{4} + 2^{3} + 2^{2} + 2^{1} + 2^{0} = 10^{20} + 10^{19} + 10^{18} + 10^{17} + 10^{16} + 10^{15} + 10^{14} + 10^{13} + 10^{12} + 10^{11} + 10^{10} + 10^{9} + 10^{8} + 10^{7} + 10^{6} + 10^{5} + 10^{4} + 10^{3} + 10^{2} + 10^{1} + 10^{0} = 10^{20} + 10^{19} + 10^{18} + 10^{17} + 10^{16} + 10^{15} + 10^{14} + 10^{13} + 10^{12} + 10^{11} + 10^{10} + 10^{9} + 10^{8} + 10^{7} + 10^{6} + 10^{5} + 10^{4} + 10^{3} + 10^{2} + 10^{1} + 10^{0} = 10^{20} + 10^{19} + 10^{18} + 10^{17} + 10^{16} + 1",
|
|
"gt_answers": "\\frac { C F } { E D } = \\frac { B F } { E B } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4093.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 3x^2 + 4x + 4 = 10.",
|
|
"gt_answers": "3 x + x = x + 2 \\sqrt { 5 x - 4 } + 5 x - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4094.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2 + 2 = 4\" in LaTeX format.",
|
|
"gt_answers": "C _ { \\Delta A B D } = 2 + \\sqrt { 1 3 } + 5 = 7 + \\sqrt { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4096.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as Y = mx + b.",
|
|
"gt_answers": "4 m = 1 2 m = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4098.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 5670m = 5535.5km.",
|
|
"gt_answers": "5 3 5 0 m = ( 5 . 3 5 ) k m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4099.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "\\overrightarrow { b } = - \\overrightarrow { c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4100.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"G1 + G2 + G3 + G4 = 10.\"",
|
|
"gt_answers": "6 \\div \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4101.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n(5x + 6y) - (5x - 6y) = 10x - 10y",
|
|
"gt_answers": "\\cdot C _ { 2 0 } ^ { k } ( \\frac { 1 } { 2 } ) ^ { k } ( \\frac { 1 } { 2 } ) ^ { 2 0 - k }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4104.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 7x + 5 = 0.\"",
|
|
"gt_answers": "x = \\frac { 7 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4106.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/x + 1/y = 1/z.",
|
|
"gt_answers": "\\frac { 1 9 5 } { 2 8 7 } = \\frac { x } { 5 . 7 4 g }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4107.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 5 0 } { 1 } = 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4110.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "4 = k \\pi + \\frac { \\pi } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4111.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as `3x^2 + 3xbx + b^2 = 6`.",
|
|
"gt_answers": "3 x + 3 - 4 + 6 x = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_4112.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 - 3x + 4 = 0.",
|
|
"gt_answers": "x = \\frac { 5 a + 1 } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4113.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 7 = 0\\)",
|
|
"gt_answers": "\\sqrt { x + 5 } - \\sqrt { 2 x - 7 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4114.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "A B = \\sqrt { A C ^ { 2 } + B C ^ { 2 } } = \\sqrt { 9 ^ { 2 } + 2 1 ^ { 2 } } = 3 \\sqrt { 5 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4115.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis is a linear equation in two variables, where x and y represent the unknown quantities. The equation states that the sum of the two variables is equal to 10.",
|
|
"gt_answers": "\\frac { V _ { 1 } } { V _ { 2 } } = \\frac { R _ { 1 } } { R _ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4116.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{8x^2 + 12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + 12}{x^2 + 12x + 12} = 8 + \\frac{12x + ",
|
|
"gt_answers": "8 x + 8 = 9 x - 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4117.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\sum_{i=1}^{10} \\left( \\sum_{j=1}^{10} \\left( \\sum_{k=1}^{10} \\left( \\sum_{l=1}^{10} \\left( \\sum_{m=1}^{10} \\left( \\sum_{n=1}^{10} \\left( \\sum_{o=1}^{10} \\left( \\sum_{p=1}^{10} \\left( \\sum_{q=1}^{10} \\left( \\sum_{r=1}^{10} \\left( \\sum_{s=1}^{10} \\left( \\sum_{t=1}^{10} \\left( \\sum_{u=1}^{10} \\left( \\sum_{v=1}^{10} \\left( \\sum_{w=1}^{10} \\left( \\sum_{x=1}^{10} \\left( \\sum_{y=1}^{10} \\left( \\sum_{z=1}^{10} \\left( \\sum_{aa=1}^{10} \\left( \\sum_{bb=1}^{10} \\left( \\sum_{cc=1}^{10} \\left( \\sum_{dd=1}^{10} \\left( \\sum_{ee=1}^{10} \\left( \\sum_{ff=1}^{10} \\left( \\sum_{gg=1}^{10} \\left( \\sum_{hh=1}^{10} \\left( \\sum_{ii=1}^{10} \\left( \\sum_{jj=1}^{10} \\left( \\sum_{kk=1}^{10} \\left( \\sum_{ll=1}^{10} \\left( \\sum_{mm=1}^{10} \\left( \\sum_{nn=1}^{10} \\left( \\sum_{oo=1}^{10} \\left( \\sum_{pp=1}^{10} \\left( \\sum_{qq=1}^{10} \\left( \\sum_{rr=1}^{10} \\left( \\sum_{ss=",
|
|
"gt_answers": "0 . 6 6 > 0 . 6 4 > 0 . 6 0 6 > 0 . 6 0 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4118.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "( t + 1 ) \\lambda + t ^ { 2 } + \\sin 1 + 7 0 ( \\lambda \\leq - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4119.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(LEP\\left(x\\right) = \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1}{2} \\left(x^2 - 1\\right) + \\frac{1}{2} \\left(x^2 + 1\\right) + \\frac{1",
|
|
"gt_answers": "\\angle E F P = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4120.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + y^2 = 49\\)",
|
|
"gt_answers": "x ^ { 2 } - 2 0 x + 1 0 0 - 4 x - 2 0 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4121.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"180\u00b0 - LDFF - MERF\".",
|
|
"gt_answers": "\\angle 2 = 1 8 0 ^ { \\circ } - \\angle D E F - \\angle M E F\n",
|
|
"image_path": "./data/HME100K/test_images/test_4122.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 25-5+7.",
|
|
"gt_answers": "2 y - 5 = \\pm 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_4123.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x2 + 5x3 = 15x4.",
|
|
"gt_answers": "\\frac { 5 } { 9 } \\times \\frac { 2 } { 3 } = \\frac { 5 \\times 2 } { 9 \\times 3 } = \\frac { 1 0 } { 2 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4124.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(A + B + C = D\\)\n\nThe formula is written in a black box with the letters A, B, C, and D inside.",
|
|
"gt_answers": "\\frac { A E } { A D } = \\frac { E C } { D F }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4127.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 5x + 6 = 0\\)",
|
|
"gt_answers": "x = \\sqrt { 2 } - 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4128.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 3(2x - 1) - 2(x - 1) - 3(x - 2) - 2(x - 3) = 0.",
|
|
"gt_answers": "\\frac { 2 \\times 3 - a } { 3 } - \\frac { 3 - a } { 2 } = 3 - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4129.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x + 2y = 12.",
|
|
"gt_answers": "2 3 x = \\frac { 5 2 9 } { 6 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4131.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"200 - 100 = 100 - 100 = 0\".",
|
|
"gt_answers": "= 9 0 ^ { \\circ } - 2 0 ^ { \\circ } = 7 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4132.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a few Chinese characters and some numbers.",
|
|
"gt_answers": "\\therefore \\frac { 1 } { x } = \\frac { 1 } { a _ { 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4133.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\angle E A P - \\angle F P A\n",
|
|
"image_path": "./data/HME100K/test_images/test_4134.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LDBE = 3\\sqrt{2} \\pi r^2\\)\n\nThis formula calculates the length of the diagonal of a square with side length `r`. The `LDBE` stands for \"Length of the diagonal of a square with side length `r`\". The `3` in the expression represents the square root of 2, which is approximately 1.414213562373. The `pi` symbol represents the constant pi, which is approximately 3.141592653589793. The `r` symbol represents the side length of the square.",
|
|
"gt_answers": "\\angle D B E = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4136.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 5\\)\n\nThe formula is written in the form of an equation, where the variables x and y are multiplied together and then added to the constant 5.",
|
|
"gt_answers": "b a \\sin \\alpha + b \\cos \\alpha = \\sqrt { a ^ { 2 } + b ^ { 2 } } \\sin ( a + \\theta )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4138.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nSAA + SAB = SBA + SBB\n\nThis formula represents the relationship between the sum of the squares of the two sides of a triangle and the sum of the squares of the two sides of its perpendicular bisector.",
|
|
"gt_answers": "S _ { \\Delta A O D } = S _ { \\Delta A O B } - S _ { \\Delta B O D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4139.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "n ) ^ { 2 } = ( m - n ) [ m n - m ( m - n ) ] = ( m - n ) ( m n\n",
|
|
"image_path": "./data/HME100K/test_images/test_4140.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(m^2 + m^2 = 2m^2\\)",
|
|
"gt_answers": "x = \\frac { 2 } { m + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4141.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBG = 150\u00b0.\"",
|
|
"gt_answers": "\\angle B O A = 1 5 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4142.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "P Q = \\sqrt { 4 ^ { 2 } + 1 4 ^ { 2 } } = 2 \\sqrt { 5 3 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4143.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 1 } { V } + \\frac { 2 } { 3 V } = \\frac { 3 } { 3 V } + \\frac { 2 } { 3 V } = \\frac { 5 } { 3 V } ( h\n",
|
|
"image_path": "./data/HME100K/test_images/test_4144.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x(x+1) - 7.",
|
|
"gt_answers": "\\frac { . 3 x + a } { 1 2 } - \\frac { 1 - 5 x } { 8 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4145.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(5 \\times 5 \\times 5 \\times 5 = 5^5\\)",
|
|
"gt_answers": "( 5 + 1 ) = 5 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4147.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "a = \\frac { 5 } { 2 } g\n",
|
|
"image_path": "./data/HME100K/test_images/test_4148.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "0 \\times 3 . 1 4 \\times 1 0 = 3 1 4 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4149.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"16.13-15.54 = 43.46 - 0.00\".",
|
|
"gt_answers": "1 6 . 1 3 - 1 5 . 4 3 = 0 . 7 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4150.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(AB = \\frac{1}{2} \\left(A^2 + B^2\\right)\\)",
|
|
"gt_answers": "\\widehat { B D } = \\widehat { C D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4151.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"GD = sin(n)\".",
|
|
"gt_answers": "G D = \\frac { 1 } { 2 } A C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4152.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "t = 8 , t = 1 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4153.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given by:\n\n\\(DE = \\frac{1}{2} \\left( \\frac{d^2y}{dx^2} + \\frac{dy}{dx} \\right) + \\frac{1}{2} \\left( \\frac{d^2x}{dy^2} + \\frac{dx}{dy} \\right)\\)",
|
|
"gt_answers": "D E = \\sqrt { ( 2 \\sqrt { 3 } ) ^ { 2 } + 1 ^ { 2 } } = \\sqrt { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4154.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4156.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 5 = 15\\)",
|
|
"gt_answers": "x : \\frac { 1 } { 1 0 } = \\frac { 1 5 } { 2 } : \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4158.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 3x + 5.",
|
|
"gt_answers": "y _ { 4 } = - \\frac { 7 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4159.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 0 0 0 0 0 c m = 1 0 0 0 k m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4160.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(11 - \\frac{1}{2} = \\frac{1}{2} \\times 2 + \\frac{1}{2} \\times 1 = 1 + 1 = 2\\)",
|
|
"gt_answers": "x = \\frac { . 1 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4161.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 15x + 10 = 0`.",
|
|
"gt_answers": "x = 1 5 \\times \\frac { 1 0 } { 2 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4165.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(CADB-45+L22\\)",
|
|
"gt_answers": "\\angle A D B = 4 5 ^ { \\circ } + \\angle 2 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4166.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(60x + 20y = 100\\)\n\nThis formula represents a linear equation in two variables, where the x-coordinate is multiplied by 60 and the y-coordinate is multiplied by 20. The result is then added to 100, which is the constant term.",
|
|
"gt_answers": "\\frac { 1 } { . x + y } = a\n",
|
|
"image_path": "./data/HME100K/test_images/test_4168.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"L'A + Cb = 450\".",
|
|
"gt_answers": "\\angle A C D = 4 8 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4169.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SaoB = 0.5 * OB\".",
|
|
"gt_answers": "S _ { \\Delta A O B } = \\frac { 1 } { 2 } A O \\cdot O B\n",
|
|
"image_path": "./data/HME100K/test_images/test_4170.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BETEF = CTFETF.\"",
|
|
"gt_answers": "B E + E F = C F + E F\n",
|
|
"image_path": "./data/HME100K/test_images/test_4171.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(9x + 5y = 45d + 100\\)",
|
|
"gt_answers": "9 \\times 5 = 4 5 d m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4172.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BRE-2SAB\" using LaTeX format.",
|
|
"gt_answers": "B E = \\frac { 1 } { 2 } A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_4173.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4175.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in the form of a chemical formula, which is a representation of the chemical structure of a substance. The formula is written in a black box, with the chemical elements and their respective atomic numbers and charges indicated. The formula is written in a way that it can be easily read and understood by chemists and other scientists.",
|
|
"gt_answers": "H _ { 2 } O _ { 2 } \\xlongequal { M n O _ { 2 } } H _ { 2 } O + O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4176.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = 2x^2 - 2ax + a^2\\)",
|
|
"gt_answers": "f ^ { \\prime } ( x ) = x ^ { 2 } - 2 a x - a\n",
|
|
"image_path": "./data/HME100K/test_images/test_4177.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 50:25m.",
|
|
"gt_answers": "5 0 \\div 2 = 2 5 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4179.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "y = \\frac { n } { m + \\sqrt { 2 } } ( x + \\sqrt { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4180.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^3 = 80 \\text{ km/h}\\)",
|
|
"gt_answers": "1 2 \\times \\frac { 2 } { 3 } = 8 ( k m / h\n",
|
|
"image_path": "./data/HME100K/test_images/test_4181.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x} + \\frac{1}{y} = \\frac{1}{x + y}\n\\end{equation}\n\nThis formula represents the basic algebraic identity of addition of fractions.",
|
|
"gt_answers": "x = - \\frac { 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4183.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\nb = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\",
|
|
"gt_answers": "b = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4184.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a few Chinese characters, which could be a representation of a mathematical expression in Chinese.",
|
|
"gt_answers": "x ^ { 2 } = \\frac { 5 } { m - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4186.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(10^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\times 2^{0.5} \\times 5^{0.5} \\",
|
|
"gt_answers": "1 9 0 \\times 5 = 9 4 0 ( k m ) .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4187.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(4x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "\\frac { 1 } { 4 } \\cdot x + \\frac { 1 } { 2 } = x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4189.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x - 5 = 25 - 40.",
|
|
"gt_answers": "\\frac { 5 } { 8 } = \\frac { 5 \\times 5 } { 8 \\times 5 } = \\frac { 2 5 } { 4 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4190.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, but it can be translated into LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{",
|
|
"gt_answers": "\\angle A B O = \\frac { \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4192.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"n-4\".",
|
|
"gt_answers": "n = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4195.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, where the sum of x and y is equal to 10.",
|
|
"gt_answers": "\\frac { 3 } { 4 } \\times \\frac { 4 } { 5 } = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4196.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\overrightarrow { B D } = ( - 1 , 1 , 0 ) .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4197.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1129\" using the LaTeX format.",
|
|
"gt_answers": "1 1 2 < 1 2 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_4198.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(A(B+C) = AB + AC + BC\\)",
|
|
"gt_answers": "A C : B C = 2 : 1 = 2 , E F :\n",
|
|
"image_path": "./data/HME100K/test_images/test_4199.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x3=12(dm).",
|
|
"gt_answers": "4 \\times 3 = 1 2 ( d m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4201.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which are not supported by LaTeX. However, I can provide a rough translation of the formula into English:\n\n\"The sum of the squares of the first n natural numbers is equal to the sum of the squares of the first n odd numbers.\"",
|
|
"gt_answers": "x = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4202.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n(3x + 2y) - (x + 3y) = 3x - 2y - 3x + 2y = 0\n\nThis is a quadratic equation in two variables, with the variables x and y.",
|
|
"gt_answers": "\\cos ( \\frac { 2 k + 1 } { 3 } \\pi x - \\frac { \\pi } { 6 } ) = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4203.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "h ^ { \\prime } ( x ) = x ^ { 2 } - 2 x - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4204.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(9 \\times 3 + 4 \\times 10 + 4 \\times 11 + 9 \\times 12 + 3 \\times 13 + 4 \\times 14 + 9 \\times 15 + 3 \\times 16 + 4 \\times 17 + 9 \\times 18 + 3 \\times 19 + 4 \\times 20 + 9 \\times 21 + 3 \\times 22 + 4 \\times 23 + 9 \\times 24 + 3 \\times 25 + 4 \\times 26 + 9 \\times 27 + 3 \\times 28 + 4 \\times 29 + 9 \\times 30 + 3 \\times 31 + 4 \\times 32 + 9 \\times 33 + 3 \\times 34 + 4 \\times 35 + 9 \\times 36 + 3 \\times 37 + 4 \\times 38 + 9 \\times 39 + 3 \\times 40 + 4 \\times 41 + 9 \\times 42 + 3 \\times 43 + 4 \\times 44 + 9 \\times 45 + 3 \\times 46 + 4 \\times 47 + 9 \\times 48 + 3 \\times 49 + 4 \\times 50 + 9 \\times 51 + 3 \\times 52 + 4 \\times 53 + 9 \\times 54 + 3 \\times 55 + 4 \\times 56 + 9 \\times 57 + 3 \\times 58 + 4 \\times 59 + 9 \\times 60 + 3 \\times 61 + 4 \\times 62 + 9 \\times 63 + 3 \\times 64 + 4 \\times 65 + 9 \\times 66 + 3 \\times 67 + 4 \\times 68 + 9 \\times 69 + 3 \\times 70 + 4 \\",
|
|
"gt_answers": "4 = b ^ { 2 } - 4 a c = 9 + 3 2 = 4 1 > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4205.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(U_{h} = \\frac{1}{2} \\left(U_{h,1} + U_{h,2}\\right)\\)\n\nThis formula represents the heat transfer between two parallel plates with different temperatures, where Uh is the heat transfer coefficient between the two plates, Uh1 and Uh2 are the heat transfer coefficients between the plates and the surrounding air, and T1 and T2 are the temperatures of the two plates.",
|
|
"gt_answers": "C H _ { 4 } + 2 O _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4206.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\nPQ = 2x + 2b\n\nThe formula is written in a black box, with the letters P, Q, and b written in white.",
|
|
"gt_answers": "P Q = \\sqrt { 4 ^ { 2 } + 1 4 ^ { 2 } } = \\sqrt { 2 2 } = 2 \\sqrt { 5 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4207.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LEBT = ZLABL + 3/2\".",
|
|
"gt_answers": "\\angle E B F = \\frac { 1 } { 2 } \\angle A B C = 3 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4208.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\nP = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "P = \\rho g h = 1 0 0 0 k g / m ^ { 3 } \\times 9 . 8 N / k g \\times 0 . 1 5 m = 1 4 7 0 P a .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4210.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(BG + AG + CG = 2G\\)\n\nThis formula represents the relationship between the three colors, blue, green, and gray, and the total amount of green in the mixture. The blue and gray colors are represented by the variables BG and CG, respectively, while the green color is represented by the variable AG. The total amount of green in the mixture is represented by the variable G. The formula states that the total amount of green in the mixture is equal to twice the amount of green in the blue and gray colors combined.",
|
|
"gt_answers": "\\frac { B G } { D G } = \\frac { A G } { C G } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4211.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2000x2=4000x3.",
|
|
"gt_answers": "2 0 0 \\times 2 = 4 0 0 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4213.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"cos(x) = sin(x) / (1 + cos(x))\".",
|
|
"gt_answers": "\\cos \\alpha = \\pm _ { 1 } ^ { 2 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4214.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(5 + 5) = 10 + 10.",
|
|
"gt_answers": "\\frac { 2 } { \\sqrt { 5 } + 1 } = \\frac { \\sqrt { 5 } + 1 } { A B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4216.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "x = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4217.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + y^2}{x^2 - y^2} = \\frac{2xy}{x^2 - y^2}\n\\end{equation}\n\nThis equation can be simplified further by rearranging the terms to obtain:\n\n\\begin{equation}\n\\frac{2xy}{x^2 - y^2} = \\frac{x^2 + y^2}{2xy}\n\\end{equation}\n\nFinally, the equation can be simplified further by dividing both sides by 2 to obtain:\n\n\\begin{equation}\n\\frac{x^2 + y^2}{2xy} = \\frac{x^2 + y^2}{2x^2}\n\\end{equation}\n\nThis is the final simplified expression of the formula in the image.",
|
|
"gt_answers": "- \\frac { 1 } { x ^ { 2 } } + \\frac { 1 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4218.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nC4 + 8g - 6g = 6g - 6g = 0\n\nThe formula is a simple algebraic equation that involves the variables C4 and g. The equation is solved by subtracting 6g from both sides, resulting in the final answer of 0.",
|
|
"gt_answers": "c \\frac { 1 } { 4 } : 8 = 1 2 : \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4219.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\sqrt{2m x^2 + 4m xy + 4y^2 + 4x^3 + 6xy^2 + 4y^3 + 2x^4 + 4xy^3 + 4y^4 + 2x^5 + 4xy^4 + 4y^5 + 2x^6 + 4xy^5 + 4y^6 + 2x^7 + 4xy^6 + 4y^7 + 2x^8 + 4xy^7 + 4y^8 + 2x^9 + 4xy^8 + 4y^9 + 2x^{10} + 4xy^{10} + 4y^{11} + 2x^{11} + 4xy^{11} + 4y^{12} + 2x^{12} + 4xy^{12} + 4y^{13} + 2x^{13} + 4xy^{13} + 4y^{14} + 2x^{14} + 4xy^{14} + 4y^{15} + 2x^{15} + 4xy^{15} + 4y^{16} + 2x^{16} + 4xy^{16} + 4y^{17} + 2x^{17} + 4xy^{17} + 4y^{18} + 2x^{18} + 4xy^{18} + 4y^{19} + 2x^{19} + 4xy^{19} + 4y^{20} + 2x^{20} + 4xy^{20} + 4y^{21} + 2x^{21} + 4xy^{21} + 4y^{22} + 2x^{22} + 4xy^{22} + 4y^{23} + 2x^{23} + 4xy^{23} + 4y^{24} + 2x^{24} + ",
|
|
"gt_answers": "y ^ { 2 } - 2 m y + 4 y + m ^ { 2 } - 2 0 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4220.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 53.23m.",
|
|
"gt_answers": "s = 3 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4221.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 2 } { 1 0 } = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4222.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x + 3 = 5.",
|
|
"gt_answers": "\\frac { x - 2 } { 2 } \\leq 1 - \\frac { 3 - 2 x } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4224.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( x + 3 ) ( x - 3 ) ( x + \\sqrt { 2 } ) ( x - \\sqrt { 2 } ) .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4225.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_e = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "C D E C = \\angle B E C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4226.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"N3\" using LaTeX format.",
|
|
"gt_answers": "n = - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4227.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(6x^2 + 4x + 5 = 10x^2 + 10x + 5\\)",
|
|
"gt_answers": "( 6 \\times 4 + 6 \\times 5 + 4 \\times 5 ) \\times 2 = 1 4 8 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4228.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(CD-EB = 2\\pi r^2\\)\n\nThis formula represents the area of a circle with a radius of r.",
|
|
"gt_answers": "\\overline { C D } = \\overline { E B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4229.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{2x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{2x^2 + 3x + 4}{x^2 + 2x + 3}\n\\end{aligned}\n\\end{equation}\n\nThis is a simple algebraic expression that can be evaluated using the rules of algebra.",
|
|
"gt_answers": "3 x ^ { 2 } - ( 2 x - 1 ) ^ { 2 } - ( 2 x - 1 ) + 3 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4230.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n2a^2 - 2b^2 = 4a^2 - 4b^2 - 4ab\n\nThis formula can be rearranged to solve for a or b:\n\na^2 - b^2 = 4a^2 - 4b^2 - 4ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 4ab - 4ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 8ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 8ab - 4ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 12ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 12ab - 4ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 16ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 16ab - 4ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 16ab - 8ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 16ab - 16ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 32ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 32ab - 32ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 64ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 64ab - 64ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 128ab\n\na^2 - b^2 = 4a^2 - 4b^2 - 128ab - 128",
|
|
"gt_answers": "2 a ^ { 2 } - 6 a - 2 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4231.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2\\pi r^2 + 2\\pi r\\cos(\u03b8) + 2\\pi r\\sin(\u03b8) = 4\\pi r^2\\)\n\nThis formula can be rearranged to solve for the angle \u03b8:\n\n\\(2\\pi r^2 + 2\\pi r\\cos(\u03b8) + 2\\pi r\\sin(\u03b8) = 4\\pi r^2 \\iff 2\\pi r^2 + 2\\pi r\\cos(\u03b8) = 4\\pi r^2 - 2\\pi r^2 \\iff 2\\pi r^2\\cos(\u03b8) = 2\\pi r^2 \\iff \\cos(\u03b8) = \\frac{1}{2}\\)\n\nTherefore, the angle \u03b8 is equal to 90 degrees.",
|
|
"gt_answers": "\\angle B O C = 2 \\angle B D E = 2 \\times 8 3 ^ { \\circ } = 1 6 6 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4232.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4}\n\\end{equation}\n\nThis equation can be simplified further to:\n\n\\begin{equation}\n\\frac{1}{2} + \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThe equation is written using the `\\frac` command to indicate a fraction, and the `\\left( \\right)` and `\\left( \\right)` commands to indicate the parentheses.",
|
|
"gt_answers": "= - 1 + \\frac { 2 } { a - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4233.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 4 = 4x + 4.",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\div \\frac { 1 } { 8 } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4234.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Russian, and it is not possible to provide a LaTeX representation of it without knowing the exact Russian characters. However, the image shows a mathematical formula with a number of symbols and letters, which could be a mathematical expression in any language.",
|
|
"gt_answers": "y _ { B C } = k x + b\n",
|
|
"image_path": "./data/HME100K/test_images/test_4235.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1.5064 + 4.5655656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4236.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"P = 1000W / 550000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "W = P t = 0 . 1 1 k w \\cdot 5 h = 0 . 5 5 k m \\cdot h = 0 . 5 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4237.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2mntm = m^2 + n^2 + 2mn\\cos\\theta\\)\n\nThe formula is a quadratic equation in the variables m and n, where m and n are the lengths of the two sides of a right triangle, and \u03b8 is the angle between the two sides. The equation can be solved for m and n using the quadratic formula.",
|
|
"gt_answers": "2 m + n = 1 2 m + \\frac { 2 } { 3 } = 1 m = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4240.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(a^2 + b^2 = c^2 + d^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the hypotenuse.",
|
|
"gt_answers": "a _ { m } ^ { 2 } + b n ^ { 2 } + 2 a m b n > a n ^ { 2 } + 6 m ^ { 2 } + 2 a n b m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4241.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(77444400 + 28184400 + 24384400 + 21384400 + 18384400 + 15384400 + 12384400 + 9384400 + 6384400 + 3384400 + 0 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "7 7 4 4 - 4 9 0 0 = 2 8 4 4 ( d m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4242.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2\\cdot 10^{5} \\cdot 10^{2} = 2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 0 0 0 \\times \\frac { 1 } { 5 0 0 0 } = 2 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4243.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 1 = 0\".",
|
|
"gt_answers": "\\frac { 1 } { 2 } A M \\cdot O C = \\frac { 1 } { 3 } \\times 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_4244.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"cost = sum(snd)\".",
|
|
"gt_answers": "\\cos \\alpha - \\sin \\alpha = - \\frac { \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4246.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 5\\)",
|
|
"gt_answers": "y = \\frac { 8 } { 5 } \\sqrt { 3 } - \\sqrt { 3 } = \\frac { 3 \\sqrt { 3 } } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4247.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"W-red hoot\" using LaTeX format.",
|
|
"gt_answers": "W = - 1 0 0 x + 5 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4249.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"pi squared equals 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148481097374967336249147581594830955054882353600812800948309384460955048820975665933446482046652109756482133932594811171679887481841861164848237536024811469519417167987938521481861164848237536024811469519417167987938521481861164848237536024811469519417167987938521481861164848237536024811469519417167987938521481861164848237536024811469519417167987938521481861164848237536024811469519417167987",
|
|
"gt_answers": "\\pi < \\alpha < \\frac { 3 } { 2 } \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_4250.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 + c^2 = d^2 + e^2 + f^2\\)",
|
|
"gt_answers": "m ^ { 2 } + \\frac { b } { a } m + \\frac { b ^ { 2 } } { 4 a ^ { 2 } } = \\frac { b ^ { 2 } } { 4 a ^ { 2 } } - \\frac { c } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4251.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "B G \\bot E F\n",
|
|
"image_path": "./data/HME100K/test_images/test_4252.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a negative sign in front of the expression, which indicates that the expression is negative.",
|
|
"gt_answers": "\\frac { 1 5 } { 2 } + k < 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4253.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)",
|
|
"gt_answers": "y _ { 3 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4257.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(AQ + Cosa = 40 cm^2\\)\n\nThe formula is a combination of two formulas: the area of a rectangle (AQ) and the area of a circle (Cosa). The area of a rectangle is calculated by multiplying its length (A) by its width (Q). The area of a circle is calculated by multiplying its radius (r) by pi (\u03c0).\n\nIn this formula, the area of the rectangle is represented by AQ, and the area of the circle is represented by Cosa. The equation combines these two areas to find the total area of the shape, which is equal to 40 cm^2.",
|
|
"gt_answers": "A Q = \\frac { A B } { \\cos A } = \\frac { 2 0 } { \\frac { 1 } { 2 } } = 4 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4258.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2(4+5) - 4(2+3) - 5(1+4) - 3(2+1) - 4(3+2) - 5(4+1) - 2(5+4) - 4(3+5) - 5(2+6) - 3(4+7) - 4(5+6) - 5(7+4) - 2(8+5) - 4(6+7) - 5(5+8) - 3(7+9) - 4(8+9) - 5(9+8) - 2(10+7) - 4(8+10) - 5(9+11) - 3(10+12) - 4(11+12) - 5(12+10) - 2(13+9) - 4(12+13) - 5(13+12) - 3(14+13) - 4(15+14) - 5(16+15) - 2(17+16) - 4(15+17) - 5(16+18) - 3(17+18) - 4(18+19) - 5(19+18) - 2(20+19) - 4(19+20) - 5(20+21) - 3(21+22) - 4(22+21) - 5(21+23) - 3(23+24) - 4(24+23) - 5(23+25) - 3(25+24) - 4(24+26) - 5(26+24) - 3(27+26) - 4(26+28) - 5(28+26) - 3(29+28) - 4(28+30) - 5(30+28) - 3(",
|
|
"gt_answers": "1 - \\frac { 2 } { 3 } \\div \\frac { 7 } { 8 } - \\frac { 4 } { 2 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4260.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\ce{NaOH + H2SO4 -> Na2SO4 + H2O}\n\\end{equation}\n\nThis equation represents the chemical reaction between sodium hydroxide (NaOH) and sulfuric acid (H2SO4) to form sodium sulfate (Na2SO4) and water (H2O).",
|
|
"gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4261.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "= \\frac { 3 - \\sqrt { 1 7 } } { 2 . } x _ { 2 } = \\frac { 3 + \\sqrt { n } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4262.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 5\\)",
|
|
"gt_answers": "y _ { 1 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4263.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "\\frac { 1 } { x + y } + \\frac { 2 } { x - y } = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4264.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as ABtana = 200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "B Q = A B \\tan A = 2 0 \\tan 6 0 ^ { \\circ } = 2 0 \\sqrt { 3 } c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4265.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 5\\)",
|
|
"gt_answers": "- \\frac { 1 } { 2 } x ^ { 2 } + 1 + x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4267.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "\\sqrt { 3 y - 2 } = 3 - \\sqrt { y + 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4268.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 15 = 30.",
|
|
"gt_answers": "x = \\frac { 1 5 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4269.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 100x(120-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x(100-t) = 100x",
|
|
"gt_answers": "\\frac { x } { 1 2 0 } = \\frac { x } { 1 6 0 } + 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_4270.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"180\u00b0 - 90\u00b0 = 90\u00b0\".",
|
|
"gt_answers": "\\angle D E C + \\angle E C B = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4271.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written in a black box, and the letters are written in a white font. The formula is written in a way that it can be easily read and understood by those familiar with the LaTeX notation.",
|
|
"gt_answers": "\\Delta A C D \\cong \\Delta C B E ( S A S ) \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_4272.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(t = \\frac{1}{2} \\left( \\sqrt{a^2 + b^2} - a \\right)\\)\n\nThis formula can be used to find the time taken by a body to travel a distance of `a` meters when it is moving with a constant speed of `b` meters per second.",
|
|
"gt_answers": "t = \\frac { 6 } { V }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4274.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"3x + 2 = 10.\"",
|
|
"gt_answers": "\\frac { 1 } { 2 } : \\frac { 1 } { 3 } = 1 5 : 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4276.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the result of dividing the numerator by the denominator, which is equal to 1/4.",
|
|
"gt_answers": ": ( 1 2 \\times 5 + 1 2 \\times 3 + 5 \\times 3 ) \\times 2 = 2 2 2 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4278.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 100.\"",
|
|
"gt_answers": "\\frac { 1 } { x } = \\frac { 1 } { 0 . 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4281.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "( 2 0 + 2 x ) ( 4 0 - x ) = 1 2 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4282.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = \\frac{1}{2}mv^2\\)\n\nThis formula represents the energy of an object in motion, where E is the energy, m is the mass of the object, and v is the velocity of the object.",
|
|
"gt_answers": "\\frac { 1 } { a ^ { 2 } - 9 } = \\frac { 1 } { ( a + 3 ) ( a - 3 ) } = \\frac { a + 3 } { ( a + 3 ) ^ { 2 } ( a - 3 ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4283.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 100x^2 - 100x + 100 = 0.",
|
|
"gt_answers": "\\frac { 1 5 ^ { x 1 6 0 } } { 1 0 0 } x - \\frac { 9 ^ { x 1 6 0 } } { 1 0 0 } = \\frac { 7 ^ { x 1 6 0 } } { 1 0 0 } x + 0 . 3 1 ^ { x 1 6 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4284.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `VA = 6 + 6`.",
|
|
"gt_answers": "V A ^ { 2 } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_4286.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(P = \\frac{mv^2}{2} + mg\\)",
|
|
"gt_answers": "P F = - \\frac { 4 } { 3 } m ^ { 2 } + \\frac { 8 } { 3 } m + 4 - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4290.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(6.06 \\times 10^{18} \\text{W} = 6.06 \\times 10^{18} \\text{J} = 6.06 \\times 10^{18} \\text{V} \\cdot \\text{A} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{W} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{J} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{V} \\cdot \\text{A} \\cdot \\text{s} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{W} \\cdot \\text{s} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{J} \\cdot \\text{s} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{V} \\cdot \\text{A} \\cdot \\text{s} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{W} \\cdot \\text{s} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{J} \\cdot \\text{s} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{V} \\cdot \\text{A} \\cdot \\text{s} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{W} \\cdot \\text{s} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{J} \\cdot \\text{s} \\cdot \\text{s} = 6.06 \\times 10^{18} \\text{V} \\cdot \\text{A} \\cdot \\text{s} \\cdot \\text{s}",
|
|
"gt_answers": "0 . 6 W = 6 V \\Delta I _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4291.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{8x^2 + 8x + 16}{x^2 + 4x + 16}\n\\end{aligned}\n\\end{equation}\n\nThis equation can be simplified by factoring out the common denominator, which is x^2 + 4x + 16. The simplified expression is then:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{8x^2 + 8x + 16}{x^2 + 4x + 16} = \\frac{8x^2 + 8x + 16}{x^2 + 4x + 16 - 16} = \\frac{8x^2 + 8x + 16 - 16}{x^2 + 4x + 16} = \\frac{8x^2 + 8x + 16 - 16}{x^2 + 4x + 16 - 16} = \\frac{8x^2 + 8x + 16 - 16}{x^2 + 4x + 16 - 16} = \\frac{8x^2 + 8x + 16 - 16}{x^2 + 4x + 16 - 16} = \\frac{8x^2 + 8x + 16 - 16}{x^2 + 4x + 16 - 16} = \\frac{8x^2 + 8x + 16 - 16}{x^2 + 4x + 16 - 16} = \\frac{8x^2 + 8x + 16 - 16}{x^2 + 4x + 16 - 16} = \\frac{8x^2 + 8x + 16 - 16}{x^2 + 4x + 16 - 16} = \\frac{8x^2 + 8x + 16 - 16}{x^2 + 4x + 16 - 16} = \\frac{",
|
|
"gt_answers": "x ^ { 2 } - 4 + 2 x ^ { 2 } + 6 x + 4 + 8 x + 8 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4292.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 9.",
|
|
"gt_answers": "\\frac { 2 \\times 3 - a } { 3 } - \\frac { 3 - a } { 2 } = 3 - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4293.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n(2x + 4) / (x + 4) = 2 / 5\n\nThe formula is a fraction with a numerator of 2x + 4 and a denominator of (x + 4). The numerator is divided by the denominator to obtain the result.",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\div \\frac { 1 } { 8 } = ( 4 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4294.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 155344 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 123456 - 123456 + 1234",
|
|
"gt_answers": "1 2 5 6 \\div 3 . 1 4 \\div 2 = 2 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4295.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3x^2 + 2y^2}{x^2 + y^2 + 3xy} = \\frac{3",
|
|
"gt_answers": "\\frac { 4 } { 3 } y = - 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_4296.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"PC + BP + BT + BC = 100.\"",
|
|
"gt_answers": "P C ^ { 2 } = B P ^ { 2 } + B C ^ { 2 } -\n",
|
|
"image_path": "./data/HME100K/test_images/test_4297.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(5515 \\times 6 \\times 5 \\times 15 = 126,725\\)",
|
|
"gt_answers": "( 4 - 0 . 5 ) 5 = 2 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_4298.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"f(x) = -x^2 + 2x + 1.\"",
|
|
"gt_answers": "f ( x ) - f ^ { \\prime } ( x ) < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4299.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4.88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888",
|
|
"gt_answers": "8 . 4 7 8 \\times 2 0 = 1 6 9 . 5 6 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4301.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 1\".",
|
|
"gt_answers": "x + y = -\n",
|
|
"image_path": "./data/HME100K/test_images/test_4302.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = (x + y)^2\\)",
|
|
"gt_answers": "x = 2 k \\pi + \\arctan \\frac { 1 } { 2 } + \\pi - a r c\n",
|
|
"image_path": "./data/HME100K/test_images/test_4303.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "x = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4304.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"E = mc^2,\" where E is energy, m is mass, and c is the speed of light in a vacuum.",
|
|
"gt_answers": "A M = M B = 5 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4305.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x + 3 = 4\" in LaTeX format.",
|
|
"gt_answers": "\\frac { 3 } { 4 } x = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4306.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 4x + 3 = 22.",
|
|
"gt_answers": "\\frac { 4 \\times 1 5 } { 3 } = 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4307.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/13 + 1/15 + 1/17 + 1/19 + 1/21 + 1/23 + 1/25 + 1/27 + 1/29 + 1/31 + 1/33 + 1/35 + 1/37 + 1/39 + 1/41 + 1/43 + 1/45 + 1/47 + 1/49 + 1/51 + 1/53 + 1/55 + 1/57 + 1/59 + 1/61 + 1/63 + 1/65 + 1/67 + 1/69 + 1/71 + 1/73 + 1/75 + 1/77 + 1/79 + 1/81 + 1/83 + 1/85 + 1/87 + 1/89 + 1/91 + 1/93 + 1/95 + 1/97 + 1/99 + 1/101 + 1/103 + 1/105 + 1/107 + 1/109 + 1/111 + 1/113 + 1/115 + 1/117 + 1/119 + 1/121 + 1/123 + 1/125 + 1/127 + 1/129 + 1/131 + 1/133 + 1/135 + 1/137 + 1/139 + 1/141 + 1/143 + 1/145 + 1/147 + 1/149 + 1/151 + 1/153 + 1/155 + 1/157 + 1/159 + ",
|
|
"gt_answers": "1 4 5 . 3 \\div 1 0 0 0 1 4 5 . 3 \\div 1 0 0 = 1 . 4 5 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4309.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{2x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{2x^2 + 3x + 4}{x^2 + 2x + 3}\n\\end{equation}\n\nThis is a simple algebraic equation that can be solved by factoring the numerator and denominator.",
|
|
"gt_answers": "( x _ { 1 } + x _ { 2 } ) ^ { 2 } - x _ { 1 } x _ { 2 } = 1 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_4311.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nNaCl + H2O + O2 --> Na2SO4 + 2H2O + O2",
|
|
"gt_answers": "N a _ { 2 } C O _ { 3 } + 2 H C l = 2 N a C l + H _ { 2 } O + C O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4312.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(y = \\frac{x^2 + 2x + 3}{x^2 - 2x + 1}\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(y = \\frac{x^2 + 2x + 3}{x^2 - 2x + 1}\\)",
|
|
"gt_answers": "( x + y - 5 ) ( x + y + 2 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4314.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x = \\frac { 2 1 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4317.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 49\\)",
|
|
"gt_answers": "\\angle 5 + \\angle 4 = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4318.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as K11 + K12 + K21 + K22 = 12.",
|
|
"gt_answers": "x = \\frac { 1 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4319.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(R = \\frac{R_1 + R_2}{R_1 + R_2 + R_3 + R_4 + R_5 + R_6 + R_7 + R_8 + R_9 + R_{10}}\\)\n\nThis formula is used to calculate the resistance of a series circuit with ten resistors connected in parallel. The total resistance of the circuit is calculated by adding the individual resistances of each resistor.",
|
|
"gt_answers": "I ^ { \\prime } = \\frac { E ^ { \\prime } } { R 1 } = \\frac { 3 B L ^ { 2 } V _ { 0 } } { 8 r }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4321.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 7x + 3\\)",
|
|
"gt_answers": "x _ { 2 } = 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_4322.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4.500046554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546554655465546",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4323.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in the form of a mathematical formula, which is a combination of the letters \"a\" and \"b\" with a subscript. The formula is written in a black font on a white background, and the letters are written in a cursive style.",
|
|
"gt_answers": "/ n + b i - a + b i\n",
|
|
"image_path": "./data/HME100K/test_images/test_4325.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V_{i} = IR_{i} + V_{o} - V_{i} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o} - V_{o} = IR_{i} + V_{o}",
|
|
"gt_answers": "V _ { 1 } = I _ { 1 } \\cdot R _ { 1 } = 0 . 2 A \\cdot 1 0 \\Omega = 2 0 V .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4326.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\cos(x) = \\frac{e^{ix} + e^{-ix}}{2}\n\\end{equation}\n\nThis formula represents the cosine of the angle x in terms of the exponential function e^{ix} and its complex conjugate e^{-ix}.",
|
|
"gt_answers": "y = 3 x - 3 0 ( x \\geq 3 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4327.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "A O = \\frac { 1 } { 2 } \\times 2 \\sqrt { 3 } = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4328.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x^2 + 3x - 9 = 0.",
|
|
"gt_answers": "\\frac { 2 x } { 3 } = \\frac { 4 \\times - 8 } { 9 } - 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4330.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"2(x + 1) - 3(x - 2) = 5x - 10.\"",
|
|
"gt_answers": "\\frac { x + 2 } { 3 } + 4 = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4331.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "a > c > b\n",
|
|
"image_path": "./data/HME100K/test_images/test_4332.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": ") - 1 ^ { 2 } + \\sqrt [ 3 ] { 6 4 } - ( - 2 ) x \\sqrt { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4333.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2+2=4\" using a red marker.",
|
|
"gt_answers": "> - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4338.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(118 = 118 \\cdot 10^{-1} + 118 \\cdot 10^{-2} + 118 \\cdot 10^{-3} + 118 \\cdot 10^{-4} + 118 \\cdot 10^{-5} + 118 \\cdot 10^{-6} + 118 \\cdot 10^{-7} + 118 \\cdot 10^{-8} + 118 \\cdot 10^{-9} + 118 \\cdot 10^{-10} + 118 \\cdot 10^{-11} + 118 \\cdot 10^{-12} + 118 \\cdot 10^{-13} + 118 \\cdot 10^{-14} + 118 \\cdot 10^{-15} + 118 \\cdot 10^{-16} + 118 \\cdot 10^{-17} + 118 \\cdot 10^{-18} + 118 \\cdot 10^{-19} + 118 \\cdot 10^{-20} + 118 \\cdot 10^{-21} + 118 \\cdot 10^{-22} + 118 \\cdot 10^{-23} + 118 \\cdot 10^{-24} + 118 \\cdot 10^{-25} + 118 \\cdot 10^{-26} + 118 \\cdot 10^{-27} + 118 \\cdot 10^{-28} + 118 \\cdot 10^{-29} + 118 \\cdot 10^{-30} + 118 \\cdot 10^{-31} + 118 \\cdot 10^{-32} + 118 \\cdot 10^{-33} + 118 \\cdot 10^{-34} + 118 \\cdot 10^{-35} + 118 \\cdot 10",
|
|
"gt_answers": "\\frac { 5 } { 1 2 } = \\frac { 9 } { 1 0 } = 2 . 5 = 8 : 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4339.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"100x150 zigzag graphic with 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 0 \\times 1 5 0 = 1 5 0 0 0 ( m l )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4340.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x _ { 4 } = - 2 - \\sqrt { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4341.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2V + 0.5S = N + 0.5H",
|
|
"gt_answers": "2 N a O H + S O _ { 2 } = N a _ { 2 } S O _ { 3 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_4342.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(F_c = \\frac{1}{2} \\left( \\frac{1}{r_1} + \\frac{1}{r_2} \\right) \\left( \\frac{1}{r_3} + \\frac{1}{r_4} \\right) \\left( \\frac{1}{r_5} + \\frac{1}{r_6} \\right) \\left( \\frac{1}{r_7} + \\frac{1}{r_8} \\right) \\left( \\frac{1}{r_9} + \\frac{1}{r_{10}} \\right) \\left( \\frac{1}{r_{11}} + \\frac{1}{r_{12}} \\right) \\left( \\frac{1}{r_{13}} + \\frac{1}{r_{14}} \\right) \\left( \\frac{1}{r_{15}} + \\frac{1}{r_{16}} \\right) \\left( \\frac{1}{r_{17}} + \\frac{1}{r_{18}} \\right) \\left( \\frac{1}{r_{19}} + \\frac{1}{r_{20}} \\right) \\left( \\frac{1}{r_{21}} + \\frac{1}{r_{22}} \\right) \\left( \\frac{1}{r_{23}} + \\frac{1}{r_{24}} \\right) \\left( \\frac{1}{r_{25}} + \\frac{1}{r_{26}} \\right) \\left( \\frac{1}{r_{27}} + \\frac{1}{r_{28}} \\right) \\left( \\frac{1}{r_{29}} + \\frac{1}{r_{30}} \\right) \\left( \\frac{1}{r_{31}} + \\frac{1}{r_{32}} \\right) \\left( \\frac{1}{r_{33}} + \\frac{1}{r_{34}} \\right) \\left( \\frac{1}{r_{35}} + \\frac{1}{r_{36}} \\right) \\left( \\frac{",
|
|
"gt_answers": "F C = 6 \\sqrt { 2 } \\cdot 2 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4343.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3.5L \\times 2mg/L \\times 1000mg/kg = 7.2TBL.\"",
|
|
"gt_answers": "t _ { 2 } = \\frac { 3 . 5 L } { V _ { m } } = \\frac { 7 B ^ { 2 } L ^ { 2 } } { 2 m g R }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4344.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 7x8 + 56 = 98.",
|
|
"gt_answers": "\\frac { 7 } { 4 } = \\frac { 7 \\times 8 } { 9 \\times 8 } = \\frac { 5 6 } { 7 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4345.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: sin(x) = sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x) + sin(x)",
|
|
"gt_answers": "\\sin 6 0 ^ { \\circ } = \\frac { E F } { C F } = \\frac { \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4346.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x^2 - 12x + 12.",
|
|
"gt_answers": "3 - 1 . 2 x = \\frac { 4 } { 5 } x - 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4347.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: y = 2x - 3.",
|
|
"gt_answers": "y _ { 2 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4348.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(E = \\frac{F_s}{m} \\cdot \\cos\\theta\\)\n\nwhere E is the electric field strength, Fs is the surface charge density, and \u03b8 is the angle between the electric field and the surface normal.",
|
|
"gt_answers": "F _ { 2 } = \\frac { F _ { 1 } l _ { 1 } } { l _ { 2 } } = \\frac { 5 N \\times 0 . 2 m } { 0 . 1 m } = 1 0 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_4349.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written in the form of a mathematical equation, with the letters \"ABCF\" representing the variables. The formula is written in a way that it can be easily read and understood by those familiar with the notation.",
|
|
"gt_answers": "\\Delta A B D \\sim \\Delta B C F\n",
|
|
"image_path": "./data/HME100K/test_images/test_4351.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a Chinese character in the middle, which could be a symbol or a number.",
|
|
"gt_answers": "x = \\frac { 1 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4352.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(A = \\frac{sin(x)}{r} + sin(y) + sin(z)\\)\n\nThe formula uses the trigonometric functions sin(x), sin(y), and sin(z) to calculate the value of A, which is the sum of the sines of the three angles x, y, and z.",
|
|
"gt_answers": "\\frac { a } { \\sin A } = 2 R\n",
|
|
"image_path": "./data/HME100K/test_images/test_4353.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\nF = 200N x 300m x 100m / 2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "F _ { 1 } = F _ { 2 } \\cdot \\frac { l _ { 2 } } { l _ { 1 } } = 3 0 0 N \\times \\frac { 6 0 c m } { ( 6 0 + 9 0 ) c m } = 1 2 0 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_4354.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 5x + 6 = 0.\"",
|
|
"gt_answers": "x = - \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4356.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ML33\" using LaTeX format.",
|
|
"gt_answers": "m < \\frac { 3 x } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4357.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written in Chinese characters, which are not easily readable by a computer. However, the image does contain a translation of the formula in English, which is \"The sum of the squares of the first n natural numbers.\"",
|
|
"gt_answers": "\\frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 1 } \\div \\frac { x ^ { 2 } - x } { x + 1 } - \\frac { 1 } { x } + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4358.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\sqrt{2} + 3\\sqrt{3} = 5\\sqrt{2 + 3} = 5\\sqrt{5} = 10\\)",
|
|
"gt_answers": "2 \\sqrt { S _ { 2 } } = \\sqrt { a _ { 1 } } + \\sqrt { S _ { 3 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4359.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBD = DAC(SAS)\".",
|
|
"gt_answers": "\\angle B A D = \\angle D A C ( S A S )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4360.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "1 \\times 1 \\times 3 . 1 4 \\times 1 . 2 = 3 . 7 6 8 ( m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4362.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = -5x + 10\\)",
|
|
"gt_answers": "x - \\frac { 1 } { 5 } + \\frac { 1 } { 5 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4364.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\n\\(y = a + bx + c\\sqrt{x}\\)\n\nwhere a, b, and c are constants.",
|
|
"gt_answers": "x = \\frac { a ^ { 2 } } { c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4366.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x + 2y = 10\\)\n\nThis formula represents the relationship between the variables x and y, where x and y are real numbers and the result is an integer. The equation states that the sum of the two variables is equal to 10.",
|
|
"gt_answers": "( \\frac { 2 } { 3 } ) ^ { 2 } \\cdot \\frac { 1 } { 3 } = \\frac { 4 } { 2 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4367.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x - y = ( 1 - \\sqrt { 2 } ) - ( 1 + \\sqrt { 2 } ) = - 2 \\sqrt { 2 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4368.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(t = \\frac{mgh}{mg} \\times \\sqrt{1 + \\frac{v^2}{g}}\\)\n\nThis formula relates the time taken by an object to fall a certain distance to its initial velocity squared, multiplied by the acceleration due to gravity, and then divided by the initial velocity.",
|
|
"gt_answers": "\\frac { 1 } { 2 } m v ^ { 2 } = m g h + \\frac { 1 } { 2 } m v _ { p } ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4369.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(e^{x} = \\sum_{n=0}^{\\infty} \\frac{x^n}{n!} \\tag{LaTeX formula for e^x}\\).",
|
|
"gt_answers": "y = - \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4370.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x^2 + 4x - 4 = 0.\"",
|
|
"gt_answers": "x ^ { 2 } + 2 + \\frac { 1 } { x ^ { 2 } } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4371.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(tan(x) = \\frac{sin(x)}{cos(x)}\\)",
|
|
"gt_answers": "\\tan ( \\pi + a ) = \\frac { 1 } { - 2 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4373.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which are not supported by LaTeX. However, I can provide a rough translation of the formula:\n\n\"The sum of the squares of the first n natural numbers is equal to the sum of the squares of the first n odd numbers.\"",
|
|
"gt_answers": "\\frac { 5 } { 6 } \\div x = 2 . 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_4374.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 2x + 1.",
|
|
"gt_answers": "y _ { 1 } = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4376.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: AB - 3.",
|
|
"gt_answers": "A B = \\frac { 2 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4377.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "S = A B ( D H + C O ) \\div 2 = 3 \\times \\frac { 2 5 } { 2 } \\div 2 = \\frac { 7 . 5 } { 4 . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4378.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"lock = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 0 x = 2 4 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4379.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a + b = c\\)\n\nThis is a basic algebraic equation that represents the addition of two numbers, a and b, to equal a third number, c.",
|
|
"gt_answers": "x ( \\frac { 1 } { 1 1 } + \\frac { 1 } { 1 3 } + \\frac { 1 } { 1 7 } ) = 4 1 ( \\frac { 1 } { 1 1 } + \\frac { 1 } { 1 3 } + \\frac { 1 } { 1 7 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4381.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a + b = c\\)\n\nThis formula represents the basic algebraic equation of addition, where a, b, and c are variables representing the values of the terms on the left and right sides of the equation.",
|
|
"gt_answers": "A g N O _ { 3 } + N a C l = A g C N + N a N O _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4383.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"S = 10 cm.\"",
|
|
"gt_answers": "S _ { 3 } = 1 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4384.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 12/6 = 2 cm.",
|
|
"gt_answers": "1 2 \\div 2 = 6 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4385.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 2x + 1 = 0`.",
|
|
"gt_answers": "x _ { 1 } = 2 , x _ { 2 } = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4386.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 3 } { x ^ { 2 } + 3 x } - ( x ^ { 2 } + 3 x ) = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4388.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"A/B = 120\u00b0.\"",
|
|
"gt_answers": "\\angle B O C = 1 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4389.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A_b = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "a _ { 3 } - a _ { 2 } = 2 . \\cdots a _ { n } - a _ { n } - 1 = n - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4390.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(5x + 6y = 11\\)",
|
|
"gt_answers": "\\boxed { 5 } \\textcircled { + } \\boxed { 6 } = \\boxed { 1 1 } ( \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4392.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "a + b + c = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4393.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x^2 + 4x - 3.",
|
|
"gt_answers": "3 \\times \\frac { 1 } { 4 } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4396.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(a^2 + b^2 - 3ab + c^2 = 0\\)\n\nThis is a quadratic equation in two variables, where a, b, and c are the coefficients of the variables.",
|
|
"gt_answers": "\\frac { 6 - a } { 3 } - \\frac { 3 - a } { 2 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4397.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which are not supported by LaTeX. However, I can provide a rough translation of the characters into English: \"The sum of the squares of the first 100 natural numbers is equal to the sum of the squares of the first 100 even numbers.\"",
|
|
"gt_answers": "\\frac { 1 } { 2 } x - 7 = \\frac { 1 } { 3 } x + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4398.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "O P _ { 2 } = \\sqrt { 1 4 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4399.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"5x = 55.\"",
|
|
"gt_answers": "5 x = - 5 S\n",
|
|
"image_path": "./data/HME100K/test_images/test_4400.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 22/50 + 92/100 = 114/150.",
|
|
"gt_answers": "\\frac { 9 2 } { 1 0 0 } = \\frac { 4 6 } { 5 0 } = \\frac { 2 3 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4401.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"a^2 + b^2 = c^2.\"",
|
|
"gt_answers": "\\cdot \\vert \\overrightarrow { b } \\vert \\cos 6 0 ^ { \\circ } = \\overrightarrow { a } \\cdot \\overrightarrow { b } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4402.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\[Zn(OH)_2 + 2NaOH \\rightarrow Na_{2}Zn(OH)_4\\]",
|
|
"gt_answers": "Z n + 2 A g N O _ { 3 } = Z n ( N O _ { 3 } ) _ { 2 } + 2 A g\n",
|
|
"image_path": "./data/HME100K/test_images/test_4404.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777",
|
|
"gt_answers": "1 7 c m : 1 7 0 0 0 0 0 0 0 = 1 : 1 0 0 0 0 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4405.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\sqrt{x^2 + 2x + 1} + 1\\)",
|
|
"gt_answers": "x ^ { 2 } + y ^ { 2 } \\geqslant 2 \\sqrt { x ^ { 2 } y ^ { 2 } } = 2 x y\n",
|
|
"image_path": "./data/HME100K/test_images/test_4406.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
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"gt_answers": "\\frac { C G } { A B } = \\frac { C F } { A F }\n",
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"image_path": "./data/HME100K/test_images/test_4408.jpg",
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"model_name": "mPLUG"
|
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},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(C_{2}H_{5}OH + H_{2}O \\rightarrow C_{2}H_{5}OH_{2} + H_{2}\\)\n\nThis formula represents the chemical reaction between ethanol (C2H5OH) and water (H2O) to produce ethanol hydroxide (C2H5OH2) and water (H2).",
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"gt_answers": "C u O + H _ { 2 } S O _ { 4 } = C u S O _ { 4 } + H _ { 2 } O\n",
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"image_path": "./data/HME100K/test_images/test_4409.jpg",
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"model_name": "mPLUG"
|
|
},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written as \"E = mc^2,\" where \"E\" represents energy, \"m\" represents mass, and \"c\" represents the speed of light in a vacuum.",
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"gt_answers": "E D = E B = \\frac { 1 } { 2 } A B\n",
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"image_path": "./data/HME100K/test_images/test_4410.jpg",
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"model_name": "mPLUG"
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},
|
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{
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|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written as follows: `2x^2 + 2y^2 = 4x^2 + 4y^2 - 4x^2 - 4y^2 = 0`.",
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"gt_answers": "0 . 2 \\times 0 . 2 \\times 0 . 2 ) \\div 0 . 2 = 0 . 0 4\n",
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"image_path": "./data/HME100K/test_images/test_4414.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(d = \\sqrt{a^2 + b^2}\\)",
|
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"gt_answers": "d = 2\n",
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"image_path": "./data/HME100K/test_images/test_4415.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2 + 2 = 4\" using the LaTeX formula notation.",
|
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"gt_answers": "e = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4416.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4417.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x ^ { 2 } + 1 = t ^ { - 1 } ( x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4418.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which are not supported by LaTeX. However, I can provide a similar expression in English using the same symbols:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "\\frac { 3 } { 4 } x = \\frac { 7 } { 9 } \\times \\frac { 3 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4419.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\therefore y = 3 \\sqrt { 3 } - \\frac { \\sqrt { 3 } } { 4 } x ^ { 2 } - \\frac { \\sqrt { 3 } } { 4 } ( 3 - x ) ^ { 2 } = - \\frac { \\sqrt { 3 } } { 2 } x ^ { 2 } + \\frac { 3 \\sqrt { 3 } } { 2 } x + \\frac { 3 } { 4 } \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4420.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2 + 100x + 1000} = \\frac{x^2 + 500x + 5000}{x^2",
|
|
"gt_answers": "\\frac { 8 0 } { 1 0 0 } x + ( 5 0 0 - x ) \\frac { 6 0 } { 1 0 0 } = 5 0 0 \\times \\frac { 7 4 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4421.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( 2 2 - 6 ) d = 2 8 - 1 2 \\therefore d = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4422.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(P(A \\cap B) = P(A) \\cdot P(B) - P(A \\cap B) \\cdot P(A \\cap B) \\cdot P(A \\cap B) \\cdot P(A \\cap B)\\)\n\nThis formula is known as the Bayes' Theorem and is used to calculate the probability of an event A and B occurring simultaneously. The formula can be simplified by using the law of total probability, which states that the probability of an event A or B occurring is equal to the sum of the probabilities of A and B occurring individually. In this case, the simplified formula is:\n\n\\(P(A \\cap B) = P(A) \\cdot P(B) - P(A \\cap B) \\cdot P(A \\cap B) \\cdot P(A \\cap B) \\cdot P(A \\cap B)\\)\n\nThis formula can be used to calculate the probability of any two events occurring simultaneously, given the probabilities of each event occurring individually.",
|
|
"gt_answers": "\\overline { A B } \\cdot \\overline { O M } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4424.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1/1333 = 0.007692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692",
|
|
"gt_answers": "\\frac { a } { 6 } = 1 . 3 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4425.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(P(X = 3) = \\frac{1}{3} \\cdot \\frac{1}{2} \\cdot \\frac{1}{3} = \\frac{1}{9}\\)",
|
|
"gt_answers": "P _ { 3 } ( 1 + \\sqrt { 3 } , 3 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4426.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x + 5 = 10.",
|
|
"gt_answers": "8 : \\frac { 2 } { 5 } = x : \\frac { 7 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4427.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2}{2} + \\frac{y^2}{2} + \\frac{z^2}{2} + \\frac{x^2y^2}{4} + \\frac{x^2z^2}{4} + \\frac{y^2z^2}{4} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^2y^2z^2}{8} + \\frac{x^",
|
|
"gt_answers": "x \\cdot ( 1 0 0 - 2 0 ( x - 2 5 ) ) = 2 7 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4428.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a negative sign, which can be represented in LaTeX as follows:\n\n\\(f(x) = -x^2\\)",
|
|
"gt_answers": "N Q = \\frac { 1 } { 2 } C Q\n",
|
|
"image_path": "./data/HME100K/test_images/test_4429.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Yb = x^2 + 2x + 1.\"",
|
|
"gt_answers": "y _ { B Q } = - \\frac { 1 } { 2 } x + 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4430.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x + 1} = \\frac{x^2 + 3x + 4}{x^2 - 2x +",
|
|
"gt_answers": "x ^ { 2 } - \\frac { 4 } { 3 } x - \\frac { 4 } { 3 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4431.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"long = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 . 9 m = 9 0 0 m m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4432.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x + 3 = 11\\)",
|
|
"gt_answers": "\\frac { 2 x - 1 } { 5 } + \\frac { x + 1 } { 2 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4433.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(75 - 1) + 1 = 156.",
|
|
"gt_answers": "\\frac { 2 5 } { 7 5 } > \\frac { 1 5 } { 7 5 } > \\frac { 9 } { 7 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4436.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"7.24444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444",
|
|
"gt_answers": "7 . ( 1 ) a m + 4 b\n",
|
|
"image_path": "./data/HME100K/test_images/test_4437.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"L2-L4 = 2L3-L5.\"",
|
|
"gt_answers": "\\angle - \\frac { 3 } { 4 } < \\frac { 2 } { 3 } < \\frac { 5 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4438.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(8\\times 2.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\times 0.5\\",
|
|
"gt_answers": "8 \\times 3 \\times 2 . 5 = 6 0 ( d m ^ { 3 } ) 6 0 d m ^ { 3 } = 6 0 L\n",
|
|
"image_path": "./data/HME100K/test_images/test_4440.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Carbon + 2HCl = C2H4Cl2.\"",
|
|
"gt_answers": "C a C O _ { 3 } + 2 H C l =\n",
|
|
"image_path": "./data/HME100K/test_images/test_4441.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A + B = C\\)\n\nThis formula represents the basic algebraic equation of addition, where A, B, and C are variables representing the unknown values.",
|
|
"gt_answers": "A B = 1 0 \\div \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4443.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 25 + 5b + c = 0.",
|
|
"gt_answers": "\\cdot \\frac { 2 5 } { 4 } + 5 b + c = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4444.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 4 = 16\\)",
|
|
"gt_answers": "x ^ { 2 } + k ^ { 2 } x ^ { 2 } - 4 k ^ { 2 } x + 4 k ^ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4445.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{4}x^2 + \\frac{1}{2}x + 1\\)",
|
|
"gt_answers": "y _ { P } = \\frac { 1 } { 2 } \\cdot \\frac { \\sqrt { 2 } } { 2 } \\cdot = \\frac { \\sqrt { 2 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4446.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "6 0 6 0 + 9 8 5 \\approx 8 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4447.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{2x^2 + 3x + 4}{x^2 + 2x + 3}\n\\end{aligned}\n\\end{equation}\n\nThe equation is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "\\frac { 2 } { 5 } \\div ( - 2 \\frac { 2 } { 5 } ) - \\frac { 8 } { 2 1 } \\times ( - 1 \\frac { 3 } { 4 } ) - 0 . 7 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4449.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\because A B / / C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_4451.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(L_{AB} = \\sqrt{L_{A}^2 + L_{B}^2 - 2L_{A}L_{B}\\cos(\\theta_{AB})}\\)\n\nThis formula calculates the length of the line segment AB, where A and B are the endpoints of the line segment, and \u03b8AB is the angle between the two endpoints.",
|
|
"gt_answers": "\\angle A O B = 1 8 0 ^ { \\circ } - \\angle A B O - \\angle B A O = 1 5 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4453.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 3x + 5}{x^2 + 2x + 4}\n\\end{equation}\n\nThis formula can be simplified by factoring out the common denominator, which is x^2 + 2x + 4. The simplified expression is then:\n\n\\begin{equation}\n\\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} = \\frac{x^2 + 3x + 5}{x^2 + 2x + 4} =",
|
|
"gt_answers": "x = 3 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4454.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Mg(OH)2 + 2H2O = Mg(OH)4 + 2H2O.\"",
|
|
"gt_answers": "M g ( O H ) _ { 2 } + 2 H C l = M g C l _ { 2 } + 2 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_4456.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{1}{1",
|
|
"gt_answers": "( x + 1 ) ( x - 2 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4457.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{26} - 2^{24} + 2^{22} - 2^{20} + 2^{18} - 2^{16} + 2^{14} - 2^{12} + 2^{10} - 2^{8} + 2^{6} - 2^{4} + 2^{2} - 1 = 3628800\\)",
|
|
"gt_answers": "5 x - 2 x = 2 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4458.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 C H _ { 3 } O H \\rightleftharpoons ( C H _ { 3 } ) _ { 2 } O + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_4460.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{1}{1",
|
|
"gt_answers": "U _ { 0 } = I _ { b } ( R _ { a } + R _ { b } ) = 0 . 3 A \\times 1 4 0 \\Omega + 1 0 \\Omega ) = 1 5 0 V ^ { - }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4461.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"s^2 + 9 = 3^2\".",
|
|
"gt_answers": "S _ { 3 } = 9 = 3 ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4462.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten style, but it can be represented in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "S = 4 + \\frac { 1 } { 2 } \\times 6 - 1 = 4 + 3 -\n",
|
|
"image_path": "./data/HME100K/test_images/test_4463.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 4x + 2 = 0.\"",
|
|
"gt_answers": "x - \\frac { 1 } { 2 } ( 4 x - 6 ) < 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4464.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "( 4 5 + 1 ) \\times \\frac { 1 } { 5 0 0 } = 0 0 1 1 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4465.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1463-465x1000.",
|
|
"gt_answers": "1 4 6 3 - 4 6 5 \\approx 1 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4466.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `3x + 2y = 10`.",
|
|
"gt_answers": "y _ { 3 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4467.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a + b = 15 + 8 = 23\\)",
|
|
"gt_answers": "\\frac { - 5 } { 2 } + a = - 1 5 + 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_4468.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\" in LaTeX format.",
|
|
"gt_answers": "x _ { 1 } = \\frac { 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4470.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BC = 1 + 0.001\".",
|
|
"gt_answers": "B C = 1 O C = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4471.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "- 1 x + x - \\frac { 2 } { 3 } x = 1 - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4472.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\pi r^2 = 4\\pi r^2 - 2\\pi r^2\\cos(2\\theta)\\)\n\nThis formula can be used to calculate the area of a circle with a radius of `r` and an angle of `theta`.",
|
|
"gt_answers": "2 5 0 0 0 0 \\div 1 0 0 0 0 0 = 2 . 5 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4473.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{2x^2 + 3x + 4}{x^2 + 2x + 3}\n\\end{aligned}\n\\end{equation}\n\nThis is a quadratic equation, where the numerator is the numerator of the first term of the fraction, and the denominator is the denominator of the first term of the fraction.",
|
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"gt_answers": "m ^ { 3 } n + 2 m ^ { 2 } n ^ { 2 } + m n ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4474.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(V_C = \\frac{BC}{2} \\sqrt{\\frac{1}{2} \\left( \\frac{V_A}{V_B} + \\frac{V_B}{V_A} \\right)} \\tag{1}\\)\n\nThe formula is a ratio of the capacitance of the capacitor to the sum of the voltages across the two plates. The equation is written in terms of the voltage across the capacitor (V_C), the voltage across the top plate (V_A), and the voltage across the bottom plate (V_B). The formula is also expressed in terms of the square root of the ratio of the voltages across the plates.",
|
|
"gt_answers": "V = \\frac { B C } { \\frac { 2 } { 3 } } = 1 5 \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4476.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "O A = O C = \\frac { 1 } { 2 } A C = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4477.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(2^{10} - 2^{9} - 2^{8} + 2^{7} - 2^{6} + 2^{5} - 2^{4} + 2^{3} - 2^{2} + 2^{1} - 2^{0} = 1023\\)",
|
|
"gt_answers": "9 a ^ { 2 } p ^ { 2 } - b ^ { 2 } 9 ^ { 2 } = ( 3 a P + 6 9 ) ( 3 a p - b p )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4478.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 13 - 28 + 16 - 125.",
|
|
"gt_answers": "\\frac { 1 3 } { 8 } = 1 3 \\div 8 = 1 . 6 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4479.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b^2 + 4(a+b) + 4(a-b) = 4a^2 + 4b^2 + 4ab + 4(-ab) = 4a^2 + 4b^2 + 8ab + 4(-ab) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^2 + 8ab + 4(a^2 - b^2) = 4a^2 + 4b^",
|
|
"gt_answers": "( b ^ { 2 } + 4 ) y ^ { 2 } =\n",
|
|
"image_path": "./data/HME100K/test_images/test_4480.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 3x + 2 = 5.",
|
|
"gt_answers": "\\frac { 4 } { 5 } : x = \\frac { 1 } { 2 } : \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4481.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(5 + 8) - 3(9 - 5) = 13 - 18 = 5.",
|
|
"gt_answers": "2 - \\frac { 5 } { 9 } = \\frac { 1 8 - 5 } { 9 } = \\frac { 1 3 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4482.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 30x30 - 400x600 = 900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 0 \\times 3 0 = 9 0 0 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4483.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(E = \\frac{1}{2}mv^2 + mgx\\)\n\nwhere E is the energy, m is the mass of the object, v is its velocity, and g is the gravitational constant.",
|
|
"gt_answers": "E C = \\frac { 1 3 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4484.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 0.3x + 0.03 = 0.499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
|
|
"gt_answers": "0 . 6 1 x + 0 . 3 ( 5 0 0 - x ) = 2 4 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4485.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "0 = k + \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4486.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "( x - 1 ) ^ { 2 } = \\frac { 7 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4487.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2.75 cm = 1 inch\".",
|
|
"gt_answers": "m > - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4488.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 60/40 = 1.5.",
|
|
"gt_answers": "\\frac { 6 0 } { 9 } = \\frac { 4 0 } { 0 . 2 4 g }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4489.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 614 = 600.",
|
|
"gt_answers": "6 1 4 \\approx 6 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4490.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 10\\)",
|
|
"gt_answers": "3 x ^ { 2 \\times 1 . 5 - 2 } - 4 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4492.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"H2O + 1/2 O2 = H2O2 + heat.\"",
|
|
"gt_answers": "S 0 _ { 2 } + O _ { 2 } + H _ { 2 } 0 = H _ { 2 } S O _ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4493.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3x + 2y = 10\\)\n\nThis is a linear equation in two variables, where the variables are x and y. The equation states that the sum of the products of x and y is equal to 10.",
|
|
"gt_answers": "- \\frac { 8 } { 3 } - \\frac { 3 } { 3 } = - \\frac { 1 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4494.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AHBH + SAB = 100.\"",
|
|
"gt_answers": "A H = B H = \\frac { 1 } { 2 } A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_4495.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V = \\frac{1}{2} \\cdot \\sqrt{E^2 - (p_x^2 + p_y^2 + p_z^2)}\\)\n\nThis formula relates the electric potential (V) to the electric field (E), momentum (p), and position (x, y, z) of a charged particle. The electric potential is defined as the work done per unit charge to move a charge from infinity to a point in space. The electric field is the force per unit charge acting on a charge at a given point in space. The momentum is the product of the charge and the velocity of the particle. The position is the vector sum of the x, y, and z components of the particle's position.",
|
|
"gt_answers": "T = \\frac { \\lambda } { V } = \\frac { 4 } { 2 0 } = \\frac { 1 } { 5 } s\n",
|
|
"image_path": "./data/HME100K/test_images/test_4496.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3x + 2y = 10\\)\n\nThis is a linear equation in two variables, where the variables are x and y. The equation states that the sum of the products of x and y is equal to 10.",
|
|
"gt_answers": "\\frac { 5 } { 6 } + \\frac { 1 } { 3 } = \\frac { 7 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4497.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x + \\frac { 1 } { 2 } x = 1 - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4498.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ey = 1/2 (1 + 2x)\" using LaTeX format.",
|
|
"gt_answers": "9 x = 4 ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_4499.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { \\cos B } { \\sin C } A B ^ { 2 } + \\frac { \\cos C } { \\sin B } \\overrightarrow { A C } \\cdot \\overrightarrow { A B } \\cdot 2 m ( \\overrightarrow { A H } + \\overrightarrow { H C } ) \\cdot \\overrightarrow { A B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4500.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4) + 3x(3-4) + 4x(3-4) + 2x(3-4)",
|
|
"gt_answers": "\\angle 4 = \\frac { 1 } { 2 } \\angle D Q N\n",
|
|
"image_path": "./data/HME100K/test_images/test_4501.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 4x^3 + 3.",
|
|
"gt_answers": "y = - \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4503.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 2 = 10.\"",
|
|
"gt_answers": "x = \\frac { 3 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4504.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LABC = 65\\%\\)",
|
|
"gt_answers": "\\angle B A C = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4505.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( a x + 1 ) ( x + 1 ) + ( a x - 1 ) ( x - 1 ) + 2 x + a + 2 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4506.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{1}{1",
|
|
"gt_answers": "( 3 ) y _ { 1 } < y _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4507.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "y = \\frac { \\sqrt { 1 1 } } { 1 1 } ( x + \\sqrt { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4509.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20 + 1/21 + 1/22 + 1/23 + 1/24 + 1/25 + 1/26 + 1/27 + 1/28 + 1/29 + 1/30 + 1/31 + 1/32 + 1/33 + 1/34 + 1/35 + 1/36 + 1/37 + 1/38 + 1/39 + 1/40 + 1/41 + 1/42 + 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48 + 1/49 + 1/50 + 1/51 + 1/52 + 1/53 + 1/54 + 1/55 + 1/56 + 1/57 + 1/58 + 1/59 + 1/60 + 1/61 + 1/62 + 1/63 + 1/64 + 1/65 + 1/66 + 1/67 + 1/68 + 1/69 + 1/70 + 1/71 + 1/72 + 1/73 + 1/74 + 1/75 + 1/76 + 1/77 + 1/78 + 1/79 + 1/80 + 1/81 + 1/82 + 1/83 + 1/84 + 1/85 + 1/86 + 1/87 + 1/8",
|
|
"gt_answers": "\\frac { 9 } { 1 1 } - \\frac { 4 } { 1 1 } = \\frac { 5 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4510.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 32b - 343x3(17205600)",
|
|
"gt_answers": "3 2 8 - ( 3 5 4 - 3 1 ) \\times 7 2 0 = 3 6 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4513.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 + c^2 + d^2 = 4(a^2 + b^2 + c^2)\\)",
|
|
"gt_answers": "a > b c > d \\frac { a } { c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4514.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible for me to accurately transcribe it into LaTeX format. However, I can provide a rough translation of the expression: \"K-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "k \\cdot \\frac { \\pi } { 2 } \\pm \\alpha ( k \\in z )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4515.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nR^2 = (R1^2 + R2^2) / 2\n\nThis formula calculates the square of the distance between two points, R1 and R2, and divides it by two to obtain the distance between the two points.",
|
|
"gt_answers": "R _ { 3 } = 2 R _ { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4516.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
|
|
"gt_answers": "1 \\times 7 - 1 . 3 = 5 . 7 c m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4517.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 4x + 1 = 0\\)",
|
|
"gt_answers": "x = 1 , y = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4518.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LAA'=4ns2\".",
|
|
"gt_answers": "A A ^ { \\prime } = 4 \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4519.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a Korean word written in the middle.",
|
|
"gt_answers": "x ^ { 2 } + 4 x + 4 = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_4520.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, but it can be translated to English as \"200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 2 } { 3 } + 1 1 y = 1 0 y - 7 \\frac { 1 } { 3 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4521.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(5.6 \\times 10^{10} \\div 2.5 \\times 10^{6} = 2.2 \\times 10^{4} \\approx 22000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { \\tan \\alpha + \\frac { 1 } { 7 } } { 1 - \\frac { 1 } { 7 } \\tan \\alpha } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4522.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2.85 - 1.79 = 1.06.",
|
|
"gt_answers": "\\frac { 5 . 8 5 g } { 1 . 7 g } = 5 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_4523.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "2 = \\frac { 1 } { 2 } x - x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4524.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": ". y = \\frac { 4 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4527.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(100 \\times 100 = 100000\\)",
|
|
"gt_answers": "x = \\frac { 1 2 0 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4528.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 9x6 = 54.",
|
|
"gt_answers": "\\frac { 4 } { 9 } \\times \\frac { 5 } { 6 } = \\frac { 1 0 } { 2 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4529.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LDBC = 5LABO.\"",
|
|
"gt_answers": "\\angle D B C = \\frac { 1 } { 2 } \\angle A B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4530.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 5x2 + 3z2 = 12.",
|
|
"gt_answers": "\\therefore S = 2 1 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4532.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 4x + 6 = 0.\"",
|
|
"gt_answers": "x = 4 \\frac { 2 5 } { 6 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4533.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the half of the half of a whole, which is equal to one fourth.",
|
|
"gt_answers": "\\because D E \\bot A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_4534.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)",
|
|
"gt_answers": "( \\overrightarrow { a } + 2 \\overrightarrow { b } ) ( \\overrightarrow { a } - 2 \\overrightarrow { b } ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4535.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `200x150x1350`.",
|
|
"gt_answers": "2 0 0 x = 1 5 0 x + 1 3 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4536.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{2^{4} + 16^{2} + 20^{2}}{2^{4} + 16^{2} + 20^{2} + 2^{4} + 16^{2} + 20^{2}}\n\\end{aligned}\n\\end{equation}\n\nThe formula is a nested expression that involves the square of four numbers, two of which are 2 and 16, and the square of two other numbers, which are 2 and 20. The result of the expression is the square of the sum of these numbers.",
|
|
"gt_answers": "2 + 4 + 6 + \\cdots + 1 6 + 1 8 + 2 0 ( 2 + 2 0 ) \\times 5 = 1 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4538.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 779.55 = 55 + 144.",
|
|
"gt_answers": "7 7 9 \\div 5 1 = 1 5 \\cdots 1 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4539.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 17 - 3 = 14.",
|
|
"gt_answers": "x = \\frac { 3 1 } { 1 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4540.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/2 + 1/2 = 1.",
|
|
"gt_answers": "\\frac { 1 } { 1 2 } = \\frac { 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4541.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(x + 2y) - 6(x - 2y) = 0.",
|
|
"gt_answers": "\\frac { 5 } { 6 } = \\frac { ( 2 0 ) } { ( 2 4 ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4542.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(3 + 1) - 2(2 + 1) = 6 - 4 = 2.",
|
|
"gt_answers": "\\frac { 6 } { 2 4 } = \\frac { 3 } { 1 2 } = \\frac { 1 } { 3 } , \\frac { 2 } { 2 4 } = \\frac { 1 } { 7 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4543.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "b _ { 3 } - b _ { 2 } = ( \\frac { 1 } { 2 } ) ^ { 2 } \\cdots b _ { n } - b _ { n } - P ( \\frac { 1 } { 2 } ) ^ { n - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4544.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(f(x) = \\frac{1}{1 + \\left( \\frac{x}{a} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{b} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{c} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{d} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{e} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{f} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{g} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{h} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{i} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{j} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{k} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{l} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{m} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{n} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{o} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{p} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{q} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{r} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{s} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{t} \\right)^2} + \\frac{1}{1 + \\left( \\frac{x}{u} \\right)^2} + \\frac{1}{1",
|
|
"gt_answers": "1 + ( a - 2 ) ^ { 2 } + 9 + ( a - 1 ) ^ { 2 } = 1 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_4545.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(25x^2 + 87y^2 - 150x + 125y - 100 = 0\\)",
|
|
"gt_answers": "( 1 0 + x ) \\times 2 5 = 8 7 0 - 1 2 V\n",
|
|
"image_path": "./data/HME100K/test_images/test_4546.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as C = 4a.",
|
|
"gt_answers": "c = 4 a\n",
|
|
"image_path": "./data/HME100K/test_images/test_4547.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x^2 - 3x + 1 = 0.",
|
|
"gt_answers": "\\vert 2 x + m - 1 \\vert + \\vert 2 x - 3 \\vert \\leq \\vert 2 x - 6 \\vert\n",
|
|
"image_path": "./data/HME100K/test_images/test_4550.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2(5-3)m = 10m.",
|
|
"gt_answers": "2 ( 5 - 3 m ) = m + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4551.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\sum_{i=1}^{10} \\left( \\frac{i}{10} \\right)^2 + \\left( \\frac{i}{10} \\right)^3 + \\left( \\frac{i}{10} \\right)^4 + \\left( \\frac{i}{10} \\right)^5 + \\left( \\frac{i}{10} \\right)^6 + \\left( \\frac{i}{10} \\right)^7 + \\left( \\frac{i}{10} \\right)^8 + \\left( \\frac{i}{10} \\right)^9 + \\left( \\frac{i}{10} \\right)^{10}\n\\end{aligned}\n\\end{equation}\n\nThis formula calculates the sum of the squares of the first ten integers, starting from 1 to 10.",
|
|
"gt_answers": "1 0 \\times 0 . 3 + 8 \\times 0 . 3 + 8 \\times 0 . 2 + 8 \\times 0 . 1 + 9 \\times 0 . 1 = 8 . 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_4552.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Hebrew, and it is not possible to provide a LaTeX representation of it without knowing the Hebrew alphabet. However, the image shows a mathematical formula with a few letters and numbers, which could be a mathematical expression in any language.",
|
|
"gt_answers": "t ^ { 2 } - 1 6 t \\geq 2 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_4553.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as E = mc^2, where E is energy, m is mass, and c is the speed of light.",
|
|
"gt_answers": "E F = \\frac { 1 } { 2 } B D C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4554.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 12x6 + 5x2 + 70.",
|
|
"gt_answers": "1 2 \\times 6 5 = 7 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4555.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"EP = PLC + BC,\" where EP stands for \"Energy Productivity,\" PLC stands for \"Power Loss Coefficient,\" and BC stands for \"Battery Capacity.\"",
|
|
"gt_answers": "\\frac { E D } { P D } / = \\frac { P C } { B C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4557.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\nBd-2j = 2j(j+1)\n\\end{equation}\n\nThis is a quadratic equation in the variable j, with the constant BD equal to 2j(j+1).",
|
|
"gt_answers": "B D = 2 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4558.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(x + 5 = 3x + 5\\)\n\nThis formula can be rewritten as:\n\n\\(x = 3x - 5\\)\n\nThe formula can also be written as:\n\n\\(x = 3x - 5 - 5\\)\n\nThis formula can be simplified further to:\n\n\\(x = 3x - 10\\)\n\nThe formula can be written in a more compact form as:\n\n\\(x = 3x - 10 - 5\\)\n\nThis formula can be written in a more compact form as:\n\n\\(x = 3x - 15\\)\n\nThe formula can be written in a more compact form as:\n\n\\(x = 3x - 15 - 5\\)\n\nThis formula can be written in a more compact form as:\n\n\\(x = 3x - 20\\)\n\nThe formula can be written in a more compact form as:\n\n\\(x = 3x - 20 - 5\\)\n\nThis formula can be written in a more compact form as:\n\n\\(x = 3x - 25\\)\n\nThe formula can be written in a more compact form as:\n\n\\(x = 3x - 25 - 5\\)\n\nThis formula can be written in a more compact form as:\n\n\\(x = 3x - 30\\)\n\nThe formula can be written in a more compact form as:\n\n\\(x = 3x - 30 - 5\\)\n\nThis formula can be written in a more compact form as:\n\n\\(x = 3x - 35\\)\n\nThe formula can be written in a more compact form as:\n\n\\(x = 3x - 35 - 5\\)\n\nThis formula can be written in a more compact form as:\n\n\\(x = 3x - 40\\)\n\nThe formula can be written in a more compact form as:\n\n\\(x = 3x - 40 - 5\\)\n\nThis formula can be written in a more compact form as:\n\n\\(x = 3x - ",
|
|
"gt_answers": "1 - \\frac { 2 x - 5 } { 6 } = \\frac { 3 - x } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4559.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"100 - 30 = 70.\"",
|
|
"gt_answers": "1 2 0 ^ { \\circ } + 3 0 ^ { \\circ } + 3 0 ^ { \\circ } = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4560.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(Zn(OH)_2 + 2HCl \\rightarrow ZnCl_2 + 2H_2O\\)",
|
|
"gt_answers": "Z n + 2 H C l = Z n C l _ { 2 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4562.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x - 2 = 13x^2 - 2x - 2\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(2x^2 + 3x - 2 = 13x^2 - 2x - 2\\)",
|
|
"gt_answers": "2 = ( 3 - 2 \\sqrt { 2 } ) x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4563.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"PexaB = 3/2 Pexa + 1/2 Pexb.\"",
|
|
"gt_answers": "S _ { \\Delta A P B } = \\frac { P E \\times A B } { 2 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4564.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)\n\nThis is a quadratic equation in the variable x, with the coefficients 2, 3, and 4. The expression can be solved using the quadratic formula, which gives the solution as x = 5.",
|
|
"gt_answers": "\\therefore L _ { 1 } = 0 . 4 5 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4565.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 7x + 23 = 100.",
|
|
"gt_answers": "x = \\frac { 2 3 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4566.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 12\\)\n\nThis is a quadratic equation in the variable x, with the coefficients 2, 3, and 4. The solution to this equation is x = 4.",
|
|
"gt_answers": "3 . 1 4 \\times 4 0 \\times 2 + 3 . 1 4 \\times ( 4 0 \\div 2 ) ^ { 2 } = 1 5 0 7 2 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4567.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 23 + 3 = 26.",
|
|
"gt_answers": "\\frac { 2 x } { x - 1 } + \\frac { 3 } { 1 - x } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4568.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1.5x10^5 + 1.5x10^4 + 1.5x10^3 + 1.5x10^2 + 1.5x10^1 + 1.5x10^0.",
|
|
"gt_answers": "\\rightarrow 1 . 5 \\times 1 0 ^ { 4 } P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_4569.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AQ/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "A D = \\frac { A B } { \\cos A } = \\frac { 2 0 } { \\frac { 1 } { 2 } } = 4 0 ( c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4571.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nb + b = 2b\n\nThis formula represents the relationship between two variables, b and b, where b is a constant. The equation states that the sum of two values of b is equal to 2b.",
|
|
"gt_answers": "b = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4572.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(5x + 19y = 100\\)\n\nThis formula represents a linear equation in two variables, where the variables x and y are related to each other by the constant 5. The equation can be solved by substituting values for x and y to find the values of x and y that make the equation true.",
|
|
"gt_answers": "a _ { 8 } - a _ { 1 } = 7 d - 1 4 = 7 d d = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4573.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LEB = ZLAB + 3/2\".",
|
|
"gt_answers": "\\angle E B F = \\frac { 1 } { 2 } \\angle A B C = 3 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4577.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LC(x) = 300 - 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle A B = \\angle C = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4578.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 0.75x.",
|
|
"gt_answers": ": 1 2 x = 0 . 7 5 \\times 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_4579.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(Y = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "x = \\frac { 3 b + a } { 2 a - 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4581.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + 3x + 5 = 10\n\\end{aligned}\n\\end{equation}\n\nThe equation is written in the form of an equation with two variables, x and y, and an equal sign. The left side of the equation is the expression to be solved, while the right side is the result of the equation.",
|
|
"gt_answers": "\\frac { x + 1 } { ( x - 3 ) ( x + 3 ) } + \\frac { 5 } { x + 3 } = 1 + \\frac { x } { x - 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4582.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 8442.",
|
|
"gt_answers": "\\frac { 8 } { 4 } = 8 \\div 4 = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4584.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 2 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4586.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "b _ { n + 1 } = 1 + \\frac { b _ { n } } { a _ { n } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4587.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x + 1\\)",
|
|
"gt_answers": "x - y = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4589.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nNH4Cl + H2O = NH3 + Cl2 + H2",
|
|
"gt_answers": "N H _ { 4 } C l + N a C H = N a C l + N H _ { 3 } \\uparrow + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_4590.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(C_2H_4O_2 + 2H_2O + 2CO_2 + 2H_2CO_3 + 2CO_2H_2O + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3 + 2CO_2H_2CO_3",
|
|
"gt_answers": "C u l _ { 2 } + 2 H _ { 2 } O \\rightarrow C u ( o n ) _ { 2 } + l _ { 2 } H _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4591.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\" in LaTeX format.",
|
|
"gt_answers": "t = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4592.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times 8 \\times",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\rho \\cos A - \\frac { \\sqrt { 3 } } { 2 } \\rho \\sin A = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_4593.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `x^2 + 14x + 19 = 0`.",
|
|
"gt_answers": "x = \\vert y \\vert = 2 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4594.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\angle D + \\angle C = 1 8 0 ^ { \\circ } \\therefore \\angle D\n",
|
|
"image_path": "./data/HME100K/test_images/test_4595.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2\\pi r^2 + 2\\pi r^2 + 2\\pi r^2 = 4\\pi r^2\\)\n\nThis formula can be rearranged to solve for the radius of the circle:\n\n\\(r^2 = \\frac{4\\pi}{3}\\)\n\nTherefore, the radius of the circle is 1.732.",
|
|
"gt_answers": "D E = \\sqrt { O E ^ { 2 } - O D ^ { 2 } } = \\sqrt { 1 2 ^ { 2 } - 6 ^ { 2 } } = 6 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4596.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as tan(30o) - tan(0o).",
|
|
"gt_answers": "\\tan 3 0 ^ { \\circ } = \\frac { O A } { O C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4597.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 2y = 9.\"",
|
|
"gt_answers": "9 . 3 \\div 5 = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4598.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as RbE = 1/m.",
|
|
"gt_answers": "A B = E D = 1 . 5 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4599.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x} + \\frac{1}{y} = \\frac{1}{x + y}\n\\end{equation}\n\nThis formula represents the basic algebraic identity of addition of fractions.",
|
|
"gt_answers": "x = \\frac { 1 0 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4600.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"T-S = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + 1000m = 6.16km + ",
|
|
"gt_answers": "t = \\frac { s } { V } = \\frac { 6 1 6 0 k m } { 7 0 0 k m / k } = 8 8 h\n",
|
|
"image_path": "./data/HME100K/test_images/test_4601.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 2y^2 = 4n^2\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\n2x^2 + 2y^2 = 4n^2\n\\end{equation}\n\nThe equation is written in the form of a mathematical expression, where the variables x, y, and n are defined as real numbers. The equation is also written in the standard mathematical notation, where the variables are separated by the equal sign (=) and the expression is enclosed within parentheses.",
|
|
"gt_answers": "2 7 \\times 2 ^ { \\frac { 1 3 } { 4 } } \\div ( 6 ^ { \\frac { 2 } { 3 } } ) ^ { \\frac { 9 } { 2 } } = \\sqrt { ( - 2 ) ^ { 4 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4603.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2.44x0.66 - 4.94.",
|
|
"gt_answers": "2 . 4 \\times 2 . 0 6 = 4 . 9 4 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4604.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "1 1 - 9 = 2 1 7 - 8 = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_4605.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "1 0 ( a - \\frac { 3 x } { 5 0 0 } ) x \\leq 1 0 \\times 1 . 2 \\% x \\cdot ( 1 0 0 0 - x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4606.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2100-1800-1300-1000-700-600-500-400-300-200-100-0\".",
|
|
"gt_answers": "2 1 0 - 6 0 ) x = ( 1 8 0 0 - 1 3 5 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4607.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "\\frac { \\vert a \\vert + \\vert b \\vert } { 1 + \\vert a \\vert + \\vert b \\vert } > \\frac { \\vert a + b \\vert } { 1 + \\vert a + b \\vert }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4609.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `0.75t + 0.05t^2 + 0.025t^3 + 0.01t^4 + 0.005t^5 + 0.001t^6 + 0.0005t^7 + 0.0001t^8 + 0.00005t^9 + 0.00001t^10 + 0.000005t^11 + 0.000001t^12 + 0.0000005t^13 + 0.000001t^14 + 0.0000005t^15 + 0.000001t^16 + 0.0000005t^17 + 0.000001t^18 + 0.0000005t^19 + 0.000001t^20 + 0.0000005t^21 + 0.000001t^22 + 0.0000005t^23 + 0.000001t^24 + 0.0000005t^25 + 0.000001t^26 + 0.0000005t^27 + 0.000001t^28 + 0.0000005t^29 + 0.000001t^30 + 0.0000005t^31 + 0.000001t^32 + 0.0000005t^33 + 0.000001t^34 + 0.0000005t^35 + 0.000001t^36 + 0.0000005t^37 + 0.000001t",
|
|
"gt_answers": ". 7 5 t : 6 t = 0 . 6 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4612.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "m = - \\frac { 3 7 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4614.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\right)^2 = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple quadratic equation, where the left side is equal to the right side.",
|
|
"gt_answers": "x _ { 2 } = \\frac { 1 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4615.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(300 \\times 256 + 1500 = 18000\\)",
|
|
"gt_answers": "3 0 0 b + 2 2 5 a = 1 5 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4617.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(P(A \\land B) = P(A) \\cdot P(B) \\cdot P(A \\land B) / (P(A) \\cdot P(B))^2\\)\n\nThis formula is used to calculate the probability of two events A and B occurring simultaneously. The expression is a combination of the probability of event A occurring (P(A)), the probability of event B occurring (P(B)), and the probability of both events occurring simultaneously (P(A \\land B)). The denominator is the square of the product of the two probabilities, which is used to normalize the result.",
|
|
"gt_answers": "a ( 3 m - a ) = 2 m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4618.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula is a quadratic equation, which can be written in LaTeX as:\n\n\\(a^2 + b^2 = c^2\\)\n\nThe LaTeX code for this equation is:\n\n\\begin{equation}\na^2 + b^2 = c^2\n\\end{equation}\n\nThe LaTeX code for the square root symbol is:\n\n\\(a^2\\)\n\nThe LaTeX code for the square symbol is:\n\n\\(b^2\\)\n\nThe LaTeX code for the square root symbol is:\n\n\\(c^2\\)",
|
|
"gt_answers": "x _ { 1 } + x _ { 2 } = \\frac { - b } { a } = \\frac { 2 a } { 2 } = a\n",
|
|
"image_path": "./data/HME100K/test_images/test_4619.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 11 + 2(44 - 4) = 11 + 88 - 8 = 11 + 80 - 8 = 11 + 72 - 8 = 11 + 64 - 8 = 11 + 56 - 8 = 11 + 48 - 8 = 11 + 40 - 8 = 11 + 32 - 8 = 11 + 24 - 8 = 11 + 16 - 8 = 11 + 8 - 8 = 11 + 0 - 8 = 11.",
|
|
"gt_answers": "1 1 - 1 1 k + \\frac { 1 } { 2 } = \\frac { 4 4 } { 3 } - \\frac { 2 k } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4620.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 24x7 - 9cm.",
|
|
"gt_answers": "5 4 \\times \\frac { 1 } { 6 } = 9 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4621.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(E = \\frac{1}{2}mv^2\\)\n\nwhere E is the energy, m is the mass, and v is the velocity.",
|
|
"gt_answers": "R _ { 2 } ^ { \\prime } = \\frac { U _ { 2 } ^ { \\prime } } { I ^ { \\prime } } = \\frac { 3 V } { 0 . 4 5 A } = \\frac { 2 0 } { 3 } \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_4622.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 2780 = 0`.",
|
|
"gt_answers": "x = \\frac { 2 7 8 0 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4623.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 4x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x _ { 1 } = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4624.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nR = U/I = 0.05/0.02 = 2.5",
|
|
"gt_answers": "R = \\frac { U } { I } = \\frac { 9 v } { 0 . 5 A } = 3 0 \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_4626.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 66\\)\n\nThe formula uses the variables x and y to represent two unknown quantities. The equation states that the sum of the two variables is equal to 66.",
|
|
"gt_answers": "\\frac { y ^ { 2 } } { 6 4 } + \\frac { x ^ { 2 } } { 1 6 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4627.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 3x + 4 = 0.\"",
|
|
"gt_answers": "x : \\frac { 3 } { 1 6 } = \\frac { 1 } { 3 } : 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4628.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nH2CO3 + 2NaOH --> Na2CO3 + H2O + CO2",
|
|
"gt_answers": "N a _ { 2 } C O _ { 3 } + 2 H C l - 2 N a C l + H _ { 2 } O + C O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4629.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX format as follows:\n\n\\(C_{2}H_{4} + 2C_{2}H_{4} \\rightarrow 2C_{2}H_{6}\\)\n\nThis formula represents the chemical reaction of two molecules of carbon dioxide (CO2) and four molecules of carbon monoxide (CO) to form two molecules of carbon dioxide (CO2) and six molecules of carbon (C).",
|
|
"gt_answers": "C a C O _ { 3 } + 2 H C L = C a C l _ { 2 } + H _ { 2 } O + C O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4630.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a handwritten formula with a few Chinese characters, which could be a mathematical equation or a formula related to Chinese culture or history.",
|
|
"gt_answers": "A B = \\frac { \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4631.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 5\\)",
|
|
"gt_answers": "x < - \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4633.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle A B O = \\angle B A O = 1 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4634.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis is a quadratic equation, where a, b, and c are the coefficients of the variables x, y, and z, respectively.",
|
|
"gt_answers": "\\frac { b } { 4 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4636.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 14.325 - 2.567 + 0.709 - 0.005 = 11.753.",
|
|
"gt_answers": "1 4 . 1 3 \\div 2 . 5 \\approx 5 . 7 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4638.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 4x + 1 = 0\\)",
|
|
"gt_answers": "c p ^ { 2 } = ( 4 - x ) ^ { 2 } + ( - x + 6 ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4640.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"y = 2x + 3.\"",
|
|
"gt_answers": "C M : y = \\frac { \\sqrt { 3 } } { 3 } x + m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4641.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\angle A O B = 1 8 0 ^ { \\circ } - \\angle A B O - \\angle B A O = 1 5 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4642.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 452-2j^2+478j+486.",
|
|
"gt_answers": "4 \\sqrt { 2 } = \\sqrt { 2 } \\cdot \\sqrt { 4 + 8 b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4643.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\frac { a } { c } < \\frac { b } { d }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4644.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5/3 - 6/2.",
|
|
"gt_answers": "\\frac { 5 } { 3 } = \\frac { - ( 1 0 ) } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4645.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2^{10} \\times 10^{10} = 10^{20}\\)",
|
|
"gt_answers": "2 . 5 \\div \\frac { 1 } { 6 0 0 0 0 0 0 } = 1 5 0 0 0 0 0 0 ( c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4646.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 3x + 2 = 0.\"",
|
|
"gt_answers": "x = 1 0 \\times \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4647.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"abbbc0\" using LaTeX format.",
|
|
"gt_answers": "a + b + c = 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4648.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Zn2+ + H2O = Zn(OH)2 + H2.\"",
|
|
"gt_answers": "Z n + 2 H C l = Z n C l _ { 2 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4649.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 6\\)",
|
|
"gt_answers": "x _ { 1 } = 3 , x _ { 2 } = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_4650.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4(1/3) + 3(1/8) + 8(1/10) + 3(1/12) + 4(1/15) + 3(1/18) + 8(1/20) + 3(1/24) + 4(1/27) + 3(1/30) + 8(1/33) + 3(1/36) + 4(1/39) + 3(1/42) + 8(1/45) + 3(1/48) + 4(1/51) + 3(1/54) + 8(1/57) + 3(1/60) + 4(1/63) + 3(1/66) + 8(1/69) + 3(1/72) + 4(1/75) + 3(1/78) + 8(1/81) + 3(1/84) + 4(1/87) + 3(1/90) + 8(1/93) + 3(1/96) + 4(1/99) + 3(1/102) + 8(1/105) + 3(1/108) + 4(1/111) + 3(1/114) + 8(1/117) + 3(1/120) + 4(1/123) + 3(1/126) + 8(1/129) + 3(1/132) + 4(1/135) + 3(1/138) + 8(1/141) + 3(1/144) + 4(1/147) + 3(1/150) + 8(1/153) + 3(1/156) + 4(1/159) + 3(1/1",
|
|
"gt_answers": "\\angle D F B = 9 0 ^ { \\circ } - \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } - - 3 \\angle C )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4651.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: AB + AD - BE - DF = 0.",
|
|
"gt_answers": "\\frac { A B } { B E } = \\frac { A D } { D F }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4652.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x _ { 1 } = - \\sqrt { 6 } , x _ { 2 } = \\frac { \\sqrt { 6 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4653.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 25\\)",
|
|
"gt_answers": "O M P W = \\frac { 3 2 } { 2 5 } x - x = \\frac { 7 } { 2 5 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4654.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 4x + 1 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 + \\sqrt { 3 3 } } { 4 } ; x = \\frac { 1 - \\sqrt { 3 3 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4655.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "b ^ { 2 } + c ^ { 2 } - 2 b c = a ^ { 2 } - b c\n",
|
|
"image_path": "./data/HME100K/test_images/test_4656.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 2 = 0\\)",
|
|
"gt_answers": "x _ { 2 } = - \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4657.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 5 = 0\\)",
|
|
"gt_answers": "\\frac { 4 } { 9 } x \\div \\frac { 4 } { 9 } = \\frac { 8 } { 1 5 } \\div \\frac { 4 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4658.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(B_{L} = \\frac{1}{2} \\left( B_{R} + B_{L} \\right) - \\frac{1}{2} \\left( B_{R} - B_{L} \\right)\\)\n\nThis formula is used to calculate the average of two binary variables, where B_{L} and B_{R} represent the binary values of the left and right halves of the image, respectively. The formula calculates the average by taking the sum of the two halves and dividing it by two.",
|
|
"gt_answers": "S _ { \\Delta } B D C = \\frac { 1 } { 2 } B C \\cdot A F .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4661.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 3 = 0.\"",
|
|
"gt_answers": "\\sqrt { x } = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4662.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 6000/60000 = 1/1000.",
|
|
"gt_answers": "t = 6 \\div 0 . 1 = 6 0 \\min\n",
|
|
"image_path": "./data/HME100K/test_images/test_4663.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 24/12 = 1.8333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
|
|
"gt_answers": "2 4 - 1 2 = 1 2 ( m L )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4664.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4x^2 + 3x - 2 = 0\\)",
|
|
"gt_answers": "\\therefore O C = 3 - 2 a = \\frac { 3 + \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4666.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as d = 7 - 7.",
|
|
"gt_answers": "d = - 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_4667.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "1 6 9 = 9 a ^ { 2 } + 1 6 9 + 4 a ^ { 2 } - 5 2 a\n",
|
|
"image_path": "./data/HME100K/test_images/test_4668.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V_{t} = V_{0} + \\int_{0}^{t} \\left(a \\cdot \\dot{x} + b \\cdot \\ddot{x} + c \\cdot \\dddot{x} + \\cdots \\right) dt\\)\n\nThe formula represents the velocity of an object as a function of time, where `V_{0}` is the initial velocity, `a`, `b`, `c`, and so on are constants, and `x` is the position of the object. The integral sign indicates that the velocity is calculated by integrating the acceleration over time.",
|
|
"gt_answers": "x = v t\n",
|
|
"image_path": "./data/HME100K/test_images/test_4669.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which are not supported by LaTeX. However, the image shows a mathematical formula with the letters \"x\" and \"y\" and the number \"2.\" It is possible that the formula is written in a different language, such as Japanese or Korean, and the characters used are not supported by LaTeX.",
|
|
"gt_answers": "x = - 1 \\pm \\frac { 1 1 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4670.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(40x^{2} + 16(12) + 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 0 \\times 2 5 \\times ( 1 6 - 1 2 ) = 4 0 0 0 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4671.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(A = \\frac{180^\\circ - 90^\\circ}{2} + \\frac{90^\\circ - 140^\\circ}{2} + \\frac{140^\\circ - 180^\\circ}{2} = 90^\\circ\\)",
|
|
"gt_answers": "\\angle A O F = 1 8 0 ^ { \\circ } - 9 0 ^ { \\circ } - 1 4 ^ { \\circ } = 7 6 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4672.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6-2/4b\".",
|
|
"gt_answers": "6 = - 2 1 c + b\n",
|
|
"image_path": "./data/HME100K/test_images/test_4674.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 100 - 100 = 0.",
|
|
"gt_answers": "\\frac { 1 0 6 } { x } = \\frac { 1 0 0 } { 2 0 } = 2 1 . 2 g\n",
|
|
"image_path": "./data/HME100K/test_images/test_4675.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3a^2 + 2a + 3 = 2(3a + 1)^2\\)",
|
|
"gt_answers": "3 a + 3 a + 2 a = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4676.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "5 6 + 4 0 = 9 6 \u3001 4 5 + 2 0 = 6 5 \u3001 6 6 - 6 0 = 6 \u3001 3 0 + 4 8 = 7 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_4677.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "5 0 \\times 2 5 \\times 1 . 2 = 1 5 0 0 ( m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4678.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"2x + 2 = 4.\"",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4679.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(A0.6 + B0.8 + AD-6 = 0\\)\n\nThe formula uses the letters A, B, and AD to represent three different values, and the number 6 to represent a constant. The expression is written in the form of an equation, where the left side represents the sum of the first two terms, and the right side represents the difference between the third term and the constant.",
|
|
"gt_answers": "A O = 6 , B O = 8 A D = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_4680.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(22.92\\times 10^{0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 8 . 2 6 \\times 1 0 = 2 8 2 . 6 ( d m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4681.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 6x0 - 0.12cm.",
|
|
"gt_answers": "6 \\times \\frac { 1 } { 5 0 } = 0 . 1 2 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4682.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) \\left( \\frac{1}{x^2} + \\frac{1}{y^2} \\right) \\left( \\frac{1}{x^3} + \\frac{1}{y^3} \\right) \\left( \\frac{1}{x^4} + \\frac{1}{y^4} \\right) \\left( \\frac{1}{x^5} + \\frac{1}{y^5} \\right) \\left( \\frac{1}{x^6} + \\frac{1}{y^6} \\right) \\left( \\frac{1}{x^7} + \\frac{1}{y^7} \\right) \\left( \\frac{1}{x^8} + \\frac{1}{y^8} \\right) \\left( \\frac{1}{x^9} + \\frac{1}{y^9} \\right) \\left( \\frac{1}{x^{10}} + \\frac{1}{y^{10}} \\right) \\left( \\frac{1}{x^{11}} + \\frac{1}{y^{11}} \\right) \\left( \\frac{1}{x^{12}} + \\frac{1}{y^{12}} \\right) \\left( \\frac{1}{x^{13}} + \\frac{1}{y^{13}} \\right) \\left( \\frac{1}{x^{14}} + \\frac{1}{y^{14}} \\right) \\left( \\frac{1}{x^{15}} + \\frac{1}{y^{15}} \\right) \\left( \\frac{1}{x^{16}} + \\frac{1}{y^{16}} \\right) \\left( \\frac{1}{x^{17}} + \\frac{1}{y^{17}} \\right) \\left( \\frac{1}{x^{18}} + \\frac{1}{y^{18}} \\right) \\left( \\frac{1}{x^{19}}",
|
|
"gt_answers": "1 . 2 \\times 1 0 ^ { 3 } \\times ( 7 - 1 . 5 ) - 2 0 0 x = \\frac { 1 } { 2 } \\times 1 0 0 \\times 6 ^ { 2 } - \\frac { 1 } { 2 } \\times 1 0 0 \\times 3 ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4683.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(K_s = \\frac{1}{1 + \\left(\\frac{RT}{F}\\right)^2}\\)\n\nwhere K_s is the solubility product constant, R is the universal gas constant, T is the absolute temperature, and F is the fugacity coefficient.",
|
|
"gt_answers": "< - 5 \\sim 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4685.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 + c^2 = a^2 + 2ab + b^2 + 2ac + c^2\\)",
|
|
"gt_answers": "\\cdot \\frac { a ^ { 2 } - 3 a } { a ^ { 2 } + a } \\div \\frac { a - 3 } { a ^ { 2 } - 1 } \\times \\frac { a + 1 } { a - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4686.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the multiplication of two fractions, each with a denominator of 2. The result is a fraction with a denominator of 4.",
|
|
"gt_answers": "2 a _ { 3 } = 6 a _ { 1 } + a _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4687.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 21x3x4 = 108.",
|
|
"gt_answers": "\\textcircled { 1 } \\frac { 1 } { 2 } \\times \\frac { 1 } { 4 } = \\frac { 1 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4689.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 150 - 60 + 30 = 100.",
|
|
"gt_answers": "\\frac { 1 5 0 } { 6 0 } = \\frac { 5 } { 2 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4690.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "6 0 x + 1 5 0 0 + 4 5 x = \\frac { 1 } { 2 } x ( x + 2 5 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4691.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\pm \\sqrt { c - 2 } = \\pm \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4693.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Y2 = Y1 + 2x.\"",
|
|
"gt_answers": "y = \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4694.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 188/1527 = 12.27%.",
|
|
"gt_answers": "x + 1 . 8 \\% x = 1 5 2 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_4695.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "y _ { 1 } = \\frac { \\sqrt { 1 0 } } { 4 } , y _ { 2 } = - \\frac { \\sqrt { 1 0 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4696.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nS(5) = 25\n\nThe formula uses the function \"S\" to calculate the sum of the digits of a number. The input is the number 5, and the output is 25.",
|
|
"gt_answers": "S _ { 5 } = 5 ^ { 2 } = 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4697.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4698.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Subb099 = 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(1",
|
|
"gt_answers": "S _ { \\Delta B D A } =\n",
|
|
"image_path": "./data/HME100K/test_images/test_4700.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20 + 1/21 + 1/22 + 1/23 + 1/24 + 1/25 + 1/26 + 1/27 + 1/28 + 1/29 + 1/30 + 1/31 + 1/32 + 1/33 + 1/34 + 1/35 + 1/36 + 1/37 + 1/38 + 1/39 + 1/40 + 1/41 + 1/42 + 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48 + 1/49 + 1/50 + 1/51 + 1/52 + 1/53 + 1/54 + 1/55 + 1/56 + 1/57 + 1/58 + 1/59 + 1/60 + 1/61 + 1/62 + 1/63 + 1/64 + 1/65 + 1/66 + 1/67 + 1/68 + 1/69 + 1/70 + 1/71 + 1/72 + 1/73 + 1/74 + 1/75 + 1/76 + 1/77 + 1/78 + 1/79 + 1/80 + 1/81 + 1/82 + 1/83 + 1/84 + 1/85 + 1/86 +",
|
|
"gt_answers": "5 9 . 0 2 > 5 8 . 5 2 > 5 8 . 1 7 > 5 8 . 0 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_4702.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.",
|
|
"gt_answers": "x ^ { 2 } = \\frac { 3 } { a + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4703.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis equation is a simple algebraic expression that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "\\frac { 1 } { x - y } = V\n",
|
|
"image_path": "./data/HME100K/test_images/test_4704.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{1}{1",
|
|
"gt_answers": "y = 1 1 x = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4705.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 3y^2 + 3z^2 + 3x + 3y + 3z + 3 = 10\\)",
|
|
"gt_answers": "3 . 1 4 \\times 3 ^ { 2 } \\times 2 . 3 \\times \\frac { 1 } { 3 } = 2 1 . 6 6 6 ( m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4706.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3.2 - 100.",
|
|
"gt_answers": "3 . 2 , - 1 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4707.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(189 + 29) = 189 + 29 + 2(189 + 29) = 189 + 29 + 588.",
|
|
"gt_answers": "W _ { k _ { 2 } C O _ { 2 } } = \\frac { 1 . 3 8 g } { 2 g } = 6 9 \\% < 7 0 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_4708.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(u^2 + b^2 = 2(a^2 + c^2)\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(u^2 + b^2 = 2(a^2 + c^2)\\)",
|
|
"gt_answers": "a = 3 b = 5 c = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4709.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "c = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4710.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)",
|
|
"gt_answers": "l _ { 2 } : 2 = 2 k _ { 2 } + 4 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4711.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"D15XL10P\" using the LaTeX format.",
|
|
"gt_answers": "\\textcircled { 1 } 1 . 5 \\times 1 0 ^ { 2 } P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_4712.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x - 1 = 0\\)",
|
|
"gt_answers": "( 1 - \\frac { 2 } { 3 } ) x = 9 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4713.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"20x5x5 = 1000\".",
|
|
"gt_answers": "2 0 = 5 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4716.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 351-11.",
|
|
"gt_answers": "3 \\div 1 1 = \\frac { 3 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4717.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4443 + 4443 = 4443 + 4443 = 8886.",
|
|
"gt_answers": "y _ { 1 } y _ { 2 } = \\frac { 4 - 4 b ^ { 2 } } { 4 k ^ { 2 } + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4718.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 8x + 5 = 0\\)",
|
|
"gt_answers": "x _ { 0 } ^ { 3 } - 5 x _ { 0 } ^ { 2 } + 8 x _ { 0 } - 4 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4720.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { C E } { A C } = \\frac { \\frac { 4 } { 3 } t } { 1 6 } = \\frac { t } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4721.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 13\\)\n\nThe formula is written in the form of an equation, where the variables x and y are multiplied together and then added to the constant 13.",
|
|
"gt_answers": "1 - \\frac { x - 2 } { 2 } \\leq \\frac { 1 + 3 x } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4722.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "2 \\times 1 0 ^ { - 2 } m ^ { 2 } \\times h \\leq 1 \\times 4 0 - m ^ { 2 } \\times h g\n",
|
|
"image_path": "./data/HME100K/test_images/test_4723.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\angle D A B = 1 8 0 ^ { \\circ } - 9 0 ^ { \\circ } - ( 1 8 0 ^ { \\circ } - 3 \\alpha ) = 3 \\alpha - 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_4726.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Feh7(H2O)6(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(OH)2(",
|
|
"gt_answers": "> F e > H > C u\n",
|
|
"image_path": "./data/HME100K/test_images/test_4727.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(m + n = 2m + 2n\\)\n\nThis is an algebraic equation that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "m = 0 , n = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4728.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 14 + 4 + 2 + 2 = 32.",
|
|
"gt_answers": "n = 1 4 + 1 4 + 2 + 2 = 3 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4729.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 3x + 2 = 0`.",
|
|
"gt_answers": "x - 3 + 6 x = \\frac { 9 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4730.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 492 + 50 - 6 - 12.",
|
|
"gt_answers": "4 9 2 \\div 8 0 = 6 \\cdots 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4732.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 4z^2 - 3y^2 = 0\\)",
|
|
"gt_answers": "3 x ^ { 2 } y ( 4 2 - 3 y )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4733.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\sin \\beta = \\sqrt { 1 - \\cos ^ { 2 } \\beta } = \\frac { 2 \\sqrt { 5 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4734.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: \"NaOH + H2SO4 --> Na2SO4 + H2O.\"",
|
|
"gt_answers": "k / C a / N a + H _ { 2 } O \\Rightarrow k O H / C a ( O H ) _ { 2 } \\vert N a O H + H _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4735.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a few Chinese characters, which could be a representation of a mathematical expression in Chinese.",
|
|
"gt_answers": "1 - \\frac { 1 } { 2 } + \\frac { 1 } { 2 } - \\frac { 1 } { 3 } + \\frac { 1 } { 3 } - \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4736.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "n = 5 0 e\n",
|
|
"image_path": "./data/HME100K/test_images/test_4737.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{3 \\pi}{4} + \\frac{4 \\pi}{3} + \\frac{6 \\pi}{5} + \\frac{7 \\pi}{6} + \\frac{8 \\pi}{9} + \\frac{9 \\pi}{10} + \\frac{10 \\pi}{11} + \\frac{11 \\pi}{12} + \\frac{12 \\pi}{13} + \\frac{13 \\pi}{14} + \\frac{14 \\pi}{15} + \\frac{15 \\pi}{16} + \\frac{16 \\pi}{17} + \\frac{17 \\pi}{18} + \\frac{18 \\pi}{19} + \\frac{19 \\pi}{20} + \\frac{20 \\pi}{21} + \\frac{21 \\pi}{22} + \\frac{22 \\pi}{23} + \\frac{23 \\pi}{24} + \\frac{24 \\pi}{25} + \\frac{25 \\pi}{26} + \\frac{26 \\pi}{27} + \\frac{27 \\pi}{28} + \\frac{28 \\pi}{29} + \\frac{29 \\pi}{30} + \\frac{30 \\pi}{31} + \\frac{31 \\pi}{32} + \\frac{32 \\pi}{33} + \\frac{33 \\pi}{34} + \\frac{34 \\pi}{35} + \\frac{35 \\pi}{36} + \\frac{36 \\pi}{37} + \\frac{37 \\pi}{38} + \\frac{38 \\pi}{39} + \\frac{39 \\pi}{40} + \\frac{40 \\pi}{41} + \\frac{41 \\pi}{42} + \\frac{42 \\pi}{43} + \\frac{43 \\pi}{44} + \\frac{44 \\pi}{45} + \\frac{45 \\pi}{4",
|
|
"gt_answers": "\\sqrt [ 3 ] { - 4 } a = \\sqrt [ 3 ] { - 6 4 } = - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4739.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle O B C = \\frac { 1 } { 2 } - A B C = 2 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4740.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a formula using LaTeX format. The formula is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "a ( C - x ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4741.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 + h^2 + i^2 + j^2 + k^2 + l^2 + m^2 + n^2 + o^2 + p^2 + q^2 + r^2 + s^2 + t^2 + u^2 + v^2 + w^2 + x^2 + y^2 + z^2 + 4(a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 + h^2 + i^2 + j^2 + k^2 + l^2 + m^2 + n^2 + o^2 + p^2 + q^2 + r^2 + s^2 + t^2 + u^2 + v^2 + w^2 + x^2 + y^2 + z^2) = 1600\\)",
|
|
"gt_answers": "5 a - 2 b - ( 5 a + 3 b ) = 1 1 - ( - 4 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4742.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"SA + AD + C = 5xTb3 + 3B\".",
|
|
"gt_answers": "S _ { \\Delta } A D C = \\frac { 1 } { 2 } \\times \\sqrt { 3 } \\times 3 = \\frac { 3 \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4743.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 1 \\div 1 0 = \\frac { 1 1 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4744.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "\\frac { 7 . 3 J } { 1 0 0 g } \\times 1 0 0 \\% = 7 . 5 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_4745.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"22 - 3x - 2 = 0\" in LaTeX format.",
|
|
"gt_answers": "\\frac { 2 2 } { \\sin 3 0 ^ { \\circ } } = \\frac { 1 8 } { \\sin B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4746.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(F = \\frac{mg}{2} \\cdot \\cos\\theta\\)\n\nThis formula relates the force (F) acting on an object to its mass (m), the acceleration due to gravity (g), and the angle (\u03b8) between the object and the direction of the force.",
|
|
"gt_answers": "\\frac { \\sqrt { 2 } c m } { 2 } = \\frac { \\sqrt { 2 } } { 2 } c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4747.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(s_n^2 + s_{n-1}^2 + s_{n-2}^2 + s_{n-3}^2 + \\cdots + s_1^2 + s_0^2 = n^2\\)\n\nThis formula represents the sum of the squares of the first n odd numbers.",
|
|
"gt_answers": "S _ { n } - n ( 2 n - 1 ) a _ { n }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4748.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: `Wf = sonx(x, y, z) + sonx(x, y, -z) + sonx(x, -y, z) + sonx(x, -y, -z)`. This formula calculates the Wave Function (Wf) of a particle in three dimensions, where x, y, and z are the coordinates of the particle. The Wf is a function that describes the probability density of finding the particle at a given position in space.",
|
|
"gt_answers": "W = F S = 5 0 N \\times 2 0 m = 1 0 0 0 J\n",
|
|
"image_path": "./data/HME100K/test_images/test_4749.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^{2} + 2x + 1 = 0\\)",
|
|
"gt_answers": "1 1 x = \\frac { 1 1 } { 2 } x = \\frac { 1 } { 2 } \\therefore y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4751.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2FeCl3 + 6H2O = Fe(OH)3 + 3Cl2 + 3H2.",
|
|
"gt_answers": "6 H C l + F e _ { 2 } O _ { 3 } = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_4752.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 3x + 5.",
|
|
"gt_answers": "y = - \\frac { 1 9 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4753.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 0.25 - 0.16 = 0.09.",
|
|
"gt_answers": "\\frac { 1 . 2 5 } { 0 . 2 5 } = \\frac { x } { 1 . 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4754.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a2 + b2 = c2.",
|
|
"gt_answers": "a _ { 1 } = a _ { 3 } - 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4755.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(w = \\frac{1}{1 + \\frac{1}{2 + \\frac{1}{3 + \\frac{1}{4 + \\frac{1}{5 + \\frac{1}{6 + \\frac{1}{7 + \\frac{1}{8 + \\frac{1}{9 + \\frac{1}{10 + \\frac{1}{11 + \\frac{1}{12 + \\frac{1}{13 + \\frac{1}{14 + \\frac{1}{15 + \\frac{1}{16 + \\frac{1}{17 + \\frac{1}{18 + \\frac{1}{19 + \\frac{1}{20 + \\frac{1}{21 + \\frac{1}{22 + \\frac{1}{23 + \\frac{1}{24 + \\frac{1}{25 + \\frac{1}{26 + \\frac{1}{27 + \\frac{1}{28 + \\frac{1}{29 + \\frac{1}{30 + \\frac{1}{31 + \\frac{1}{32 + \\frac{1}{33 + \\frac{1}{34 + \\frac{1}{35 + \\frac{1}{36 + \\frac{1}{37 + \\frac{1}{38 + \\frac{1}{39 + \\frac{1}{40 + \\frac{1}{41 + \\frac{1}{42 + \\frac{1}{43 + \\frac{1}{44 + \\frac{1}{45 + \\frac{1}{46 + \\frac{1}{47 + \\frac{1}{48 + \\frac{1}{49 + \\frac{1}{50 + \\frac{1}{51 + \\frac{1}{52 + \\frac{1}{53 + \\frac{1}{54 + \\frac{1}{55 + \\frac{1}{56 + \\frac{1}{57 + \\frac{1}{58 + \\frac{1}{59 + \\frac{1}{60 + \\frac{1}{61 + \\frac{1}{62 + \\frac{1}{",
|
|
"gt_answers": "W _ { 2 } = \\frac { 1 7 } { 6 } \\cdot 1 = \\frac { 1 7 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4756.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4 \\times 4 = 16\\)",
|
|
"gt_answers": "\\angle 4 = \\frac { 1 } { 2 } \\angle 1 = \\frac { 1 } { 2 } \\angle 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4757.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle E B P = \\frac { 3 } { 2 } \\angle H B E\n",
|
|
"image_path": "./data/HME100K/test_images/test_4758.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, but I can provide the LaTeX code for the formula:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "2 \\frac { 2 } { 4 } = a + \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4759.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 1 = 3.\"",
|
|
"gt_answers": "x _ { 2 } = \\frac { 1 5 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4760.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = \\frac{1}{2}mv^2\\)\n\nThis formula states that the energy (E) of an object is equal to one-half the product of its mass (m) and its velocity squared (v^2).",
|
|
"gt_answers": "\\frac { P C } { E C } = t \\cdot \\frac { 3 } { 4 t } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4761.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Up(Rp) = 20x(0.14) + 0.02x(0.01) + 0.01x(0.001) + 0.001x(0.0001)\".",
|
|
"gt_answers": "U _ { P ^ { \\prime } } = R _ { P ^ { \\prime } } \\cdot I P = 2 0 \\Omega \\times 0 . 1 4 A\n",
|
|
"image_path": "./data/HME100K/test_images/test_4762.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(P(A) = \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + 4h} \\cdot \\frac{4}{4 + ",
|
|
"gt_answers": "P _ { A } = \\frac { F _ { A } } { 4 h ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4763.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6} + \\frac{1}{7} + \\frac{1}{8} + \\frac{1}{9} + \\frac{1}{10} + \\frac{1}{11} + \\frac{1}{12} + \\frac{1}{13} + \\frac{1}{14} + \\frac{1}{15} + \\frac{1}{16} + \\frac{1}{17} + \\frac{1}{18} + \\frac{1}{19} + \\frac{1}{20} + \\frac{1}{21} + \\frac{1}{22} + \\frac{1}{23} + \\frac{1}{24} + \\frac{1}{25} + \\frac{1}{26} + \\frac{1}{27} + \\frac{1}{28} + \\frac{1}{29} + \\frac{1}{30} + \\frac{1}{31} + \\frac{1}{32} + \\frac{1}{33} + \\frac{1}{34} + \\frac{1}{35} + \\frac{1}{36} + \\frac{1}{37} + \\frac{1}{38} + \\frac{1}{39} + \\frac{1}{40} + \\frac{1}{41} + \\frac{1}{42} + \\frac{1}{43} + \\frac{1}{44} + \\frac{1}{45} + \\frac{1}{46} + \\frac{1}{47} + \\frac{1}{48} + \\frac{1}{49} + \\frac{1}{50} + \\frac{1}{51} + \\frac{1}{52} + \\frac{1}{53} + \\frac{1}{54} + \\frac{1}{55} + \\frac{1}{56} + \\",
|
|
"gt_answers": "\\frac { x + 1 } { 2 } - 1 = \\frac { 5 - x } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4764.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x + 8 = 11.\"",
|
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"gt_answers": "\\frac { 1 } { 8 } \\times 4 = \\frac { 4 } { 8 } \\frac { 2 } { 4 } \\frac { 1 } { 2 }\n",
|
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"image_path": "./data/HME100K/test_images/test_4765.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "C P _ { 2 } = 5 , C P = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4768.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666",
|
|
"gt_answers": "\\frac { 6 } { 6 } \\frac { 6 } { 5 } \\frac { 6 } { 4 } \\frac { 6 } { 3 } \\frac { 6 } { 2 } \\frac { 6 } { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4769.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(N_{s} = \\frac{B_{s} \\cdot T_{s}}{R_{s}}\\)\n\nwhere Ns is the number of seconds, Bs is the base speed, Ts is the time taken, and Rs is the resistance.",
|
|
"gt_answers": "N a _ { 2 } S O _ { 4 } + B a ( O H _ { 2 } ) _ { 2 1 } = B a S O _ { 4 } \\downarrow + 2 N a O H\n",
|
|
"image_path": "./data/HME100K/test_images/test_4770.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/x + 1 = 1\".",
|
|
"gt_answers": "\\frac { x } { x - 1 } = y\n",
|
|
"image_path": "./data/HME100K/test_images/test_4771.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4.942 x 10^23\" using scientific notation.",
|
|
"gt_answers": "1 1 . a \\div 1 2 , c \\times 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4772.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 5x + 6}{x^2 + 4x + 5} = \\frac{x^2 + 5x + 6}{x^2 + 4x + 5}\n\\end{equation}\n\nThis is a simple algebraic equation that can be solved by factoring the numerator and denominator.",
|
|
"gt_answers": "x _ { 1 } = \\frac { 3 + \\sqrt { 4 1 } } { 4 } x _ { 2 } = \\frac { 3 - \\sqrt { 4 1 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4773.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x = \\frac { 3 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4774.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\n\\(C_{6}H_{5}O_{2} + 2NaOH \\rightarrow Na_{2}CO_{3} + 2C_{6}H_{5}OH\\)",
|
|
"gt_answers": "2 C H _ { 3 } C O O H + C a C O _ { 3 } \\rightarrow C a ( C H C O O ) _ { 2 } . + H _ { 2 } O + C O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4775.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)\n\nThis formula can be represented using the LaTeX code:\n\n\\(2x^2 + 3x - 4 = 0\\)\n\nThe LaTeX code uses the `\\( \\)` and `\\)` symbols to denote the beginning and end of the formula, respectively. The `\\( \\)` symbol is used to enclose the entire formula, while the `\\)` symbol is used to enclose the entire expression within the parentheses. The `x^2` and `x` symbols are written using the `\\( \\)` and `\\(` symbols, respectively, to denote the exponentiation operator. The `+` and `-` symbols are written using the `\\+` and `\\-` symbols, respectively, to denote the addition and subtraction operators. The `=` symbol is written using the `\\=` symbol to denote the equality operator. Finally, the `\\)` symbol is used to close the entire expression.",
|
|
"gt_answers": "2 x = 1 \\frac { 1 } { 6 } - \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4776.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\sqrt{x^2 + 1} - 1\\)",
|
|
"gt_answers": "2 \\sqrt { y + 5 } = y - 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4777.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 14 x 360\u00b0 / 84\u00b0 = 1080\u00b0.",
|
|
"gt_answers": "\\frac { 1 4 } { 6 0 } \\times 3 6 0 ^ { \\circ } = 8 4 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4778.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(C_2H_5OH + 2NaOH \\rightarrow 2NaC_2H_5O + H_2O\\)\n\nThis formula represents the chemical reaction between two molecules of ethanol (C_2H_5OH) and two molecules of sodium hydroxide (NaOH) to produce two molecules of sodium cyanide (NaC_2H_5O) and water (H_2O).",
|
|
"gt_answers": "C H _ { 3 } - C - C H _ { 2 } - C H _ { 3 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4779.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 6000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "6 3 0 c m ^ { 3 } = ( 0 . 6 3 ) d m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4781.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "1 0 y - 5 y + 5 = 1 0 - 2 y + 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4782.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/2 + 1/4 = 1/2 + 1/8 = 3/8.\"",
|
|
"gt_answers": "\\Delta E C F \\sim \\Delta O F N\n",
|
|
"image_path": "./data/HME100K/test_images/test_4783.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = 2(m_1 + m_2)\\)\n\nThis formula represents the relationship between two masses, m1 and m2, where m is the total mass of the two masses.",
|
|
"gt_answers": "m - 2 = ( 2 - m ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4785.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as Na2O + 2HCl --> 2NaCl + H2O.",
|
|
"gt_answers": "2 N a O H + C O _ { 2 } = N a _ { 2 } C O _ { 3 } + H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_4786.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mixture of Japanese and English, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few symbols, including a circle, a square, and a triangle.",
|
|
"gt_answers": "x = \\frac { 8 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4787.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 100.45MB = 100.45 \u00d7 10^6 \u00d7 10^2 / 1000 = 100.45 \u00d7 10^6 \u00d7 1000 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 = 100.45 \u00d7 10^6 / 1000 =",
|
|
"gt_answers": "4 . 0 5 m ^ { 3 } = ( 4 ) m ^ { 3 } ( 5 0 ) d m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4788.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(s = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "S _ { n } = n ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4789.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: X-42 + 54 = 96.",
|
|
"gt_answers": "x = \\frac { 4 5 } { 5 4 } - \\frac { 4 2 } { 5 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4790.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"5x2 + 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x2 - 2x2 - 5x2 - 3x",
|
|
"gt_answers": "S _ { 5 } = 5 ^ { 2 } = 2 5 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4791.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `1000/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\Delta V = \\frac { 7 8 0 } { 1 0 0 } \\times 0 . 6 L = 4 . 6 8 L\n",
|
|
"image_path": "./data/HME100K/test_images/test_4792.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(72dm = 170cm\\)\n\nThis formula is written in the form of a mathematical equation, where the variable \"d\" represents the distance in meters and \"m\" represents the distance in centimeters. The equation states that 72 dm is equal to 170 cm.",
|
|
"gt_answers": "7 2 d m ^ { 2 } = 7 2 0 0 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4793.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m(t) = m_0 + \\int_{0}^{t} \\left( \\frac{dv}{dt} \\right) dt\\)\n\nThis formula represents the motion of a particle with mass m and initial velocity v at time t. The integral represents the change in the particle's momentum over time, which is equal to the product of the particle's mass and its acceleration. The initial velocity is denoted by v0, and the initial momentum is m0v0.",
|
|
"gt_answers": "( \\frac { 1 } { m } + \\frac { 1 } { 1 - m } ) ( m + 1 - m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4794.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V_{i} = \\sqrt{\\frac{2}{3} \\pi R_{i}^{3} \\rho_{i} \\epsilon_{0} \\epsilon_{r} \\mu_{0} \\left(1 - \\frac{2}{3} \\left(1 - \\frac{4}{3} \\frac{R_{i}}{r_{0}}\\right)^{3}\\right)}\\)\n\nThe formula is for calculating the potential energy of a spherical conductor of radius Ri in a uniform magnetic field B. The variables in the formula are:\n\n* Vi: potential energy of the conductor\n* Ri: radius of the conductor\n* \u03c1i: density of the conductor material\n* \u03b50: permittivity of free space\n* \u03b5r: relative permittivity of the conductor material\n* \u03bc0: permeability of free space\n* r0: radius of the conductor in the absence of the magnetic field\n\nThe formula uses the following relationships:\n\n* 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - 4/3 (Ri/r0)^3) = 1 - 2/3 (1 - ",
|
|
"gt_answers": "v _ { 1 } = \\frac { 1 } { \\sqrt { 3 } } V _ { 0 } = 3 m / s\n",
|
|
"image_path": "./data/HME100K/test_images/test_4795.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x = 7 \\div \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4796.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "O E = \\frac { 6 \\sqrt { 3 } . } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4798.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5.7 + 11.9 = 19.6.",
|
|
"gt_answers": "\\frac { 5 } { 1 9 } + \\frac { 7 } { 1 9 } = \\frac { 1 1 } { 1 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4800.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written in the form of a mathematical equation, with the letters \"a\" and \"b\" representing unknown variables. The expression is written in a way that it can be easily read and understood by those familiar with the LaTeX formula notation.",
|
|
"gt_answers": "a ^ { 2 } + b ^ { 2 } > c ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4802.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(x + 4) - 4(x - 2) = 0.",
|
|
"gt_answers": "\\frac { 5 } { - 1 } = \\frac { x + 4 } { x + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4803.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 - 4x + 0 = 0`.",
|
|
"gt_answers": "\\frac { x - 4 } { 2 x } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4804.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(B_o = \\frac{B_1 + B_2 + B_3 + B_4 + B_5}{5}\\)",
|
|
"gt_answers": "C D = B C - B D = \\frac { 2 8 } { 5 } - 5 = \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4805.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1",
|
|
"gt_answers": "( 4 0 - 3 0 + x ) ( 6 0 0 - 1 0 x ) = 1 0 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4806.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(1/3) + 3(1/2) = 90/2.",
|
|
"gt_answers": "\\angle 1 + \\angle 3 = \\angle B C A = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4808.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(AP = \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^2 - y^2}{2} + \\frac{x^2 + y^2}{2} + \\frac{x^",
|
|
"gt_answers": "H P = A P = x , C P = 1 0 - 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_4809.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "\\frac { 3 } { 4 . } - \\frac { 1 } { 4 } = \\frac { 2 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4810.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LA-LC = 60\u00b0\".",
|
|
"gt_answers": "\\angle A = \\angle C = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4811.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(11 + 14 = 25\\)",
|
|
"gt_answers": "B H = 1 + \\frac { \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4813.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"an-nan-nan\" using LaTeX format.",
|
|
"gt_answers": "a _ { n } = n a _ { n + 1 } - n a _ { n }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4814.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the multiplication of two fractions, each with a denominator of 2. The result is a fraction with a denominator of 4.",
|
|
"gt_answers": "\\cos A = \\frac { \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4815.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 1500x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 10x5000 - 5x10000) - 10000x(6x5000 - 3x10000 + 1",
|
|
"gt_answers": "( 5 . 4 - 3 . 6 ) x + 6 \\cdot \\frac { 1 5 2 0 } { 8 } - 3 . 6 x \\geq 1 0 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4817.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 54x(66-x) = 366.",
|
|
"gt_answers": "5 4 - x = \\frac { 1 } { 3 } ( 6 6 - x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4819.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\angle E A F - \\angle 2 = \\angle G A C - \\angle 2 E\n",
|
|
"image_path": "./data/HME100K/test_images/test_4820.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x + 3\\)",
|
|
"gt_answers": "1 y = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4821.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "a + \\sqrt { a ^ { 2 } + 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4822.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "u = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4824.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x + 2 = 4`.",
|
|
"gt_answers": "x = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4828.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x - 3 x = 6 x = 2 - 3 + 1 0 J .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4829.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: PD = AB + CD.",
|
|
"gt_answers": "\\frac { A B } { P D } = \\frac { B D } { C D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4830.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "\\angle E C F = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4831.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(F_{LBP} = \\frac{1}{2} \\sum_{i=1}^{N} \\sum_{j=1}^{N} \\sum_{k=1}^{N} \\sum_{l=1}^{N} \\sum_{m=1}^{N} \\sum_{n=1}^{N} \\sum_{o=1}^{N} \\sum_{p=1}^{N} \\sum_{q=1}^{N} \\sum_{r=1}^{N} \\sum_{s=1}^{N} \\sum_{t=1}^{N} \\sum_{u=1}^{N} \\sum_{v=1}^{N} \\sum_{w=1}^{N} \\sum_{x=1}^{N} \\sum_{y=1}^{N} \\sum_{z=1}^{N} \\sum_{a=1}^{N} \\sum_{b=1}^{N} \\sum_{c=1}^{N} \\sum_{d=1}^{N} \\sum_{e=1}^{N} \\sum_{f=1}^{N} \\sum_{g=1}^{N} \\sum_{h=1}^{N} \\sum_{i=1}^{N} \\sum_{j=1}^{N} \\sum_{k=1}^{N} \\sum_{l=1}^{N} \\sum_{m=1}^{N} \\sum_{n=1}^{N} \\sum_{o=1}^{N} \\sum_{p=1}^{N} \\sum_{q=1}^{N} \\sum_{r=1}^{N} \\sum_{s=1}^{N} \\sum_{t=1}^{N} \\sum_{u=1}^{N} \\sum_{v=1}^{N} \\sum_{w=1}^{N} \\sum_{x=1}^{N} \\sum_{y=1}^{N} \\sum_{z=1}^{N} \\sum_{a=1}^{N} \\sum_{b=1}^{N} \\sum_{c=1}^{N} \\sum_{d=1}^{N} \\sum_{e=1}^{N} \\sum_{f=1}^{N} \\sum_{g=1}^{N} \\sum_{h=1}^{N} \\sum_{i=1}^{N} \\sum_{j=1",
|
|
"gt_answers": "F \\bot B P\n",
|
|
"image_path": "./data/HME100K/test_images/test_4832.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as a75.",
|
|
"gt_answers": "a > \\frac { 6 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4833.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows: `20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 5 0 0 \\times 5 0 0 0 = 1 2 5 0 0 0 0 0 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4834.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: `a/b = 5/7`.",
|
|
"gt_answers": "a + b = \\frac { 5 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4835.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x^2 + 1} = \\frac{1}{x^2} + \\frac{1}{1}\n\\end{equation}\n\nThis equation can be simplified further by factoring out the common denominator, which results in:\n\n\\begin{equation}\n\\frac{1}{x^2 + 1} = \\frac{1}{x^2} \\cdot \\frac{1}{1}\n\\end{equation}\n\nFinally, the expression can be rearranged to obtain the desired result:\n\n\\begin{equation}\n\\frac{1}{x^2 + 1} = \\frac{1}{x^2} \\cdot \\frac{1}{1} = \\frac{1}{x}\n\\end{equation}\n\nThis equation shows that the square root of the sum of the squares of two numbers is equal to the square root of the smaller number.",
|
|
"gt_answers": "x _ { 1 } < x _ { 2 } < x _ { 3 } - : a > 0 , b < 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4836.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{",
|
|
"gt_answers": "\\angle F Q N = \\frac { 1 } { 2 } \\angle D Q N\n",
|
|
"image_path": "./data/HME100K/test_images/test_4837.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "8 0 0 0 \\times \\frac { 1 } { 2 0 0 0 } = 4 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4838.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"x^2 + 3x - 1 = 0.\"",
|
|
"gt_answers": "x > \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4839.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\nBdE + CdE + DdE = Odd\n\nThe formula is a combination of three terms, each of which is a product of two letters and a number. The letters represent the variables, and the numbers represent the coefficients. The first term, BdE, is a product of the letters B, D, and E, with a coefficient of 1. The second term, CdE, is a product of the letters C, D, and E, with a coefficient of 1. The third term, DdE, is a product of the letters D, E, and E, with a coefficient of 1. The letter O represents the constant term, which is equal to 1. The formula is written using the equation operator \"=\", which indicates that the terms on both sides of the equation are equal.",
|
|
"gt_answers": "B D = O D = O C = O B = O C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4840.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: Fe + 6H2O = Fe(OH)3 + 3H2.",
|
|
"gt_answers": "F e + H _ { 2 } S O _ { 4 } = F e S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4841.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 3x + 1\\)",
|
|
"gt_answers": "y = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4842.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "- 9 y \\times ( - \\frac { 1 } { 9 } ) \\leq 6 \\times ( - \\frac { 1 } { 9 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4846.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(t^2 + z^2 = k^2 + 2at + b\\)\n\nwhere `t`, `z`, `k`, `a`, and `b` are variables.",
|
|
"gt_answers": "\\vert t \\vert t = 2 k \\pi + \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4847.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 96/16 = 12/2 cm.",
|
|
"gt_answers": "9 6 + 1 6 = 1 1 2 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4848.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4x^2 + 4x + 1 = 16\\)",
|
|
"gt_answers": "\\frac { x } { 4 } = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4849.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "V = I _ { 1 } R _ { 1 } = 3 A \\times 4 W = 1 2 V\n",
|
|
"image_path": "./data/HME100K/test_images/test_4850.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"k = 1/2 (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024 + 1/2048 + 1/4096 + 1/8192 + 1/16384 + 1/32768 + 1/65536 + 1/131072 + 1/262144 + 1/524288 + 1/1048576 + 1/2097152 + 1/4194304 + 1/8388608 + 1/16777216 + 1/33554432 + 1/67108864 + 1/134217728 + 1/268435456 + 1/536870912 + 1/1073741824 + 1/2147483648 + 1/4294967296 + 1/8589934592 + 1/17179869184 + 1/34359738368 + 1/687194767384 + 1/1374389534568 + 1/275879907374184 + 1/551459496729688 + 1/1103519987194768 + 1/22070399703947688 + 1/4414319967296888 + 1/8828639953456",
|
|
"gt_answers": "k = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4851.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(12 \\times 0.15 = 1.80\\)",
|
|
"gt_answers": "\\frac { 1 2 } { 1 2 + 4 } = 0 . 7 5 = 7 5 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_4852.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2(a+b) = 2a + 2b\".",
|
|
"gt_answers": "\\vert a \\vert + 1 = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4854.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 4\\)",
|
|
"gt_answers": "y = - \\frac { 1 } { 3 } ( m - \\frac { 1 } { 2 } ) ^ { 2 } + \\frac { 4 9 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4855.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(14 = 1 + 2 \\cdot 3 \\cdot 4\\)",
|
|
"gt_answers": "x _ { 4 } = - \\frac { 9 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4856.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x = \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4857.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2.357 - 0.002 = 2.355.",
|
|
"gt_answers": "1 . 3 7 5 x = - 2 . 7 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4858.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CL-3DPP12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697989909192939495969798990919293949596979899091929394959697989909192939495969798990919293949596979899091929394959697989909192939495969798990919293949596979899091929394959697989909192939495969798990919293949596979899091929394959697989909192939495969798990919293949596979899091929394959697989909192939495969798990919",
|
|
"gt_answers": "( 1 1 - 3 D P ) ^ { 2 } + 1 2 ^ { 2 } = 1 3 ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4859.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten style, but it can be represented in LaTeX format as follows:\n\n\\(f(x) = 2x + 3\\)",
|
|
"gt_answers": "D E = 2 \\sqrt { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4860.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(R_s = \\frac{R_0}{1 + \\left(\\frac{R_0}{R_s}\\right)^2}\\)\n\nThis formula is commonly used to calculate the resistance of a resistor when it is subjected to a specific temperature. The resistance of the resistor is represented by the variable Rs, and the resistance at room temperature is represented by the variable R0. The resistance at a specific temperature is calculated by multiplying the resistance at room temperature by the square of the ratio of the new temperature to the room temperature.",
|
|
"gt_answers": "R = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4861.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "2 a ^ { 2 } = 1 2 \\times ( \\frac { 1 } { 2 } ) ^ { 2 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4862.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 12.",
|
|
"gt_answers": "= \\frac { x } { \\frac { 2 5 } { 2 } } = \\frac { \\frac { 1 2 } { 5 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4863.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(A^2 + B^2 = C^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the sum of the squares of the lengths of two sides of a right triangle is equal to the square of the length of the third side.",
|
|
"gt_answers": "( A D + O A + O D ) - ( A B + O A + O B ) = ( A D + O A + O D ) -\n",
|
|
"image_path": "./data/HME100K/test_images/test_4864.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 7y = 14.",
|
|
"gt_answers": "\\frac { 7 x } { 2 0 } = \\frac { x } { 5 } + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4865.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a negative sign, which could be a formula for calculating the area of a circle.",
|
|
"gt_answers": "P ( \\xi = 0 ) = \\frac { 1 } { 4 } \\times \\frac { 1 } { 2 } = \\frac { 1 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4866.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "x = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4867.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: `sqrt(x^2 + 12 cm^2)`.",
|
|
"gt_answers": "( 5 + 1 ) \\times 2 = 1 2 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4868.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 15x4 - 4x3 + 3x2 - 2x1 + 1x0.",
|
|
"gt_answers": "x = - \\frac { 1 5 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4869.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x + 2y = 10\\)\n\nThis formula represents the relationship between the variables x and y, where x is equal to 3 and y is equal to 2. The result of the equation is 10.",
|
|
"gt_answers": "( 1 8 ) \\div 2 4 = \\frac { 9 } { ( 1 2 ) } = \\frac { ( 1 5 } { 2 0 } ) = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4870.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 0 L = 4 0 0 0 0 c m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4872.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt{2} \\cdot 2\\sqrt",
|
|
"gt_answers": "\\angle B A C + \\angle A B C + \\angle C = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4874.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 3(a-2) - 2(a-1) = 3a - 4.",
|
|
"gt_answers": "\\frac { 3 + x + a } { x - a - 2 } = \\frac { 7 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4875.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(5 \\cdot 10^{-5} \\cdot 10^{-3} \\cdot 10^{-2} \\cdot 10^{-1} = 5 \\cdot 10^{-8}\\)",
|
|
"gt_answers": "\\cos B = \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4877.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"V-Vthish\" using a handwritten style.",
|
|
"gt_answers": ": V = ( \\pi r ^ { 2 } ) h\n",
|
|
"image_path": "./data/HME100K/test_images/test_4878.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(15 \\times 0.5 = 7.5\\)",
|
|
"gt_answers": "\\frac { x } { 1 5 } = \\frac { 1 . 5 } { 0 . 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4879.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nx^2 + 2a x + a^2 = 3a^2 + 2a x + 3x^2\n\nThis is a quadratic equation in the variable x, with a and b as constants.",
|
|
"gt_answers": "x = 2 a - 3 = a\n",
|
|
"image_path": "./data/HME100K/test_images/test_4880.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4B-130\u00b0\".",
|
|
"gt_answers": "\\angle B = 1 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4881.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(S = 4 \\times 18 \\times 18 \\times 4 \\times 88 = 16884\\)",
|
|
"gt_answers": "S _ { 8 } = [ ( - 4 ) + ( - 1 8 ) ] \\times 4 = - 8 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_4882.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2000x(2000-2000) = 40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": ": 2 0 0 \\times 1 0 0 = 2 0 0 0 0 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4883.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(a + b = 4\\)\n\nThis is a simple algebraic equation that states that the sum of two numbers a and b is equal to 4.",
|
|
"gt_answers": "a \\neq \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4884.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nL_{B} &= L_{PC} + L_{PB} + L_{PCB} + L_{PBC} + L_{PBCB} + L_{PBCFB} + L_{PBCFBG} + L_{PBCFBH} + L_{PBCFBJ} + L_{PBCFBK} + L_{PBCFBL} + L_{PBCFBM} + L_{PBCFBN} + L_{PBCFBO} + L_{PBCFBP} + L_{PBCFBQ} + L_{PBCFBR} + L_{PBCFBS} + L_{PBCFBT} + L_{PBCFBU} + L_{PBCFBV} + L_{PBCFBW} + L_{PBCFBX} + L_{PBCFBY} + L_{PBCFBZ} + L_{PBCFBa} + L_{PBCFBb} + L_{PBCFBc} + L_{PBCFBd} + L_{PBCFBe} + L_{PBCFBf} + L_{PBCFBg} + L_{PBCFBh} + L_{PBCFBi} + L_{PBCFBj} + L_{PBCFBk} + L_{PBCFBl} + L_{PBCFBm} + L_{PBCFBn} + L_{PBCFBo} + L_{PBCFBp} + L_{PBCFBq} + L_{PBCFBr} + L_{PBCFBs} + L_{PBCFBt} + L_{PBCFBu} + L_{PBCFBv} + L_{PBCFBw} + L_{PBCFBx} + L_{PBCFBy} + L_{PBCFBz} + L_{PBCFBa} + L_{PBCFBb} + L_{PBCFBc} + L_{PBCFBd} + L_{PBCFBe} + L_{PBCFBf} + L_{PBCFBg} + L_{PBCFBh} + L_{PBCFBi} + L_{PBCFBj} + L_{",
|
|
"gt_answers": "\\angle B O D = \\angle D O C : 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4886.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 2x - 3.",
|
|
"gt_answers": "x + y - 3 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4887.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"100 - 0.06 = 99.94.\"",
|
|
"gt_answers": "0 . 0 6 = \\frac { 6 0 } { 1 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4888.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x - 1 = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4889.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as DE = 3BC.",
|
|
"gt_answers": "D E = \\frac { 1 } { 2 } B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4890.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "9 0 ^ { \\circ } - \\angle 1 = \\angle 1 + \\angle 1 \\therefore \\angle 1 = 3 0 ^ { \\circ } \\therefore \\angle 3 = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4891.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: DC = DT + DB.",
|
|
"gt_answers": "\\frac { D C } { D E } = \\frac { D O } { D B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4892.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2.35 g/mol x 0.001 mL = 0.0000235 g.\"",
|
|
"gt_answers": "n _ { o 2 } = \\frac { m _ { o 2 } } { M _ { o 2 } } = \\frac { 3 . 2 g } { 3 2 g / m o l } = 0 . 1 m o l\n",
|
|
"image_path": "./data/HME100K/test_images/test_4894.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2(3x + 1) - 9 = 12.",
|
|
"gt_answers": "\\frac { 7 } { 9 } - \\frac { 5 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4895.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written as:\n\n\\(ACB = \\frac{1}{2}AB + \\frac{1}{2}BC\\)\n\nThe formula represents the area of a triangle with sides AB, BC, and AC. The formula can be rearranged to solve for any two sides of the triangle, such as AB and BC.",
|
|
"gt_answers": "A C \\bot B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4896.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AE = 2/3.\"",
|
|
"gt_answers": "A E = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4897.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle C P A = 9 0 ^ { \\circ } \\therefore \\Delta A B C \\sim \\Delta A C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_4898.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nsin(x) = -sin(x) + sin(x)",
|
|
"gt_answers": "\\sin x = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4899.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "( b - 2 ) ( b - 5 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4900.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 3x1.22 = 4.",
|
|
"gt_answers": "\\frac { 3 } { 4 } \\times 1 . 2 = \\frac { 9 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4901.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x - 4.",
|
|
"gt_answers": "x = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4903.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible for me to accurately transcribe it into LaTeX format. However, I can provide a rough translation of the formula:\n\n\"The sum of the squares of the first n natural numbers is equal to the sum of the squares of the first n odd numbers.\"",
|
|
"gt_answers": "y _ { 1 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4904.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3/5 + 5/3 = 10/3.",
|
|
"gt_answers": "\\frac { 3 } { 4 } : \\frac { 3 } { 5 } = \\frac { 5 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4905.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 3 } { 2 } \\vert m \\vert + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4906.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(n = \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4} + \\frac{1}{4} = 1\\)",
|
|
"gt_answers": "T _ { m } = \\frac { 1 - 2 ^ { n } } { 1 - 2 } = 2 ^ { n } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_4907.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"11x4 + 4x3 + 3x2 + 2x + 1 = 144.\"",
|
|
"gt_answers": "x _ { 1 } = 4 x _ { 2 } = - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4910.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A) \\cdot P(B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(",
|
|
"gt_answers": "\\frac { \\sqrt { 1 3 } + 3 } { 2 } P _ { 2 } = \\frac { - \\sqrt { 1 3 } + 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4911.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 144 + 60 + 16 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 +",
|
|
"gt_answers": "O C = O A + A C = 1 4 1 - 1 6 = 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4912.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 4x + 5.",
|
|
"gt_answers": "y _ { 4 } = - \\frac { 7 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4913.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 133.07884422x^2 + 84.422428844x + 4 = 133.07884422x^2 + 84.422428844x + 4\\)",
|
|
"gt_answers": "9 3 . 6 - 7 . 8 x - 8 4 . 2 4 = 4 . 2 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4915.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x(1+y) = 10.",
|
|
"gt_answers": "\\frac { 3 } { 6 } \\times \\frac { 1 } { 3 } + 5 y = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4916.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{x^2 + 3x + 4}{x^2 + 2x +",
|
|
"gt_answers": "x ^ { 2 } - x = \\frac { 9 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4917.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "A E \\bot B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4918.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 100\\)\n\nThis formula represents the relationship between the variables x and y, where x and y are real numbers and the result is an integer. The formula states that the square of the sum of x and y is equal to 100.",
|
|
"gt_answers": "\\frac { 1 5 } { 1 0 0 } x - \\frac { 9 } { 1 0 0 } = \\frac { 7 } { 1 0 0 } x + \\frac { 3 1 } { 1 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4919.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Festby th(h) + Fesby th(h) = 1.\"",
|
|
"gt_answers": "F e + H _ { 2 } S O _ { 4 } = F e S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_4920.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "A M = \\sqrt { ( 0 - a ) ^ { 2 } + ( 1 - 0 ) ^ { 2 } } = \\sqrt { a ^ { 2 } + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4921.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x^2 + 4x - 6 = 0\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(3x^2 + 4x - 6 = 0\\)",
|
|
"gt_answers": "\\frac { 3 ^ { 2 } + 4 ^ { 2 } - ( \\sqrt { 3 } ) ^ { 2 } } { 2 \\cdot 3 \\cdot 4 } = \\frac { 1 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4922.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "h n = \\lambda a _ { n - 1 } + \\frac { 2 } { 3 } + \\frac { 2 } { 3 ( A - 1 ) } = \\lambda a _ { n - 1 } + \\frac { 2 } { 3 } ( 1 + \\frac { 1 } { \\Lambda - 1 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4923.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(x^2 + 2x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x _ { 1 } , - 2 8 x _ { 2 } ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4924.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LA = 46.6 lb + 40 lb = 87.2 lb.\"",
|
|
"gt_answers": "\\angle A = 4 6 ^ { \\circ } , \\angle B = 4 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4925.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 3x - 9 = 0\\)",
|
|
"gt_answers": "[ 2 ( x + 3 ) - 3 ( x - 3 ) ] = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_4927.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "/ 9 4 0 d m ^ { 3 } / m ^ { 3 } = 1 0 0 0 d m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4929.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LB0 = 2(AB0) + 150\".",
|
|
"gt_answers": "\\cdot \\angle A B O = \\angle B A O = 1 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4930.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 3x + 2 = 0\\)\n\nThis formula represents a quadratic equation, where x is the unknown variable and the other terms represent constants.",
|
|
"gt_answers": "x - \\frac { 1 } { 3 } x = \\frac { 2 } { 3 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4931.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis is a simple algebraic equation that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "f ( - x ) = f ( x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4932.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(y = 3x^2 + 2x + 1\\)",
|
|
"gt_answers": "y _ { 1 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4933.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(F = \\frac{F_c}{1 + \\frac{F_c}{F_0}} = \\frac{F_c}{1 + \\frac{F_c}{F_0} \\cdot \\frac{F_0}{F_c}} = \\frac{F_c}{1 + \\frac{F_c}{F_0} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c}} = \\frac{F_c}{1 + \\frac{F_c}{F_0} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c}} = \\frac{F_c}{1 + \\frac{F_c}{F_0} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c}} = \\frac{F_c}{1 + \\frac{F_c}{F_0} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c}} = \\frac{F_c}{1 + \\frac{F_c}{F_0} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c}} = \\frac{F_c}{1 + \\frac{F_c}{F_0} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c}} = \\frac{F_c}{1 + \\frac{F_c}{F_0} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c} \\cdot \\frac{F_0}{F_c}} = \\frac{F_c}{1 + \\frac{F_c}{F_0} \\cdot \\frac{F_0}{F",
|
|
"gt_answers": "D F = F C = \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_4934.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 7\\)\n\nThis formula represents the relationship between two variables, x and y, and the constant 7. The equation can be solved by substituting values for x and y to find the values of x and y that satisfy the equation.",
|
|
"gt_answers": "x _ { 1 } = - \\frac { 2 } { 3 } x _ { 2 } = - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4935.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Bd 16c + 60g = 100.\"",
|
|
"gt_answers": "B D \\bot A C \\cong A O = C 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4936.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBD(2,0) = 2LBD(1,1) + LBD(1,0)\".",
|
|
"gt_answers": "\\angle A B C - \\angle 1 = \\angle B C D - \\angle 2 (\n",
|
|
"image_path": "./data/HME100K/test_images/test_4937.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `225cm = 2.5dun`.",
|
|
"gt_answers": "r = 2 5 c m = 2 . 5 d m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4938.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"21:12:December\".",
|
|
"gt_answers": "\\angle 2 = \\angle D E C\n",
|
|
"image_path": "./data/HME100K/test_images/test_4939.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBDEB = 180\u00b0 - 30\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - 10\u00b0 - ",
|
|
"gt_answers": "\\angle B D E = \\angle D E B = \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } - 3 0 ^ { \\circ } ) = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4940.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4500/4500 = 1\" using LaTeX format.",
|
|
"gt_answers": "\\angle A E B = 4 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4941.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "\\cos C = \\frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { 2 a b } = - \\frac { 4 \\sqrt { 2 } } { 8 } = - \\frac { \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4942.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(n = 2 \\times 3^{1/4} \\times 5^{1/5} \\times 7^{1/6} \\times 9^{1/7} \\times 11^{1/8} \\times 13^{1/9} \\times 15^{1/10} \\times 17^{1/11} \\times 19^{1/12} \\times 21^{1/13} \\times 23^{1/14} \\times 25^{1/15} \\times 27^{1/16} \\times 29^{1/17} \\times 31^{1/18} \\times 33^{1/19} \\times 35^{1/20} \\times 37^{1/21} \\times 39^{1/22} \\times 41^{1/23} \\times 43^{1/24} \\times 45^{1/25} \\times 47^{1/26} \\times 49^{1/27} \\times 51^{1/28} \\times 53^{1/29} \\times 55^{1/30} \\times 57^{1/31} \\times 59^{1/32} \\times 61^{1/33} \\times 63^{1/34} \\times 65^{1/35} \\times 67^{1/36} \\times 69^{1/37} \\times 71^{1/38} \\times 73^{1/39} \\times 75^{1/40} \\times 77^{1/41} \\times 79^{1/42} \\times 81^{1/43} \\times 83^{1/44} \\times 85^{1/45} \\times 87^{1/46} \\times 89^{1/47} \\times 91^{1/48} \\times 93",
|
|
"gt_answers": "( n = 3 , 4 , 5 \\cdots )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4943.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nZn(OH)2 + 2H2SO4 \u2192 ZnSO4 + 2H2O + O2",
|
|
"gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
|
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"image_path": "./data/HME100K/test_images/test_4944.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LAOF = 80\u00b0\".",
|
|
"gt_answers": "\\angle A O F = 1 8 0 ^ { \\circ } - \\angle 2 + \\angle 3 - \\angle 2 - \\angle 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4945.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\ny = 4x^2 - 2x + 1\n\\end{equation}\n\nThis is a quadratic equation in the form of y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = 4, b = -2, and c = 1.",
|
|
"gt_answers": "y _ { 4 } = - \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4946.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n(2x + 3y) = 10\n\nThe formula is written in LaTeX format using the following code:\n\n(2x + 3y) = 10\n\nThe equation is written in the form of an algebraic expression, where the variables x and y are multiplied together and then added to the constant 10.",
|
|
"gt_answers": "1 0 0 \\times \\frac { 2 } { 1 0 } = 2 0 ( g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4947.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x + 5 = 10.",
|
|
"gt_answers": "\\frac { 1 } { 2 } + \\frac { 2 } { 5 } = \\frac { 9 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4948.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, which are not supported by LaTeX. However, I can provide a rough translation of the expression using the English alphabet:\n\n\"3HV5, 26.5\"",
|
|
"gt_answers": "F _ { 3 } ( 1 + \\sqrt { 5 } , 2 \\sqrt { 5 } ) .\n",
|
|
"image_path": "./data/HME100K/test_images/test_4950.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: (6x^2 - 3x + 1)^2 - 4x^2 - 2x + 1.",
|
|
"gt_answers": "6 ( 2 x - 1 ) - 5 ( x - 1 ) = 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4952.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) = 2(k^2 + 2k + 1) =",
|
|
"gt_answers": "2 - \\frac { 1 } { 3 } ( k + 1 ) = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4953.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "2 x ^ { 2 } + 6 x - 2 x - 6 - x ^ { 2 } - 6 x - 9 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4954.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(4(x^2 + 4x + 1) - 4(x^2 + 4x + 1) = 0\\)\n\nThis can be written in LaTeX as:\n\n\\(4(x^2 + 4x + 1) - 4(x^2 + 4x + 1) = 0\\)\n\nThe LaTeX code for this expression is:\n\n\\begin{equation}\n4(x^2 + 4x + 1) - 4(x^2 + 4x + 1) = 0\n\\end{equation}",
|
|
"gt_answers": "\\Delta = 1 6 k ^ { 4 } - 4 ( 1 + k ^ { 2 } ) ( 4 k ^ { 2 } - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4955.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "x _ { 2 } = \\frac { 3 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4956.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "1 4 \\times ( 2 0 \\div 2 ) ^ { 2 } = 3 1 4 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4957.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"M2 orms3\".",
|
|
"gt_answers": "m > 2 o r m = - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_4959.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\Delta P B D \\sim \\Delta E C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_4960.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(L_2(x) = \\frac{1}{2} \\int_{-1}^{1} \\left(x^2 - 2x + 1\\right)^2 dx\\)",
|
|
"gt_answers": "\\angle E D B = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4962.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nNa2CO3 + H2SO4 --> Na2SO4 + CO2 + H2O",
|
|
"gt_answers": "2 N a O H + C O _ { 2 } = N a _ { 2 } C O _ { 3 } + H _ { 2 } V\n",
|
|
"image_path": "./data/HME100K/test_images/test_4963.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\nP(x) = 0.5 + 0.5 * (1 - e^(-0.005x))\n\nThe formula is a probability density function, which describes the probability of a random variable x taking a value between 0 and 1. The probability density function is defined as the derivative of the cumulative distribution function (CDF) with respect to the variable x. The CDF is the probability that a random variable x takes a value less than or equal to a given value y.\n\nIn this case, the CDF is given by:\n\nF(x) = 0.5 + 0.5 * (1 - e^(-0.005x))\n\nThe derivative of this function with respect to x is:\n\nf(x) = 0.5 + 0.5 * (-e^(-0.005x))\n\nThe probability density function is then given by:\n\nP(x) = f(x) / (1 - e^(-0.005x))\n\nIn this case, the probability density function is a step function, which is a function that takes on a constant value at a specific point and then jumps to a different constant value at another point. The specific points are determined by the values of the variable x.",
|
|
"gt_answers": "P _ { 2 } = \\frac { T 2 } { T 1 } P _ { 1 } = \\frac { 4 0 0 } { 3 0 0 } \\times 1 . 0 \\times 1 0 ^ { 5 } \\approx 1 . 3 3 \\times 1 0 ^ { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4964.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a number and a symbol, which could be a mathematical operator such as \"+\" or \"-\".",
|
|
"gt_answers": "\\frac { 4 7 } { 2 } + \\frac { 1 } { 2 } \\pi = 1 3 + \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_4966.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x + 15 = 30`.",
|
|
"gt_answers": "x - 2 = \\pm 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_4967.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-2",
|
|
"gt_answers": "\\vert - 2 . 2 \\vert = 2 . 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4968.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few letters and numbers, which could be a representation of a mathematical expression in Korean.",
|
|
"gt_answers": "2 x \\epsilon [ 0 , \\frac { \\pi } { 6 } ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_4969.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Japanese.",
|
|
"gt_answers": "x _ { 1 } = \\sqrt { 7 - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4973.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 12345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890",
|
|
"gt_answers": "7 0 \\times 4 0 - 4 0 \\times 4 0 = 1 2 0 0 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4974.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 4 = 10.\"",
|
|
"gt_answers": "x _ { 4 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4975.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"Ao = Co Do Bo.\"",
|
|
"gt_answers": "A O = C O = D O = B O\n",
|
|
"image_path": "./data/HME100K/test_images/test_4976.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "F = F _ { A } + m a = \\frac { B ^ { 2 } L ^ { 2 } V } { R } + m a = \\frac { B ^ { 2 } L ^ { 2 } a t } { R } + m a = \\frac { 0 . 2 ^ { 2 } \\times 0 . 4 ^ { 2 } \\times 2 t } { 1 9 } + 0 . 0 5 \\times 2 = ( 0 . 0 0 0 6 7 3 7 t + 0 . 1 ) N\n",
|
|
"image_path": "./data/HME100K/test_images/test_4977.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\Delta A B C \\cong \\Delta D E F ( S S S )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4978.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3\\sqrt{2} - 2\\sqrt{3} = 2\\sqrt{2} - 2\\sqrt{3} = 2\\sqrt{2} - 2\\sqrt{6} = 2\\sqrt{2} - 4\\sqrt{3} = 2\\sqrt{2} - 4\\sqrt{6} = 2\\sqrt{2} - 4\\sqrt{12} = 2\\sqrt{2} - 4\\sqrt{24} = 2\\sqrt{2} - 4\\sqrt{36} = 2\\sqrt{2} - 4\\sqrt{72} = 2\\sqrt{2} - 4\\sqrt{144} = 2\\sqrt{2} - 4\\sqrt{288} = 2\\sqrt{2} - 4\\sqrt{576} = 2\\sqrt{2} - 4\\sqrt{1152} = 2\\sqrt{2} - 4\\sqrt{2304} = 2\\sqrt{2} - 4\\sqrt{4608} = 2\\sqrt{2} - 4\\sqrt{9216} = 2\\sqrt{2} - 4\\sqrt{18432} = 2\\sqrt{2} - 4\\sqrt{36624} = 2\\sqrt{2} - 4\\sqrt{73248} = 2\\sqrt{2} - 4\\sqrt{146496} = 2\\sqrt{2} - 4\\sqrt{293744} = 2\\sqrt{2} - 4\\sqrt{587496} = 2\\sqrt{2} - 4\\sqrt{1174968} = 2\\sqrt{2} - 4\\sqrt{2359936} = 2\\sqrt{2} - 4\\sqrt{4719872} = 2\\sqrt{2} - 4\\sqrt{9439744} = 2\\sqrt{2",
|
|
"gt_answers": "\\sqrt { 4 b ^ { 2 } - 8 b + 1 3 } = \\sqrt { b ^ { 2 } - 6 b + 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4979.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"y = 2x + 1.\"",
|
|
"gt_answers": "S y = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_4980.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "y = 3 1 \\times \\frac { 1 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4982.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(WPT = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\",
|
|
"gt_answers": "w = P t\n",
|
|
"image_path": "./data/HME100K/test_images/test_4983.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "a < - b < 0 < b < - a\n",
|
|
"image_path": "./data/HME100K/test_images/test_4984.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(L = \\frac{1}{2} \\left( \\sqrt{AB} + \\sqrt{CD} \\right)\\)\n\nThe formula is a quadratic equation, where L is the length of the hypotenuse of a right triangle with sides AB and CD. The formula can be used to find the length of the hypotenuse given the lengths of the other two sides.",
|
|
"gt_answers": "\\angle 4 = \\frac { 1 } { 2 } \\angle A B D\n",
|
|
"image_path": "./data/HME100K/test_images/test_4985.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "O A = O D , \\angle A = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4986.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 4x20 - 3x100 = 1000 - 300 = 700.",
|
|
"gt_answers": "4 \\times \\frac { 2 5 0 } { 3 } = \\frac { 1 0 0 0 \\cdot } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4987.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(13300 \\text{dm}^2 \\cdot 13.5 \\text{m} = 178000 \\text{dm}^3\\)",
|
|
"gt_answers": "1 3 5 0 0 d m ^ { 3 } = 1 3 . 5 m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4988.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x} = \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{x} \\cdot \\frac{1}{",
|
|
"gt_answers": "C a O : 0 \\% = \\frac { o } { C a O } \\times 1 0 0 \\% = \\frac { 1 6 } { 5 6 } \\times 1 0 0 \\% = 2 8 . 6 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_4989.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4.8x3.2 = 3.32m.",
|
|
"gt_answers": "4 . 8 \\times \\frac { 2 } { 3 } = 3 . 2 k m\n",
|
|
"image_path": "./data/HME100K/test_images/test_4990.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{0.00333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
|
|
"gt_answers": "7 . 2 > 0 . 3 6 > \\frac { 1 } { 5 } > 0 . 0 1 8 \u3002\n",
|
|
"image_path": "./data/HME100K/test_images/test_4991.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "x _ { 2 } = \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4992.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/x + 1/y = 1/z.",
|
|
"gt_answers": "x _ { 1 } = \\frac { \\sqrt { 1 0 } } { 2 } + \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4993.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `8x8 + 8x8 = 64`.",
|
|
"gt_answers": "4 + 4 = 8 8 > 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_4995.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{B}{A} \\right)^2 + \\left( \\frac{B}{A} \\right)^4 + \\left( \\frac{B}{A} \\right)^6 + \\left( \\frac{B}{A} \\right)^8 + \\left( \\frac{B}{A} \\right)^{10} + \\left( \\frac{B}{A} \\right)^{12} + \\left( \\frac{B}{A} \\right)^{14} + \\left( \\frac{B}{A} \\right)^{16} + \\left( \\frac{B}{A} \\right)^{18} + \\left( \\frac{B}{A} \\right)^{20} + \\left( \\frac{B}{A} \\right)^{22} + \\left( \\frac{B}{A} \\right)^{24} + \\left( \\frac{B}{A} \\right)^{26} + \\left( \\frac{B}{A} \\right)^{28} + \\left( \\frac{B}{A} \\right)^{30} + \\left( \\frac{B}{A} \\right)^{32} + \\left( \\frac{B}{A} \\right)^{34} + \\left( \\frac{B}{A} \\right)^{36} + \\left( \\frac{B}{A} \\right)^{38} + \\left( \\frac{B}{A} \\right)^{40} + \\left( \\frac{B}{A} \\right)^{42} + \\left( \\frac{B}{A} \\right)^{44} + \\left( \\frac{B}{A} \\right)^{46} + \\left( \\frac{B}{A} \\right)^{48} + \\left( \\frac{B}{A} \\right)^{50} + \\left( \\frac{B}{A} \\right)^{52} + \\left( \\frac{B}{A} \\right)^{54} + \\left( \\frac{B}{A} \\right)^{56} + \\left( \\frac{B}{A",
|
|
"gt_answers": "\\angle 1 = 1 8 0 ^ { \\circ } - \\angle B = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4996.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "a x ^ { 2 } + 5 x + c = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_4997.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "( y + 3 ) ( y - 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_4998.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `x^2 + 6x - 6 = 0`.",
|
|
"gt_answers": "x = \\frac { 6 } { k - 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_4999.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(s_k = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "- 5 k = - 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5001.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222",
|
|
"gt_answers": "1 \\times 2 2 2 2 = 2 2 2 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5002.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(I = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
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"gt_answers": "\\frac { I } { I _ { 2 } } = \\frac { I _ { 1 } + I _ { 2 } } { I _ { 2 } }\n",
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"image_path": "./data/HME100K/test_images/test_5003.jpg",
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"model_name": "mPLUG"
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|
},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as follows: 10x20 - 3x10 - 2x10 = 100 - 30 - 20 = 50.",
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"gt_answers": "\\frac { 1 0 x - 2 0 } { 2 } - \\frac { 1 0 x + 1 0 } { 5 } = 3\n",
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"image_path": "./data/HME100K/test_images/test_5004.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
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|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + y^2 = 16\\)\n\nThis is a quadratic equation in two variables, where x and y represent the two unknowns. The expression can be solved using the quadratic formula, which gives the solutions as follows:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\)\n\nIn this case, the quadratic formula gives the solutions as follows:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} = \\frac{-b \\pm \\sqrt{4(16) - 4(1)(1)}}{2(1)} = \\frac{-b \\pm \\sqrt{16 - 4}}{2} = \\frac{-b \\pm 8}{2} = \\frac{-b \\pm 4}{2} = \\frac{-b \\pm 2}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{2} = \\frac{-b \\pm 1}{",
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"gt_answers": "D C = 2 \\times ( 8 - 4 \\sqrt { 3 } ) = 1 6 - 8 \\sqrt { 3 }\n",
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"image_path": "./data/HME100K/test_images/test_5006.jpg",
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"model_name": "mPLUG"
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|
},
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{
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|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
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|
"answer": "The expression of the formula in the image is written as follows: 0.400 - 0.004 = 0.396.",
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"gt_answers": "0 . 4 0 = 0 . 4 0 0\n",
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"image_path": "./data/HME100K/test_images/test_5007.jpg",
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"model_name": "mPLUG"
|
|
},
|
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{
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|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(P(A \\cap B) = P(A) \\cdot P(B) - P(A \\cap B) = P(A) \\cdot P(B) - P(A) \\cdot P(B \\cap C) + P(A \\cap C) \\cdot P(B) - P(A \\cap B \\cap C)\\)\n\nThe formula is a combination of two other formulas: the multiplication rule for independent events and the addition rule for dependent events. The first part of the formula, \\(P(A \\cap B) = P(A) \\cdot P(B)\\), represents the multiplication rule for independent events, which states that the probability of two independent events occurring simultaneously is the product of the individual probabilities. The second part of the formula, \\(P(A \\cap B) = P(A) \\cdot P(B) - P(A \\cap B) = P(A) \\cdot P(B) - P(A) \\cdot P(B \\cap C) + P(A \\cap C) \\cdot P(B)\\), represents the addition rule for dependent events, which states that the probability of two dependent events occurring simultaneously is the sum of the individual probabilities, with the addition of the probability of one event occurring and the probability of the other event occurring, multiplied by the probability of the first event occurring.",
|
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"gt_answers": "= \\frac { D G } { A G } = \\frac { 8 } { 4 \\sqrt { 5 } }\n",
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"image_path": "./data/HME100K/test_images/test_5008.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x - 4 = 0\\)",
|
|
"gt_answers": ": \\sqrt { x + 5 } = 4 - \\sqrt { x - 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5009.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2.54 - 0.075 = 2.465.",
|
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"gt_answers": "5 + \\frac { 3 } { 4 } - \\frac { 1 } { 2 } = 0 . 7 5\n",
|
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"image_path": "./data/HME100K/test_images/test_5010.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LA = \\frac{LC}{60}\\)\n\nThis formula represents the relationship between the load angle (LA) and the load current (LC) in a transformer. The load angle is the angle between the primary and secondary windings of the transformer, and it is measured in degrees. The load current is the current flowing through the secondary winding, and it is measured in amperes. The ratio of the load angle to the load current is represented by the formula above.",
|
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"gt_answers": "\\angle A = \\angle C = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5011.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(e^{x} = \\sum_{n=0}^{\\infty} \\frac{x^n}{n!} \\tag{LaTeX formula for e to the power x}\\)`",
|
|
"gt_answers": "\\frac { 3 } { 5 } : x = \\frac { 3 } { 8 } : \\frac { 5 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5012.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4} \\left( 1 + 1 \\right) = \\frac{1}{4} \\cdot 2 = \\frac{1}{2} \\cdot 2 = \\frac{1}{4} \\cdot 4 = \\frac{1}{8} \\cdot 8 = \\frac{1}{16} \\cdot 16 = \\frac{1}{32} \\cdot 32 = \\frac{1}{64} \\cdot 64 = \\frac{1}{128} \\cdot 128 = \\frac{1}{256} \\cdot 256 = \\frac{1}{512} \\cdot 512 = \\frac{1}{1024} \\cdot 1024 = \\frac{1}{2048} \\cdot 2048 = \\frac{1}{4096} \\cdot 4096 = \\frac{1}{8192} \\cdot 8192 = \\frac{1}{16384} \\cdot 16384 = \\frac{1}{32768} \\cdot 32768 = \\frac{1}{65536} \\cdot 65536 = \\frac{1}{131072} \\cdot 131072 = \\frac{1}{262144} \\cdot 262144 = \\frac{1}{524288} \\cdot 524288 = \\frac{1}{1048576} \\cdot 1048576 = \\frac{1}{2097152} \\cdot 2097152 = \\frac{1}{4194304} \\cdot 4194304 = \\frac{1}{8388608} \\cdot 8388608 = \\frac{1}{16777216}",
|
|
"gt_answers": "\\frac { 3 } { 2 } < c < \\frac { 5 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5013.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBOC = 2LBOC/LBOC + 60\".",
|
|
"gt_answers": "\\angle B O D = \\angle C O D = \\frac { 1 } { 2 } \\cdot \\angle B O C = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5014.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: V = I \\* R.",
|
|
"gt_answers": "I _ { \\min } = \\frac { U } { R _ { m a x } } = \\frac { 3 V } { 2 0 \\Omega } = 0 . 1 5 A\n",
|
|
"image_path": "./data/HME100K/test_images/test_5016.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "O B = O A = \\frac { A B } { 2 } = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5017.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2\\cdot 2\\cdot 2 + 3\\cdot 3\\cdot 3 + 4\\cdot 4\\cdot 4 + 5\\cdot 5\\cdot 5 + 6\\cdot 6\\cdot 6 + 7\\cdot 7\\cdot 7 + 8\\cdot 8\\cdot 8 + 9\\cdot 9\\cdot 9 + 10\\cdot 10\\cdot 10 + 11\\cdot 11\\cdot 11 + 12\\cdot 12\\cdot 12 + 13\\cdot 13\\cdot 13 + 14\\cdot 14\\cdot 14 + 15\\cdot 15\\cdot 15 + 16\\cdot 16\\cdot 16 + 17\\cdot 17\\cdot 17 + 18\\cdot 18\\cdot 18 + 19\\cdot 19\\cdot 19 + 20\\cdot 20\\cdot 20 + 21\\cdot 21\\cdot 21 + 22\\cdot 22\\cdot 22 + 23\\cdot 23\\cdot 23 + 24\\cdot 24\\cdot 24 + 25\\cdot 25\\cdot 25 + 26\\cdot 26\\cdot 26 + 27\\cdot 27\\cdot 27 + 28\\cdot 28\\cdot 28 + 29\\cdot 29\\cdot 29 + 30\\cdot 30\\cdot 30 + 31\\cdot 31\\cdot 31 + 32\\cdot 32\\cdot 32 + 33\\cdot 33\\cdot 33 + 34\\cdot 34\\cdot 34 + 35\\cdot 35\\cdot 35 + 36\\cdot 36\\cdot 36 + 37\\cdot 37\\cdot 37 + 38\\cdot 38\\cdot 38 + 39\\",
|
|
"gt_answers": "_ { 2 } O _ { 3 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
|
|
"image_path": "./data/HME100K/test_images/test_5018.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + y^2 = 25\\)\n\nThis is a quadratic equation in two variables, where x and y represent the two unknowns. The equation can be solved using the quadratic formula, which is:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\)\n\nSubstituting the values of a, b, and c from the equation into the quadratic formula, we get:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 4(25)}}{2(25)} = \\frac{-b \\pm \\sqrt{b^2 - 100}}{25}\\)\n\nSolving for x, we get:\n\n\\(x = \\frac{-b \\pm \\sqrt{b^2 - 100}}{25} = \\frac{-b \\pm \\sqrt{b^2 - 50}}{25} = \\frac{-b \\pm 7}{25} = \\frac{-b \\pm 3}{15} = \\frac{-b \\pm 3}{15} \\pm 3\\)\n\nTherefore, the solution to the quadratic equation is:\n\n\\(x = \\frac{-b \\pm 3}{15} \\pm 3\\)\n\nThe image shows the solution to the quadratic equation in the form of a table, where the values of x and y are given for each possible value of the variable b.",
|
|
"gt_answers": "2 x ^ { 2 } + x = 2 ( x ^ { 2 } + 1 + 2 x )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5019.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317673832795523446128481117450284102701953125948077193259483091758417664709384460955058223176738327955234461284811174502841027019531259480771932594830917584176647093844609550582231767383279552344612848111745028410270195312594807719325948309175841766470938446095505822317673832795523446128481117450284102701953125948077193259483091758417664709384460955058223",
|
|
"gt_answers": "\\textcircled { 2 } 3 . 1 4 \\times 2 = 6 . 2 8 c m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5020.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{b^2}{a^2} + \\frac{b^2}{c^2} + \\frac{b^2}{d^2} + \\frac{b^2}{e^2} + \\frac{b^2}{f^2} + \\frac{b^2}{g^2} + \\frac{b^2}{h^2} + \\frac{b^2}{i^2} + \\frac{b^2}{j^2} + \\frac{b^2}{k^2} + \\frac{b^2}{l^2} + \\frac{b^2}{m^2} + \\frac{b^2}{n^2} + \\frac{b^2}{o^2} + \\frac{b^2}{p^2} + \\frac{b^2}{q^2} + \\frac{b^2}{r^2} + \\frac{b^2}{s^2} + \\frac{b^2}{t^2} + \\frac{b^2}{u^2} + \\frac{b^2}{v^2} + \\frac{b^2}{w^2} + \\frac{b^2}{x^2} + \\frac{b^2}{y^2} + \\frac{b^2}{z^2} + \\frac{b^2}{aa^2} + \\frac{b^2}{bb^2} + \\frac{b^2}{cc^2} + \\frac{b^2}{dd^2} + \\frac{b^2}{ee^2} + \\frac{b^2}{ff^2} + \\frac{b^2}{gg^2} + \\frac{b^2}{hh^2} + \\frac{b^2}{ii^2} + \\frac{b^2}{jj^2} + \\frac{b^2}{kk^2} + \\frac{b^2}{ll^2} + \\frac{b^2}{mm^2} + \\frac{b^2}{nn^2} + \\frac{b^2}{oo^2} + \\frac{",
|
|
"gt_answers": "( b + 2 ) ( b - 1 ) = 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5021.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{4x^2 + 5x + 3}{x^2 + 2x + 1}\n\\end{aligned}\n\\end{equation}\n\nThis formula can be simplified by factoring out the common denominator, which is x^2 + 2x + 1. The simplified expression is then:\n\n\\begin{equation}\n\\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1} = \\frac{4x^2 + 5x + 3}{x^2 + 2x + 1",
|
|
"gt_answers": "( 1 - 1 ) x ^ { 2 } + ( 4 + 3 ) x + 3 - 5 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5022.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LEDB-903\" using the LaTeX format.",
|
|
"gt_answers": "\\angle E D B = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5023.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x(2.56 cm) = 7.68 cm^2.",
|
|
"gt_answers": "3 . 1 4 \\times 2 ^ { 2 } = 1 2 . 5 6 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5024.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "( x + 1 ) ^ { 2 } > 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5025.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 106x + 7t = 100.",
|
|
"gt_answers": "\\frac { 1 0 6 } { 7 5 } = \\frac { x } { 7 . 3 g }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5026.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 188 - 78 = 110.",
|
|
"gt_answers": "7 8 - 7 8 \\textcircled { < } 7 8 \\div 7 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5027.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(S = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "S _ { n } \\cdot \\frac { 2 } { n + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5028.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "x = \\frac { 5 0 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5029.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Delab(x,y) = 2x^2 + 3y^2 - 4xy.\"",
|
|
"gt_answers": "D E \\bot A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_5030.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"204 + 181 = 385.\"",
|
|
"gt_answers": "4 2 \\rightarrow 2 4 \\rightarrow 1 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5031.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"H2O + NaOH + NaCl = Na2SO4 + H2O + NaCl.\"",
|
|
"gt_answers": "N H _ { 4 } N O _ { 3 } + N a O H = N a N O _ { 3 } + N H _ { 3 } \\uparrow + H _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5032.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(12x^2 + 672d^2 = 12x^2 + 672(d^2 + 2d) = 12x^2 + 672(d^2 + 2d) + 2d(d^2 + 2d) = 12x^2 + 672d^2 + 2d(d^2 + 2d) + 2d(d^2 + 2d) = 12x^2 + 672d^2 + 2d(d^2 + 2d) + 2d(d^2 + 2d) + 2d(d^2 + 2d) = 12x^2 + 672d^2 + 2d(d^2 + 2d) + 2d(d^2 + 2d) + 2d(d^2 + 2d) = 12x^2 + 672d^2 + 2d(d^2 + 2d) + 2d(d^2 + 2d) + 2d(d^2 + 2d) = 12x^2 + 672d^2 + 2d(d^2 + 2d) + 2d(d^2 + 2d) + 2d(d^2 + 2d) = 12x^2 + 672d^2 + 2d(d^2 + 2d) + 2d(d^2 + 2d) + 2d(d^2 + 2d) = 12x^2 + 672d^2 + 2d(d^2 + 2d) + 2d(d^2 + 2d) + 2d(d^2 + 2d) = 12x^2 + 672d^2 + 2d(d^2 + 2d) + 2d(d^2 + 2d) + 2d(d^2 + 2d) = 12x^2",
|
|
"gt_answers": "1 2 \\times 6 = 7 2 ( d m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5033.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(4 \\times (9 \\times (3 \\times 2)) = 4 \\times 27 = 108\\)",
|
|
"gt_answers": "4 = \\frac { 4 } { 9 } ( x - 3 + m ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5034.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: `59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.65 + 59.02 + 55.78 + 78.",
|
|
"gt_answers": "5 9 . 0 2 > 5 8 . 5 2 > 5 8 . 1 7 > 5 8 . 0 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5035.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "\\frac { x - a - b } { c } + \\frac { x - b - c } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5036.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "x _ { 1 } = 2 , x _ { 2 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5037.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 4x^2 + 4x + 1\\)",
|
|
"gt_answers": "y = \\frac { x ^ { 2 } - 4 x + 1 } { x } = x + \\frac { 1 } { x } - 4 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5038.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 25\\)",
|
|
"gt_answers": "- 2 5 0 x + 5 0 0 0 = - 8 0 x + 2 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5040.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: (30 + 50) / (25 + 20) = 15 / 45.",
|
|
"gt_answers": "( 3 0 + 1 5 + 1 0 ) - ( 2 5 + 2 0 + 1 0 ) = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5041.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3(2x + 1) + 4(x - 1) = 12x^2 + 12x - 4\\)",
|
|
"gt_answers": "6 2 . 8 + 7 8 . 5 = 1 4 1 . 3 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5042.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 0.02x + 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "x - \\frac { 1 } { 5 } = 0 . 2 \\times 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5043.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 0 0 \\div 1 0 0 = 1 0 ( k g )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5044.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 15 - 3 = 12.",
|
|
"gt_answers": "\\frac { 4 } { 1 5 } \\div \\frac { 2 } { 3 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5045.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 3x + 3y = 33 + 3x - 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 33 - 3x + 3y = 3",
|
|
"gt_answers": "x ^ { 3 } - 3 x ^ { 2 } - 3 x - 3 x ^ { 3 } +\n",
|
|
"image_path": "./data/HME100K/test_images/test_5046.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "P ( 2 + 2 \\sqrt { 2 } , - 2 \\sqrt { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5047.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(Z_{n,m} = \\frac{1}{2} \\left( \\sqrt{n^2 + m^2} + \\sqrt{n^2 - m^2} \\right)\\)\n\nThis formula calculates the distance between two points on a circle, represented by the variables n and m. The distance is calculated as the square root of the sum of the squares of the two distances between the points and the center of the circle.",
|
|
"gt_answers": "2 x ^ { 2 } + x = 2 ( x ^ { 2 } + 2 x + 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5048.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "5 0 0 7 5 \\times 1 0 \\div 1 0 0 \\times 1 0 0 0 0 = 5 0 0 7 5 0 0 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5049.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3-0.1-3.",
|
|
"gt_answers": "\\vert 3 - 0 \\vert = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5050.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = z^2\\)",
|
|
"gt_answers": "x _ { 1 } = - \\sqrt [ 4 ] { 1 2 8 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5052.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `W = 3355 + 600.55`.",
|
|
"gt_answers": "W = - ( x - 3 . 5 ) ^ { 2 } + 6 0 . 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5053.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = - \\frac { 3 a } { a - 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5055.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "0 . 6 6 > 0 . 6 4 > 0 . 6 0 6 > 0 . 6 0 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5056.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"10x15 + 70g = 1000g.\"",
|
|
"gt_answers": "1 0 \\times 7 = 7 0 ( k m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5057.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{8} \\left( \\frac{1}{16} \\left( \\frac{1}{32} \\left( \\frac{1}{64} \\left( \\frac{1}{128} \\left( \\frac{1}{256} \\left( \\frac{1}{512} \\left( \\frac{1}{1024} \\left( \\frac{1}{2048} \\left( \\frac{1}{4096} \\left( \\frac{1}{8192} \\left( \\frac{1}{16384} \\left( \\frac{1}{32768} \\left( \\frac{1}{65536} \\left( \\frac{1}{131072} \\left( \\frac{1}{262144} \\left( \\frac{1}{524288} \\left( \\frac{1}{1048576} \\left( \\frac{1}{2097152} \\left( \\frac{1}{4194304} \\left( \\frac{1}{8388608} \\left( \\frac{1}{16777216} \\left( \\frac{1}{33554432} \\left( \\frac{1}{67108864} \\left( \\frac{1}{134217728} \\left( \\frac{1}{268435456} \\left( \\frac{1}{536870912} \\left( \\frac{1}{1073741824} \\left( \\frac{1}{2147483648} \\left( \\frac{1}{4294967296} \\left( \\frac{1}{8589934592}",
|
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"gt_answers": "\\frac { \\frac { \\sqrt { 2 } } { 2 } } { b } = \\frac { \\sqrt { 1 0 } } { 3 }\n",
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"image_path": "./data/HME100K/test_images/test_5058.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"256^2 + 512^2 = 1024^2.\"",
|
|
"gt_answers": "5 9 . 0 2 > 5 8 . 5 2 > 5 8 . 1 7 > 5 8 . 0 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5060.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "1 - 8 ) ^ { - \\frac { 2 } { 5 } } = \\frac { 1 } { \\sqrt [ 5 ] { ( - 8 } ) ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5061.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 3\\)",
|
|
"gt_answers": "l : x = - \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5064.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\frac { 1 } { S h } = 4 + 4 ( n - 1 ) = 4 n\n",
|
|
"image_path": "./data/HME100K/test_images/test_5065.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1/2 + 1/3 = 1/6.",
|
|
"gt_answers": "\\tan \\angle A C D = \\frac { A P } { A C } = 1 / 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5066.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "3 9 7 + \\xrightarrow { 7 } ( 4 0 4 ) \\xrightarrow { + 2 0 3 } ( 6 0 7 ) \\xrightarrow { + 1 8 0 } ( 7 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5068.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( a + b + c + d ) \\times e = a \\times e + b \\times e + c \\times e + d \\times e\n",
|
|
"image_path": "./data/HME100K/test_images/test_5070.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 25\\)",
|
|
"gt_answers": "\\frac { 2 a x } { a b + a + 1 } = \\frac { 2 a C x } { a b c + a c + c } = \\frac { 2 a c x } { c a + c + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5071.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 3x + 9 = 5x^2 + 3x + 9\\)\n\nThis formula can be rearranged to solve for x:\n\n\\(x^2 + 3x + 9 = 5x^2 + 3x + 9\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x - 9 = 0\\)\n\n\\(x^2 + 3x + 9 - 5x^2 - 3x -",
|
|
"gt_answers": "\\frac { 4 \\tan \\alpha - 2 } { 5 \\tan \\alpha + 3 } = \\frac { 4 \\times 3 - 2 } { 5 \\times 3 + 3 } = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5072.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(G + M + K + N = 100\\)\n\nThis formula represents the relationship between the four elements of the periodic table, where G represents the number of protons in the nucleus, M represents the number of electrons in the outermost shell, K represents the number of neutrons in the nucleus, and N represents the number of neutrons in the outermost shell. The total number of protons, electrons, and neutrons in the nucleus is equal to 100.",
|
|
"gt_answers": "G = m g = 1 5 k g \\times 9 . 8 N / k g = 1 4 7 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_5073.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"B0 = 2A3.\"",
|
|
"gt_answers": "B O = \\frac { 1 } { 2 } A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_5074.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"My = f(e^x)\" using LaTeX format.",
|
|
"gt_answers": "M _ { y } > F e > C u\n",
|
|
"image_path": "./data/HME100K/test_images/test_5075.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 1 } { 4 } = 1 - 2 \\sin ( \\frac { 1 } { 2 } ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5076.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(F = \\frac{mg \\cdot \\sin \\theta}{r^2} \\cdot \\cos \\theta\\)\n\nThis formula relates the force applied on an object to its mass, the angle of inclination, and the distance from the center of gravity. The force is calculated as the product of the mass, the gravitational constant (G), and the sine of the angle of inclination, multiplied by the cosine of the angle of inclination. The distance from the center of gravity is squared and then multiplied by the force to obtain the total force acting on the object.",
|
|
"gt_answers": "F _ { M } = \\frac { O N } { M O } F _ { N } = \\frac { 3 } { 2 } \\times 7 . 2 = 1 0 . 8 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_5077.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4x^2 + 4x + 4 = 16x^2 + 16x + 4\\)",
|
|
"gt_answers": "\\frac { 4 } { 6 } + \\frac { 3 } { 6 } = \\frac { 1 } { 4 } x + ( - \\frac { 1 } { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5078.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LAEc = 100 - 100/100 * 100\". This formula is used to calculate the loss angle of a lens, which is the angle between the principal ray and the image ray after passing through the lens. The loss angle is an important parameter in optical design and is used to determine the performance of the lens.",
|
|
"gt_answers": "\\angle A E C = 1 1 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5079.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CE5 = 5.\"",
|
|
"gt_answers": "C E = \\frac { 5 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5080.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5081.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle B D E = \\angle E D O . \\angle D O E = \\angle D E B = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5082.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5/32 + 5/32 = 5/32 + 5/32 = 10/32.",
|
|
"gt_answers": "x = \\frac { 5 } { 3 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5083.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: Na+ + 800 mg/L = Na+ + 0.800 g/L.",
|
|
"gt_answers": "N a _ { 2 } O + S O _ { 3 } = N a _ { 2 } S O _ { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5084.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "y = \\max = \\frac { 6 3 } { 4 } + \\frac { 1 } { 2 } \\sin ( 2 x + \\frac { \\pi } { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5085.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 12/8 = 1.5.",
|
|
"gt_answers": "x = - \\frac { 1 5 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5088.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2 \\pi r^2 = 4 \\pi r^2 \\cos^2 \\theta\\)\n\nThis formula relates the area of a circle to its radius squared and the cosine of its central angle.",
|
|
"gt_answers": "2 \\sqrt { 1 3 } < x < 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5089.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a black background and a white text, which could be a representation of a mathematical expression in Japanese.",
|
|
"gt_answers": "( 1 ) 4 \\div 1 7 = \\frac { 4 } { 1 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5090.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x + 3y = 12.",
|
|
"gt_answers": "1 . 8 \\times 1 2 . 5 6 \\div 3 = 7 . 5 3 6 m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5091.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nF = Gm1m2/r^2\n\nwhere F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.",
|
|
"gt_answers": "P = \\frac { F } { S } = \\frac { G } { S } = \\frac { m g } { 2 S }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5092.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 12x5x60 = 720.",
|
|
"gt_answers": "1 2 \\times \\frac { 5 } { 1 8 } = \\frac { 1 2 \\times 5 } { 1 8 } = \\frac { 6 0 } { 1 8 } = \\frac { 1 0 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5093.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LitLabs = 160\\)",
|
|
"gt_answers": "\\angle 1 + \\angle A C B = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5094.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(x^2 + y^2 = 75\\)\n\nThe formula is written in the form of an equation, with the variables x and y on the left side and the constant 75 on the right side. The expression is enclosed in a box, which is a common way to denote a formula in LaTeX.",
|
|
"gt_answers": "\\angle D O E = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5095.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "1 g c _ { 1 } + 1 g a m 9 = 0 ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_5096.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `y = 1/x + 1`.",
|
|
"gt_answers": "y = \\frac { 1 } { 3 } x - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5097.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) = \\frac{1}{4}\n\\end{equation}\n\nThis equation can be interpreted as the sum of two halves, each of which is equal to one half. The result is a quarter.",
|
|
"gt_answers": "y = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5098.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b_1 + b_2 = 100 \\text{ and } b_1 \\cdot b_2 = 130\\)",
|
|
"gt_answers": "\\angle B O N + \\angle M O B = 1 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5099.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as: PD = PB + BF.",
|
|
"gt_answers": "\\frac { P D } { B E } = \\frac { F P } { B F }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5100.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 m = 1 0 0 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5102.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(A \\cdot B \\cdot P \\cdot Q \\cdot R \\cdot S \\cdot T \\cdot U \\cdot V \\cdot W \\cdot X \\cdot Y \\cdot Z = P \\cdot Q \\cdot R \\cdot S \\cdot T \\cdot U \\cdot V \\cdot W \\cdot X \\cdot Y \\cdot Z \\cdot A \\cdot B\\)",
|
|
"gt_answers": "\\angle A P O _ { 2 } = \\angle B P O _ { 1 } = \\angle P A O _ { 2 } = \\angle P B O _ { 1 } = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5103.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\begin{equation}\n\\ce{Tb(OC2H5)3 + CO2 -> Tb(OC2H5)4 + CO}\n\\end{equation}\n\nThis formula represents the chemical reaction between thallium tris(ethylhexanoate) (Tb(OC2H5)3) and carbon dioxide (CO2) to produce thallium tris(ethylhexanoate) tetraacetate (Tb(OC2H5)4) and carbon (CO).",
|
|
"gt_answers": "E B = E C , O C = O B\n",
|
|
"image_path": "./data/HME100K/test_images/test_5104.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"45\u00b0-150\u00b0\".",
|
|
"gt_answers": "\\angle D _ { 1 } A _ { 1 } A = 1 5 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5105.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 3x + 4 = 10\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\nx^2 + 3x + 4 = 10\n\\end{equation}\n\nThe equation is written in the form of an equation with the variable \"x\" on the left side and the expression on the right side. The equation is also written in the form of a mathematical expression, with the equal sign \"=\" separating the two sides.",
|
|
"gt_answers": "\\frac { 1 } { 2 } ( \\frac { 1 } { 2 c } + \\frac { 1 } { 2 a } ) \\geq \\frac { 1 } { c + a } \\Rightarrow \\frac { 1 } { 2 a } + \\frac { 1 } { 2 b } + \\frac { 1 } { 2 c } \\geq \\frac { 1 } { b + c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5107.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten format, so it is difficult to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few letters and numbers, which can be represented using the following LaTeX code:\n\n\\begin{equation}\n\\begin{aligned}\n\\text{A} + \\text{B} + \\text{C} + \\text{D} + \\text{E} + \\text{F} + \\text{G} + \\text{H} + \\text{I} + \\text{J} + \\text{K} + \\text{L} + \\text{M} + \\text{N} + \\text{O} + \\text{P} + \\text{Q} + \\text{R} + \\text{S} + \\text{T} + \\text{U} + \\text{V} + \\text{W} + \\text{X} + \\text{Y} + \\text{Z}\n\\end{aligned}\n\\end{equation}\n\nThis equation represents a combination of letters and numbers, which can be used in various mathematical contexts.",
|
|
"gt_answers": "e ^ { 2 } < 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5108.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 5\\)",
|
|
"gt_answers": "y = \\sqrt { 2 } \\sin ( x + \\frac { \\pi } { 4 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5109.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3b^2 - 3a^2 = 4b^2 - 4a^2\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\n3b^2 - 3a^2 = 4b^2 - 4a^2\n\\end{equation}",
|
|
"gt_answers": "\\frac { 1 } { 3 } \\overrightarrow { b } - \\frac { 1 } { 3 } \\overrightarrow { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5110.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(F = \\frac{GMm}{r^2}\\)\n\nwhere F is the force, G is the gravitational constant, M is the mass of the object, and r is the distance between the object and the center of mass of the Earth.",
|
|
"gt_answers": "F _ { 1 } = G = m ^ { \\prime } g = 0 . 1 k g \\times 9 . 8 N / k g = 0 . 9 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5111.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to write it out in LaTeX format. However, the image shows a formula with a negative sign, which is typically written as a minus sign (-).",
|
|
"gt_answers": "y = \\frac { k } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5112.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a-c^2b-l^2.",
|
|
"gt_answers": "a - c > b - c .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5113.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(16844444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444",
|
|
"gt_answers": "S = \\frac { ( 1 8 + 2 4 ) 2 1 } { 2 } = 4 4 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5114.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the formula is likely a mathematical expression involving trigonometric functions, such as sine, cosine, or tangent.",
|
|
"gt_answers": "\\sqrt { 2 } \\sin a ( x - \\frac { \\pi } { 4 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5117.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x2x3-3\".",
|
|
"gt_answers": "\\frac { 1 } { 4 } \\times \\frac { 1 } { 2 } \\times 2 \\times 3 = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5118.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{X^2 + Y^2}{X^2 - Y^2} = \\frac{X^2 + Y^2}{X^2 - Y^2}\n\\end{equation}\n\nThis is a simple algebraic expression that can be used to verify the identity of the square root of a number.",
|
|
"gt_answers": "x - 2 y = 0 , x + y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5119.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the formula is likely a mathematical equation or a chemical formula.",
|
|
"gt_answers": "x = - 7 \\frac { 4 } { 5 } \\div [ - 3 \\frac { 1 } { 4 } ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_5120.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"a^2 + b^2 = c^2.\"",
|
|
"gt_answers": "a ^ { 2 } - 6 = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5122.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x _ { 1 } = 3 x _ { 2 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5124.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 4y^2 - 12xy + 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x^2 - 12y^2 + 12xy - 12x + 12y - 12x",
|
|
"gt_answers": "[ 2 1 x ^ { 2 } y - 1 4 x y ^ { 2 } ] \\div 7 x y\n",
|
|
"image_path": "./data/HME100K/test_images/test_5125.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "a b = 3 ( 3 + \\sqrt { 7 } ) ( 3 - \\sqrt { 7 } ) = 3 ^ { 2 } - ( \\sqrt { 7 } ) ^ { 2 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5126.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x - 4 = 0.",
|
|
"gt_answers": "\\varphi ^ { \\prime } ( x ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5127.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "S _ { 2 } ^ { 2 } = \\frac { 1 } { 5 0 } [ 8 \\times 1 5 5 - 7 5 ) ^ { 2 } + 1 0 \\times ( 6 5 - 7 5 ) ^ { 2 } + 1 4 \\times ( 7 5 - 7 5 ) ^ { 2 } + 1 0 \\times ( 8 5 - 1 5 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5130.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x(56-6) = 180 - 36.",
|
|
"gt_answers": "\\frac { 1 } { 3 } \\times 1 2 . 5 6 \\times 1 . 5 = 6 . 2 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5131.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 14 + 285 = 299.",
|
|
"gt_answers": "\\frac { 7 } { 1 0 } = \\frac { 1 4 } { ( 2 0 ) } = \\frac { ( 2 8 ) } { 3 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5134.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, so I cannot provide a LaTeX representation of it. However, I can provide a translation of the formula into English:\n\n\"The sum of the squares of the first 100 natural numbers is equal to the sum of the squares of the first 100 even numbers.\"",
|
|
"gt_answers": "x = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5135.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: (10/6) + (12/7) = 28/21.",
|
|
"gt_answers": "( 1 0 + 6 + 1 2 ) \\times 4 = 2 8 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5136.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 1/2(x + 3) - 1/2(x - 3) = 1/2(x - 3) - 1/2(x - 3) = 0.",
|
|
"gt_answers": "- \\frac { 1 1 } { 2 1 } < \\frac { 1 } { 2 } < \\frac { 1 9 } { 3 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5137.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 12 + 4 = 16.",
|
|
"gt_answers": "- 1 2 k ^ { 2 } + 4 = c\n",
|
|
"image_path": "./data/HME100K/test_images/test_5138.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x \\geq 4 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5139.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\ny = 3x^2 + 3y + 2\n\\end{equation}\n\nThis is a quadratic equation in the form of y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = 3, b = 3, and c = 2.",
|
|
"gt_answers": "y _ { 1 } = \\frac { 1 } { 3 } , y _ { 2 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5140.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(P(A \\land B \\land C) = P(A) \\cdot P(B) \\cdot P(C)\\)",
|
|
"gt_answers": "P A \\cdot P B = P C \\cdot P D\n",
|
|
"image_path": "./data/HME100K/test_images/test_5141.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x = - \\frac { 2 8 5 } { 0 . 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5142.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(54\\times 4 = 216\\)",
|
|
"gt_answers": "5 4 \\times 5 4 = 2 9 1 6 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5143.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x + 1 - 8/6 - 16/3 - 8/2 - 16/1 - 8/0.",
|
|
"gt_answers": "4 x - 1 . 8 = 1 6 \\div 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5144.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(4\\times 2 + 2\\times 3 + 3\\times 4 + 4\\times 5 + 5\\times 6 + 6\\times 7 + 7\\times 8 + 8\\times 9 + 9\\times 10 + 10\\times 11 + 11\\times 12 + 12\\times 13 + 13\\times 14 + 14\\times 15 + 15\\times 16 + 16\\times 17 + 17\\times 18 + 18\\times 19 + 19\\times 20 + 20\\times 21 + 21\\times 22 + 22\\times 23 + 23\\times 24 + 24\\times 25 + 25\\times 26 + 26\\times 27 + 27\\times 28 + 28\\times 29 + 29\\times 30 + 30\\times 31 + 31\\times 32 + 32\\times 33 + 33\\times 34 + 34\\times 35 + 35\\times 36 + 36\\times 37 + 37\\times 38 + 38\\times 39 + 39\\times 40 + 40\\times 41 + 41\\times 42 + 42\\times 43 + 43\\times 44 + 44\\times 45 + 45\\times 46 + 46\\times 47 + 47\\times 48 + 48\\times 49 + 49\\times 50 + 50\\times 51 + 51\\times 52 + 52\\times 53 + 53\\times 54 + 54\\times 55 + 55\\times 56 + 56\\times 57 + 57\\times 58",
|
|
"gt_answers": "\\angle K F C = \\angle D B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_5145.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, and their sum. The equation states that the sum of the two variables is equal to 10.",
|
|
"gt_answers": "1 = \\frac { 6 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5146.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{a \\cdot x^2 + b \\cdot x + c}{d \\cdot x + e}\\)",
|
|
"gt_answers": "y = a ( x + m ) ^ { 2 } + k\n",
|
|
"image_path": "./data/HME100K/test_images/test_5147.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ABACUS 1962.\"",
|
|
"gt_answers": "A E = A C , \\angle 1 = \\angle 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5148.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the formula notation, which is a mathematical notation that represents a mathematical expression as a sequence of symbols. The formula is written in the form of a mathematical equation, with the variable \"V\" representing voltage, \"R\" representing resistance, and \"I\" representing current. The formula is written as follows:\n\nV = IR\n\nThis formula represents the relationship between voltage, resistance, and current in an electrical circuit. The voltage is the potential difference between two points in the circuit, and the current is the flow of charge through the circuit. The resistance represents the opposition to the flow of current, and the formula shows that the voltage is proportional to the current multiplied by the resistance.",
|
|
"gt_answers": "I = \\frac { U } { R } = \\frac { 2 2 0 V } { 1 2 1 0 \\Omega } \\approx 0 . 1 8 A )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5149.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with two numbers and a sign, which could be a simple addition or subtraction problem.",
|
|
"gt_answers": "\\vert - \\frac { 1 } { 7 } \\vert = \\frac { 1 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5150.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the formula is likely a mathematical equation or a chemical formula.",
|
|
"gt_answers": "A H = \\frac { 1 } { 2 } A C = \\frac { 3 - x } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5151.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(AB = \\frac{sin(A)sin(B)}{sin(A+B)}\\)\n\nThis formula is used to calculate the area of a triangle when the lengths of its sides are given.",
|
|
"gt_answers": "\\sin \\alpha = \\frac { B C } { A B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5152.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20 + 1/21 + 1/22 + 1/23 + 1/24 + 1/25 + 1/26 + 1/27 + 1/28 + 1/29 + 1/30 + 1/31 + 1/32 + 1/33 + 1/34 + 1/35 + 1/36 + 1/37 + 1/38 + 1/39 + 1/40 + 1/41 + 1/42 + 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48 + 1/49 + 1/50 + 1/51 + 1/52 + 1/53 + 1/54 + 1/55 + 1/56 + 1/57 + 1/58 + 1/59 + 1/60 + 1/61 + 1/62 + 1/63 + 1/64 + 1/65 + 1/66 + 1/67 + 1/68 + 1/69 + 1/70 + 1/71 + 1/72 + 1/73 + 1/74 + 1/75 + 1/76 + 1/77 + 1/78 + 1/79 + 1/80 + 1/81 + 1/82 + 1/83 + 1/84 + 1/85 + 1/86",
|
|
"gt_answers": "5 9 . 0 2 > 5 8 . 5 2 > 5 8 . 1 7 > 5 8 . 0 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5153.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 3x + 2 = 0\\)",
|
|
"gt_answers": "x _ { 1 } = 3 x _ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5157.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written in the form of a mathematical equation, with the letters \"Anis\" and \"Ani\" representing the variables. The expression is written in a way that it can be easily read and understood by those familiar with the LaTeX formula notation.",
|
|
"gt_answers": "1 \\geq \\sin A > \\sin B \\geq - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5158.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(168 \\times 100 = 16800\\)",
|
|
"gt_answers": "\\frac { 4 \\sqrt { 2 } } { 3 } = \\frac { 1 6 \\sqrt { 2 } } { 8 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5159.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x < \\frac { 9 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5160.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LB-105\u00b0\".",
|
|
"gt_answers": "\\angle B = 1 0 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5161.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(K_b = \\frac{1}{2} \\left( \\frac{RT}{PV} \\right) \\ln \\left( \\frac{PV}{RT} \\right)\\)\n\nThis formula relates the equilibrium constant for the reaction between a weak acid and its conjugate base to the partial pressure of the acid, the partial pressure of the base, and the temperature. The equilibrium constant is a measure of the strength of the acid-base reaction and is used to predict the relative amounts of acid and base present in a solution at equilibrium.",
|
|
"gt_answers": "k ^ { 2 } = \\frac { 5 } { 4 } b ^ { 2 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5164.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2\\pi r^2 = \\pi r^2 + 2\\pi r^2\\)",
|
|
"gt_answers": "\\frac { \\pi } { 2 } + 2 k \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_5165.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2.33 = 3.2125m.",
|
|
"gt_answers": "2 . 5 \\times 1 . 3 = 2 . 2 5 d m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5166.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A = \\sqrt{AD^2 + BC^2}\\)",
|
|
"gt_answers": "A D = \\frac { 2 } { 5 } \\sqrt { 5 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5167.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{3} \\left( \\frac{1}{2} \\left( \\frac{1}{3} \\left( \\frac{1}{4} \\left( \\frac{1}{5} \\left( \\frac{1}{6} \\left( \\frac{1}{7} \\left( \\frac{1}{8} \\left( \\frac{1}{9} \\left( \\frac{1}{10} \\left( \\frac{1}{11} \\left( \\frac{1}{12} \\left( \\frac{1}{13} \\left( \\frac{1}{14} \\left( \\frac{1}{15} \\left( \\frac{1}{16} \\left( \\frac{1}{17} \\left( \\frac{1}{18} \\left( \\frac{1}{19} \\left( \\frac{1}{20} \\left( \\frac{1}{21} \\left( \\frac{1}{22} \\left( \\frac{1}{23} \\left( \\frac{1}{24} \\left( \\frac{1}{25} \\left( \\frac{1}{26} \\left( \\frac{1}{27} \\left( \\frac{1}{28} \\left( \\frac{1}{29} \\left( \\frac{1}{30} \\left( \\frac{1}{31} \\left( \\frac{1}{32} \\left( \\frac{1}{33} \\left( \\frac{1}{34} \\left( \\frac{1}{35} \\left( \\frac{1}{36} \\left( \\frac{1}{37} \\left( \\frac{1}{38} \\left( \\frac{1}{39} \\left( \\frac{1}{40} \\left( \\frac{1}{41} \\left( \\frac{1}{42} \\left( \\frac{1}{43} \\left( \\frac{1}{44} \\left( \\frac{1}{45} \\left( \\frac{1",
|
|
"gt_answers": "3 x ( x + 1 ) - ( x + 1 ) ( x - 1 ) = x ( x + 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5169.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 2 = 0\\)",
|
|
"gt_answers": "x _ { 3 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5170.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x + 2y = 4.",
|
|
"gt_answers": "2 C O + 2 N O = 2 C O _ { 2 } + H _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5171.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(b^2-2ab+a^2=0\\)",
|
|
"gt_answers": "( 2 b - 3 c ) - ( 2 a - 3 b ) = - d i\n",
|
|
"image_path": "./data/HME100K/test_images/test_5172.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "2 1 \\times 1 0 ^ { 4 } K J + 8 0 \\times 1 0 ^ { 4 } K J + 9 \\times 1 0 ^ { 4 } K J + 6 0 \\times 1 0 ^ { 4 } K J = 1 7 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5174.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x + 2y = 6cm.",
|
|
"gt_answers": "3 \\times 2 = 6 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5175.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "7 5 : 6 = 0 . 5 : 0 . 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5176.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 6.\"",
|
|
"gt_answers": "2 k \\pi - \\frac { \\pi } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5177.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a mixture of Chinese and English, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a green background, which could be related to a physics or engineering context.",
|
|
"gt_answers": "1 \\div 1 1 = \\frac { 1 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5178.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 10.\"",
|
|
"gt_answers": "a = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5179.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 - 2ab = (a + b)^2 - 2ab\\)",
|
|
"gt_answers": "4 ) \\frac { a } { a - b } \\cdot ( \\frac { b - a } { b } ) ^ { 2 } b\n",
|
|
"image_path": "./data/HME100K/test_images/test_5180.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "y _ { 1 } = 2 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5181.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x + z - ( y + z ) - ( x - y ) = x + z - y - z - x + y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5182.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 30x33 - 32.",
|
|
"gt_answers": "3 0 \\times \\frac { 3 2 } { 3 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5183.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{2} - 2^{1} = 3^{2} - 3^{1} = 5^{2} - 5^{1} = 10^{2} - 10^{1} = 11^{2} - 11^{1} = 12^{2} - 12^{1} = 13^{2} - 13^{1} = 14^{2} - 14^{1} = 15^{2} - 15^{1} = 16^{2} - 16^{1} = 17^{2} - 17^{1} = 18^{2} - 18^{1} = 19^{2} - 19^{1} = 20^{2} - 20^{1} = 21^{2} - 21^{1} = 22^{2} - 22^{1} = 23^{2} - 23^{1} = 24^{2} - 24^{1} = 25^{2} - 25^{1} = 26^{2} - 26^{1} = 27^{2} - 27^{1} = 28^{2} - 28^{1} = 29^{2} - 29^{1} = 30^{2} - 30^{1} = 31^{2} - 31^{1} = 32^{2} - 32^{1} = 33^{2} - 33^{1} = 34^{2} - 34^{1} = 35^{2} - 35^{1} = 36^{2} - 36^{1} = 37^{2} - 37^{1} = 38^{2} - 38^{1} = 39^{2} - 39^{1} = 40^{2} - 40^{1} = 41^{2} - 41^{1} = 42^{2} - 42^{",
|
|
"gt_answers": "O B = \\frac { 2 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5184.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LA = 2x80\u00b0 + 40\u00b0.\"",
|
|
"gt_answers": "\\angle A = \\frac { 1 } { 2 } \\times 8 0 ^ { \\circ } = 4 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5186.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 244 - 18 = 226.",
|
|
"gt_answers": "1 8 \\div 2 4 2 = \\frac { 1 8 } { 2 4 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5187.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "2 t = 2 t\n",
|
|
"image_path": "./data/HME100K/test_images/test_5188.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\nR = (Y1 - Y2) / (X1 - X2)\n\nwhere R is the correlation coefficient, Y1 and Y2 are the values of the two variables, and X1 and X2 are the values of the two variables.",
|
|
"gt_answers": "k = \\frac { y _ { 1 } - y _ { 2 } } { x _ { 1 } - x _ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5189.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 13 = 18.",
|
|
"gt_answers": "x = \\frac { 1 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5190.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 5\\)",
|
|
"gt_answers": "x = - \\frac { 2 8 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5191.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, and the constant 10. The equation states that the sum of the two variables is equal to 10.",
|
|
"gt_answers": "\\frac { 5 0 } { 9 } = 5 \\frac { 5 } { 9 } \\frac { 4 3 } { 1 2 } = 3 \\frac { 7 } { 1 2 } \\frac { 6 9 } { 2 0 } = 3 \\frac { 9 } { 2 0 } \\frac { 3 } { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5192.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{y} \\right)\n\\end{equation}\n\nThis formula can be used to solve for the value of x or y when given the other value. For example, if we know that y = 2, we can solve for x by substituting y = 2 into the formula and solving for x:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{2} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{2} \\right)\n\\end{equation}\n\nSolving for x:\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} - \\frac{1}{2} \\right) = \\frac{1}{2}\n\\end{equation}\n\nSolving for x:\n\\begin{equation}\nx = \\frac{1}{2}\n\\end{equation}\n\nTherefore, the value of x is 1/2.",
|
|
"gt_answers": "1 \u3001 \\sqrt { 2 5 - x ^ { 2 } } = x - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5193.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V = \\frac{R_0 \\cdot z}{r \\cdot s \\cdot l} \\cdot \\sqrt{1 + \\frac{z^2}{r^2 \\cdot s^2 \\cdot l^2}}\\)\n\nThis formula calculates the voltage across a capacitor with a given capacitance, C, and a given distance, d, between the plates. The formula uses the following variables:\n\n* R0: The resistance of the capacitor's internal resistance, in ohms.\n* z: The distance between the plates, in meters.\n* r: The radius of the plates, in meters.\n* s: The separation between the plates, in meters.\n* l: The length of the capacitor, in meters.\n\nThe formula calculates the voltage across the capacitor as a function of these variables and the square root of the product of the distance between the plates and the square of the capacitance.",
|
|
"gt_answers": "w = \\frac { V _ { 4 } } { r } = \\frac { 2 } { 0 . 2 } r a d / s = 1 0 r a d / s\n",
|
|
"image_path": "./data/HME100K/test_images/test_5194.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 8x(3-8) = 24.",
|
|
"gt_answers": "\\frac { 1 } { 5 } - \\frac { 1 } { 8 } = \\frac { 1 } { 8 } \\times A\n",
|
|
"image_path": "./data/HME100K/test_images/test_5195.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 0.538 x 100 = 26.5.",
|
|
"gt_answers": "c \\% = \\frac { 5 . 3 g } { 2 0 g } \\times 1 0 0 \\% = 2 6 . 5 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_5196.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6x8 = 48.\"",
|
|
"gt_answers": "\\frac { 1 } { 6 } + \\frac { 1 } { 8 } = \\frac { 7 } { 2 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5198.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(F_e = F_o + F_l\\)\n\nwhere F_e is the total force on the object, F_o is the force on the object due to the external field, and F_l is the force on the object due to the Lorentz force.",
|
|
"gt_answers": "F _ { 1 } l _ { 1 } = F _ { 2 } l _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5199.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"11375/11375\" using LaTeX format.",
|
|
"gt_answers": "= 3 5 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5200.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 3x + 2 = 0.\"",
|
|
"gt_answers": "x = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5201.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few Chinese characters, which could be related to a mathematical equation or a mathematical symbol.",
|
|
"gt_answers": "\\sqrt { x + y } = \\pm \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5202.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(cos(x) = \\frac{1}{2} \\left( \\sqrt{1 + \\left( \\frac{x}{\\pi} \\right)^2} - 1 \\right)\\)\n\nThis formula is a trigonometric identity that relates the cosine of an angle x to the square root of the sum of the squares of the sine and cosine of the angle. The angle x is measured in radians, and the expression is valid for all values of x.",
|
|
"gt_answers": "\\cos \\theta = \\frac { \\sqrt { 2 1 } } { 1 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5203.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: (2x + 3)(2x - 5) = 2x^2 - 10x + 15.",
|
|
"gt_answers": "( 2 - x ) ^ { 2 } + ( 1 . 5 + 0 . 5 ) ^ { 2 } = ( 2 . 5 ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5204.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x _ { 2 } =\n",
|
|
"image_path": "./data/HME100K/test_images/test_5205.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(G = \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2R} + \\frac{Li^2}{2",
|
|
"gt_answers": "( G - F _ { 1 } ) L _ { 1 } = G _ { 2 } l _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5206.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 12 + 3 = 5 + 3 = 8.",
|
|
"gt_answers": "\\frac { 1 2 } { 5 } < R \\leq 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5207.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "k = \\pm \\frac { 1 } { \\sqrt { 1 1 } } = \\pm \\frac { \\sqrt { 1 1 } } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5208.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 18x + 18 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\therefore = 1 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5209.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2\\cdot 4 - 2\\cdot 3 + 4\\cdot 2 - 4\\cdot 1 + 3\\cdot 2 - 3\\cdot 1 = 12 - 6 + 8 - 8 + 6 - 6 = 0\\)",
|
|
"gt_answers": "\\frac { \\cdot - 2 - 4 } { 2 } = \\frac { 0 + y } { 2 } \\cdot H ( 4 , - 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5210.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(L = 180\u00b0 - 120\u00b0 = 60\u00b0\\)",
|
|
"gt_answers": "\\angle 1 = 1 8 0 ^ { \\circ } - 1 2 0 ^ { \\circ } = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5211.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"8x2 + 4x3 + 5x4 + 6x5 + 7x6 + 8x7 + 9x8 + 10x9 + 11x10 + 12x11 + 13x12 + 14x13 + 15x14 + 16x15 + 17x16 + 18x17 + 19x18 + 20x19 + 21x20 + 22x21 + 23x22 + 24x23 + 25x24 + 26x25 + 27x26 + 28x27 + 29x28 + 30x29 + 31x30 + 32x31 + 33x32 + 34x33 + 35x34 + 36x35 + 37x36 + 38x37 + 39x38 + 40x39 + 41x40 + 42x41 + 43x42 + 44x43 + 45x44 + 46x45 + 47x46 + 48x47 + 49x48 + 50x49 + 51x50 + 52x51 + 53x52 + 54x53 + 55x54 + 56x55 + 57x56 + 58x57 + 59x58 + 60x59 + 61x60 + 62x61 + 63x62 + 64x63 + 65x64 + 66x65 + 67x66 + 68x67 + 69x68 + 70x69 + 71x70 + 72x71 + 73x72 + 74x73 + 75x74 + 76x75 +",
|
|
"gt_answers": "x _ { 1 } + x _ { 2 } = \\frac { 8 k b } { 4 k ^ { 2 } + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5212.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3 = 5.",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5213.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few numbers and letters, which could be a mathematical expression in any language.",
|
|
"gt_answers": "y = 4 \\therefore O O A = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5214.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 2xy\\)",
|
|
"gt_answers": "x _ { 2 } = \\frac { \\sqrt { 6 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5215.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 134.62 x 113.34 cm = 15,400.08 cm^2.",
|
|
"gt_answers": "3 1 4 \\times 6 ^ { 2 } = 1 1 3 . 0 4 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5216.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2} \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 + 4} + 2 \\right) \\left( \\sqrt{x^2 + 4} - 2 \\right) \\left( \\sqrt{x^2 +",
|
|
"gt_answers": "y = \\ln ( 1 + \\frac { M } { m } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5217.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 3}{x^2 - 4x",
|
|
"gt_answers": "\\therefore B C = \\sqrt { 3 ^ { 2 } + 4 ^ { 2 } } = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5218.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nCO2 + NaOH --> Na2CO3 + H2O",
|
|
"gt_answers": "C a ( O H ) _ { 2 } + N a _ { 2 } C O _ { 3 } = C a C O _ { 3 } \\downarrow + 2 N a O H\n",
|
|
"image_path": "./data/HME100K/test_images/test_5219.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LAX = 30\u00b0.\"",
|
|
"gt_answers": "\\angle A O C = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5220.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(V = \\frac{1}{2}mv^2\\)\n\nwhere V is the volume of the object, m is its mass, and v is its velocity.",
|
|
"gt_answers": "V < 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5221.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": ": x _ { 1 } = - \\frac { \\sqrt { 1 7 } + 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5223.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 3 - x } { 2 - x } = \\frac { 1 } { x - 2 } + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5224.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BGD2 = BD2 + BGD2.\"",
|
|
"gt_answers": "B C = \\frac { 1 } { 2 } B D = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5225.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `x^2 + 3x + 4 = 0`.",
|
|
"gt_answers": "x = \\frac { 1 } { 3 } + \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5226.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{3}x^3 + \\frac{1}{4}x^4 + \\frac{1}{5}x^5 + \\frac{1}{6}x^6 + \\frac{1}{7}x^7 + \\frac{1}{8}x^8 + \\frac{1}{9}x^9 + \\frac{1}{10}x^{10} + \\frac{1}{11}x^{11} + \\frac{1}{12}x^{12} + \\frac{1}{13}x^{13} + \\frac{1}{14}x^{14} + \\frac{1}{15}x^{15} + \\frac{1}{16}x^{16} + \\frac{1}{17}x^{17} + \\frac{1}{18}x^{18} + \\frac{1}{19}x^{19} + \\frac{1}{20}x^{20} + \\frac{1}{21}x^{21} + \\frac{1}{22}x^{22} + \\frac{1}{23}x^{23} + \\frac{1}{24}x^{24} + \\frac{1}{25}x^{25} + \\frac{1}{26}x^{26} + \\frac{1}{27}x^{27} + \\frac{1}{28}x^{28} + \\frac{1}{29}x^{29} + \\frac{1}{30}x^{30} + \\frac{1}{31}x^{31} + \\frac{1}{32}x^{32} + \\frac{1}{33}x^{33} + \\frac{1}{34}x^{34} + \\frac{1}{35}x^{35} + \\frac{1}{36}x^{36} + \\frac{1}{37}x^{37} + \\frac{1}{38}x",
|
|
"gt_answers": "G ( 2 , \\frac { 1 } { 2 } a ^ { 2 } - 2 a - 6 ) , G N = \\vert a - 2 \\vert\n",
|
|
"image_path": "./data/HME100K/test_images/test_5227.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 4x + 5 = 2(x^2 + 2x + 5)\\)",
|
|
"gt_answers": "3 ( x ^ { 2 } + 5 x + 1 ) + 2 \\sqrt { x ^ { 2 } + 5 x + 1 } = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5228.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "\\therefore \\Delta = ( - 1 ) ^ { 2 } - 4 ( a - 1 ) \\leq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5229.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\overrightarrow { m } \\bot \\overrightarrow { n } = \\overrightarrow { m } \\cdot \\overrightarrow { n } = 2 \\cos ^ { 2 } x + 2 \\sqrt { 3 } \\sin x \\cos - y = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5230.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"T3 = 40 - 3L.\"",
|
|
"gt_answers": "x = \\frac { 4 0 } { 1 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5231.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis equation is a simple algebraic expression that can be solved using the distributive property of multiplication.",
|
|
"gt_answers": "\\therefore y = - \\frac { ( x _ { 1 } - x _ { 2 } ) ^ { 2 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5232.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"X = 300 + 100\".",
|
|
"gt_answers": "x = 3 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5233.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 0.675x2 = 1.5cm.",
|
|
"gt_answers": "0 . 7 5 \\times 2 = 1 . 5 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5234.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"b-b+b^2.\"",
|
|
"gt_answers": "b _ { 2 } - b _ { 1 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5235.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"25434-13388-15368-18356-21344-24334-27324-30314-33304-36394-39384-42374-45364-48354-51344-54334-57324-60314-63304-66394-69384-72374-75364-78354-81344-84334-87324-90314-93304-96394-99384-102374-105364-108354-111344-114334-117324-120314-123304-126394-129384-132374-135364-138354-141344-144334-147324-150314-153304-156394-159384-162374-165364-168354-171344-174334-177324-180314-183304-186394-189384-192374-195364-198354-201344-204334-207324-210314-213304-216394-219384-222374-225364-228354-231344-234334-2",
|
|
"gt_answers": "2 5 4 . 3 4 - 1 5 3 . 8 6 = 1 0 0 . 4 8 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5236.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(P = \\frac{1}{2} \\left( \\frac{1}{3} \\left( \\frac{1}{4} \\left( \\frac{1}{5} \\left( \\frac{1}{6} \\left( \\frac{1}{7} \\left( \\frac{1}{8} \\left( \\frac{1}{9} \\left( \\frac{1}{10} \\left( \\frac{1}{11} \\left( \\frac{1}{12} \\left( \\frac{1}{13} \\left( \\frac{1}{14} \\left( \\frac{1}{15} \\left( \\frac{1}{16} \\left( \\frac{1}{17} \\left( \\frac{1}{18} \\left( \\frac{1}{19} \\left( \\frac{1}{20} \\left( \\frac{1}{21} \\left( \\frac{1}{22} \\left( \\frac{1}{23} \\left( \\frac{1}{24} \\left( \\frac{1}{25} \\left( \\frac{1}{26} \\left( \\frac{1}{27} \\left( \\frac{1}{28} \\left( \\frac{1}{29} \\left( \\frac{1}{30} \\left( \\frac{1}{31} \\left( \\frac{1}{32} \\left( \\frac{1}{33} \\left( \\frac{1}{34} \\left( \\frac{1}{35} \\left( \\frac{1}{36} \\left( \\frac{1}{37} \\left( \\frac{1}{38} \\left( \\frac{1}{39} \\left( \\frac{1}{40} \\left( \\frac{1}{41} \\left( \\frac{1}{42} \\left( \\frac{1}{43} \\left( \\frac{1}{44} \\left( \\frac{1}{45} \\left( \\frac{1}{46} \\left( \\frac{1}{",
|
|
"gt_answers": "P Q = C Q = C Q \\sin C = ( 6 0 - 2 0 \\sqrt { 3 } ) \\sin 6 0 ^ { \\circ } = 3 0 ( \\sqrt { 3 } -\n",
|
|
"image_path": "./data/HME100K/test_images/test_5237.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2\\pi r^2 = 4\\pi r^2 - 4\\pi r^2 \\cos(2\\theta)\\)\n\nThe formula is a mathematical equation that relates the area of a circle to its radius squared and the angle between the radius and the center of the circle.",
|
|
"gt_answers": "2 \\cos \\alpha = \\frac { 5 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5238.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"x^2 + y^2 = 1.\"",
|
|
"gt_answers": "\\frac { 1 } { 2 } x + 1 - 1 = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5239.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 3x^2 - 2x + 3.",
|
|
"gt_answers": "\\sqrt { 3 x - 2 } - \\sqrt { x + 3 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5241.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "2 1 0 3 < 2 1 3 0 < 2 3 0 1 < 2 3 1 0 < 3 0 1 2 < 3 0 2 1 < 3 1 0 2 < 3 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5242.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 46x + 46^2 = 1000\\)",
|
|
"gt_answers": "1 \\times 6 = 4 8 6 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5243.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555",
|
|
"gt_answers": "5 5 - 5 ( > ) 5 5 - 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5244.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"L2 + ADF = 160\u00b0.\"",
|
|
"gt_answers": "\\angle 2 + \\angle A D E = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5245.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2-k(3-k)2k.",
|
|
"gt_answers": "2 - k = 3 + 2 k\n",
|
|
"image_path": "./data/HME100K/test_images/test_5246.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 5x4 - 4x7 = 16 - 28 = -12.",
|
|
"gt_answers": ": \\frac { 5 } { 2 } = 4 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5247.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x4 - 5x2 + 12.",
|
|
"gt_answers": "\\frac { 3 } { 5 } = \\frac { 3 \\times 4 } { 5 \\times 4 } = \\frac { 1 2 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5248.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{8}{3} \\cdot \\frac{3}{2} \\cdot \\frac{2}{3} \\cdot \\frac{1}{2} \\cdot \\frac{1}{3} \\cdot \\frac{1}{4} \\cdot \\frac{1}{5} \\cdot \\frac{1}{6} \\cdot \\frac{1}{7} \\cdot \\frac{1}{8} \\cdot \\frac{1}{9} \\cdot \\frac{1}{10} \\cdot \\frac{1}{11} \\cdot \\frac{1}{12} \\cdot \\frac{1}{13} \\cdot \\frac{1}{14} \\cdot \\frac{1}{15} \\cdot \\frac{1}{16} \\cdot \\frac{1}{17} \\cdot \\frac{1}{18} \\cdot \\frac{1}{19} \\cdot \\frac{1}{20} \\cdot \\frac{1}{21} \\cdot \\frac{1}{22} \\cdot \\frac{1}{23} \\cdot \\frac{1}{24} \\cdot \\frac{1}{25} \\cdot \\frac{1}{26} \\cdot \\frac{1}{27} \\cdot \\frac{1}{28} \\cdot \\frac{1}{29} \\cdot \\frac{1}{30} \\cdot \\frac{1}{31} \\cdot \\frac{1}{32} \\cdot \\frac{1}{33} \\cdot \\frac{1}{34} \\cdot \\frac{1}{35} \\cdot \\frac{1}{36} \\cdot \\frac{1}{37} \\cdot \\frac{1}{38} \\cdot \\frac{1}{39} \\cdot \\frac{1}{40} \\cdot \\frac{1}{41} \\cdot \\frac{1}{42} \\cdot \\frac{1}{43} \\cdot \\frac{1}{44} \\cdot \\frac{1}{45} \\cdot \\frac{1}{46} \\cdot \\frac{1}{47} \\cdot \\frac{1}{48} \\cdot \\",
|
|
"gt_answers": "x ^ { 9 m } = ( x ^ { 3 m } ) ^ { 3 } = 2 ^ { 3 } = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5249.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\begin{equation}\n\\frac{2x^2 - 1}{x^2 + 1} = \\frac{2x^2 - 1}{x^2 + 1}\n\\end{equation}\n\nThis is a mathematical equation that can be solved using the method of factoring.",
|
|
"gt_answers": "x = \\frac { 1 2 0 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5250.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 2 } \\times ( \\frac { 6 } { 5 } x - \\frac { 3 6 } { 5 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5251.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"do ta, uzt, tag\" using LaTeX format.",
|
|
"gt_answers": "a _ { 0 } + a _ { 1 } + a _ { 2 } + \\cdots + a _ { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5253.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 360\u00b0 - 7\u00b0 = 353\u00b0.",
|
|
"gt_answers": "x < \\frac { 3 6 0 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5255.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\nx^2 + y^2 = 3\n\\end{equation}\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. In this case, the variable is x, and the square of x is x^2. The variable y is also involved in the equation, and its square is y^2. The equation is solved by adding the squares of both variables and then subtracting the result from 3.",
|
|
"gt_answers": "\\frac { 1 } { x + y } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5256.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3 = 5.",
|
|
"gt_answers": "h = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5257.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 13x^2 - 12x + 4\\)",
|
|
"gt_answers": "\\{ x \\vert 3 \\leq x \\leq - b \\}\n",
|
|
"image_path": "./data/HME100K/test_images/test_5258.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 3x3x4x9x13x19x25x31x37x43x49x55x61x67x73x79x85x91x97x103x109x115x121x127x133x139x145x151x157x163x169x175x181x187x193x199x205x211x217x223x229x235x241x247x253x259x265x271x277x283x289x295x2",
|
|
"gt_answers": "3 \\times 3 \\times 3 . 1 4 \\times 1 \\times \\frac { 1 } { 3 } = 9 . 4 2 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5259.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\varphi = c m \\Delta t = 4 2 0 0 \\times 2 \\times 1 0 = 8 4 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5260.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "( a - 1 ) x = b + 2 a\n",
|
|
"image_path": "./data/HME100K/test_images/test_5261.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\n\\(b^2 - 4ac = 0\\)\n\nThis formula is used to solve quadratic equations, where b is the square root of the discriminant, a is the coefficient of the quadratic term, and c is the coefficient of the linear term.",
|
|
"gt_answers": "\\sin B = \\frac { 2 R } { 2 R } = \\frac { b } { 2 R }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5262.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LAC_{360} = \\frac{180^{\\circ}}{2} \\times \\left(LAC_{180} + \\frac{180^{\\circ}}{2} \\times LAC_{90}\\right)\\)\n\nThis formula calculates the angle of the line of action (LAC) in degrees when the line is viewed from two different directions, 180 degrees apart. The first part of the formula, \\(LAC_{180}\\), represents the angle of the line of action when viewed from the top, and the second part, \\(\\frac{180^{\\circ}}{2} \\times LAC_{90}\\), represents the angle of the line of action when viewed from the bottom. The result of the formula is the angle of the line of action in degrees when viewed from any direction.",
|
|
"gt_answers": "\\angle A O C = 3 6 0 ^ { \\circ } - 1 5 8 ^ { \\circ } - 1 2 2 ^ { \\circ } = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5263.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 3x^2 + 2x + 1\\)",
|
|
"gt_answers": "3 y - 2 - 9 - y - 3 = - . \\sqrt { y + 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5264.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 1 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5265.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 9x + 5y = 12.",
|
|
"gt_answers": "= 9 \\times ( - \\frac { 3 } { 5 } ) - 1 2 = - 1 7 \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5266.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x - 8 = 0.",
|
|
"gt_answers": "1 2 . 5 x - 8 . 3 x = 1 8 . 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5268.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(2a^2 + 2b^2 = 4a^2 + 4b^2\\)",
|
|
"gt_answers": "x = \\frac { - b \\pm \\sqrt { \\Delta } } { 2 a } = \\frac { 4 \\sqrt { 3 } \\pm 2 \\sqrt { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5269.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x ^ { 2 } ( m - 1 ) = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5270.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2900/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "2 9 \\approx 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5271.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "A l = \\sqrt { A B ^ { 2 } - B C ^ { 2 } } = \\frac { \\sqrt { 3 } c } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5272.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(1 + 2) - 3(1 + 2) = 4(1 + 2) - 3(1 + 2) = 4(3) - 3(3) = 12 - 9 = 3.",
|
|
"gt_answers": "\\frac { 1 } { 1 8 } + \\frac { 5 } { 1 8 } + \\frac { 7 } { 1 8 } = \\frac { 1 3 } { 1 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5273.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + 2x + 1 = 0\n\\end{aligned}\n\\end{equation}\n\nThis is the quadratic equation in the form of a polynomial equation.",
|
|
"gt_answers": "( x _ { 1 } - x _ { 2 } ) ^ { 2 } >\n",
|
|
"image_path": "./data/HME100K/test_images/test_5274.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 6 0 0 0 \\times 1 0 \\% + 4 0 0 0 \\times 2 0 \\% + 2 0 0 0 \\times 2 0 \\% } { 6 0 0 0 + 4 0 0 0 + 2 0 0 0 } = 1 5 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_5275.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x^2 + 3y^2 + 2xy + 3y - 4x - 2y - 3.",
|
|
"gt_answers": "4 x ^ { 2 } y \\cdot 3 x y ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5276.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "\\frac { C E } { Q A } = \\frac { A E } { P A }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5278.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 4 = 12.\"",
|
|
"gt_answers": "\\frac { 2 } { 3 } x + 1 = \\frac { 3 } { 4 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5279.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "y = x ^ { 2 } - 2 x + 3 = x ^ { 2 } - 2 x + 1 - 1 + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5280.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(F = \\frac{AC}{2} + \\frac{BC}{2} + \\frac{AB}{2}\\)",
|
|
"gt_answers": "A F ^ { 2 } + F C ^ { 2 } = A C ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5282.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nC2H5OH + 2NaOH \u2192 2NaC2H5OH + H2O",
|
|
"gt_answers": "a _ { n } = \\frac { [ 1 + ( 2 n - 1 ) ] \\cdot ( n + 5 ) } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5283.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(n = \\frac{1}{2} \\left( \\sqrt{a^2 + b^2} + \\sqrt{c^2 + d^2} \\right)\\)\n\nThe formula is used to find the area of a parallelogram with sides a, b, c, and d.",
|
|
"gt_answers": "x + \\frac { \\pi } { 4 } = \\frac { \\pi } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5284.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"100% - 100% = 0%\".",
|
|
"gt_answers": "A D = A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_5285.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/2(x + 1) - 1/2(x - 1) = 1/4(x^2 - 1).",
|
|
"gt_answers": "\\frac { 1 } { y } = 0 ,\n",
|
|
"image_path": "./data/HME100K/test_images/test_5286.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(W = \\frac{AC}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC}{2} + \\frac{CA}{2} + \\frac{AB}{2} + \\frac{BC",
|
|
"gt_answers": "U = U _ { 1 } + U _ { 2 } = 2 V + 0 . 2 A \\times 2 0 \\Omega = 6 V\n",
|
|
"image_path": "./data/HME100K/test_images/test_5289.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/4 + 4/4 = 16/",
|
|
"gt_answers": "y = \\frac { 1 6 } { 4 } y = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5290.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2(4x + 3) - 4(2x + 3) = 8x^2 - 12x - 12 + 8x^2 - 12x - 12 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "\\frac { 4 0 } { 6 0 } = \\frac { 8 } { 1 2 } = \\frac { 4 } { 6 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5291.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation in two variables, where x and y represent the two unknowns. The expression represents the relationship between the two variables and the constant 1, which is the square of the hypotenuse of a right triangle.",
|
|
"gt_answers": "x = \\pm \\sqrt { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5292.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as y = 2x - 1.",
|
|
"gt_answers": "y - \\frac { 2 } { y } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5294.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x^2 + 8y^2 = 36.\"",
|
|
"gt_answers": "3 a - 1 2 + 5 8 = 8 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5295.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"E = mc^2,\" where E is energy, m is mass, and c is the speed of light.",
|
|
"gt_answers": "x = \\frac { \\sqrt { 5 m - 1 } } { 1 m - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5297.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LBOA = 30\u00b0.\"",
|
|
"gt_answers": "- \\angle B O A = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5298.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 10 - 2(36 - 18) = 10 - 72 = 62.",
|
|
"gt_answers": "\\frac { 3 6 } { 1 8 } = \\frac { 2 } { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5299.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = k^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "4 \\in \\{ x \\vert x = k \\pi , k \\in z \\}\n",
|
|
"image_path": "./data/HME100K/test_images/test_5300.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(3x^2 + 3x + 1 = 10\\)",
|
|
"gt_answers": "x _ { 2 } = - \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5301.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "y _ { 1 } = \\frac { 8 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5302.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 1 = 0\\)\n\nThis formula represents the quadratic equation, which is a type of polynomial equation that has two terms and two variables. The first term is the constant term, which is 1, and the second term is the linear term, which is 2x. The variable x represents the unknown quantity, and the equation states that the sum of these two terms must equal zero.",
|
|
"gt_answers": "\\frac { 3 } { x + 2 } - \\frac { x - 1 } { ( x + 2 ) ( x - 2 ) } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5303.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { 1 } { 5 0 0 + 1 } = \\frac { x } { 1 0 0 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5304.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\left(2\\",
|
|
"gt_answers": "\\angle D B C = 2 8 ^ { \\circ } , \\angle B D C = 2 8 ^ { \\circ } , \\angle D C E = 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5305.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x^2 + 3x - 4 = 0\".",
|
|
"gt_answers": ": y = - \\frac { 1 } { 4 } x ^ { 2 } + \\frac { 1 } { 2 } x + 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5306.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 10x + 10 = 0.\"",
|
|
"gt_answers": "x _ { 2 } = - \\frac { \\sqrt { 1 0 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5307.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as 4x + 2y = 10x - 10y + 12.",
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"gt_answers": "\\frac { x + 2 } { 5 } = 2 - \\frac { 1 0 x - 1 0 } { 2 }\n",
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"image_path": "./data/HME100K/test_images/test_5308.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as \"4x4 = 48.\"",
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"gt_answers": "4 \\sqrt { 3 } \\times 4 \\sqrt { 3 } = 4 8 ( m ^ { 2 } )\n",
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"image_path": "./data/HME100K/test_images/test_5309.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
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"gt_answers": "\\frac { 5 x } { y } \\cdot \\frac { y } { 1 5 x ^ { 2 } } = \\frac { 5 x - y } { y . 1 5 x ^ { 2 } } = \\frac { 1 } { 3 x }\n",
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"image_path": "./data/HME100K/test_images/test_5310.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
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"gt_answers": "x _ { 1 } = - \\sqrt { 2 1 } x _ { 2 } = \\sqrt { 2 }\n",
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"image_path": "./data/HME100K/test_images/test_5311.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as 40 + 4 = 44 + 8 + 12.",
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"gt_answers": "4 0 8 \\div 4 \u3001 8 1 2 \\div 4\n",
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"image_path": "./data/HME100K/test_images/test_5313.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as F = 3.333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
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"gt_answers": "F = P S = 3 . 3 \\times 1 0 ^ { 3 } P a\n",
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"image_path": "./data/HME100K/test_images/test_5315.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(2x + 4) - 6(6x - 8) = 12x - 12.",
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"gt_answers": "\\frac { 1 } { 2 . 2 } = \\frac { 2 } { 4 . 4 } = \\frac { 3 } { 6 . 6 } = \\frac { 4 } { 8 . 8 } = \\frac { 5 } { 1 1 }\n",
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"image_path": "./data/HME100K/test_images/test_5316.jpg",
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"model_name": "mPLUG"
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|
},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as \"C2H5OH + O2 --> CO2 + H2O + heat.\"",
|
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"gt_answers": "C H _ { 2 } = C H - C O O C _ { 2 } H _ { 5 }\n",
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"image_path": "./data/HME100K/test_images/test_5317.jpg",
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"model_name": "mPLUG"
|
|
},
|
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{
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|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 + y^2}{x^2 - y^2} = \\frac{1}{1}\n\\end{equation}\n\nThis equation is a quadratic equation, which can be solved using the quadratic formula.",
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"gt_answers": "\\frac { x + y + 2 \\sqrt { x y } } { x + y } = 1 + \\frac { 2 \\sqrt { x y } } { x + y } \\leq 1 + 1\n",
|
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"image_path": "./data/HME100K/test_images/test_5318.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{y} \\right)\n\\end{equation}\n\nThis is a simple algebraic equation that can be solved using the distributive property of multiplication.",
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|
"gt_answers": "x _ { 2 } = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5319.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x _ { 3 } = \\frac { 1 } { 2 } + \\frac { \\sqrt { 2 1 } } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5320.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x15-8x10-12x10-10x15-15x10-15x15-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-10x15-15x10-",
|
|
"gt_answers": "\\frac { 4 0 x - 1 5 } { 5 } - \\frac { 5 0 x - 8 } { 2 } = 1 2 - 1 0 x + 3 y\n",
|
|
"image_path": "./data/HME100K/test_images/test_5322.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a few numbers and letters, which can be represented in LaTeX using the following code:\n\n\\begin{equation}\n\\begin{aligned}\nx^2 + y^2 = z^2\n\\end{aligned}\n\\end{equation}\n\nThis equation represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "\\frac { 1 } { x } = \\frac { 1 } { 0 . 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5325.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `A = 1/2 * (B + C) + 1/2 * (D + E) + 1/2 * (F + G) + 1/2 * (H + J) + 1/2 * (K + L) + 1/2 * (M + N) + 1/2 * (O + P) + 1/2 * (Q + R) + 1/2 * (S + T) + 1/2 * (U + V) + 1/2 * (W + X) + 1/2 * (Y + Z)`.",
|
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"gt_answers": "A C = \\frac { 1 0 0 \\sin 3 5 ^ { \\circ } } { \\sin 6 7 ^ { \\circ } } \\approx 5 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5327.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "A E = \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5328.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "\\angle D F B = \\angle D E B = \\angle H B C = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5329.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 2x^2 + 3x - 11 = 0.",
|
|
"gt_answers": "6 0 \\times \\frac { 6 + 3 } { 1 + 3 + 7 + 6 + 3 } = 2 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_5331.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(E = \\frac{F \\cdot d}{m} = \\frac{300 \\cdot 300 \\cdot 1000 \\cdot 1000}{1000 \\cdot 1000 \\cdot 1000 \\cdot 1000} = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\cdot 1000 \\cdot 1000 \\cdot 1000 = 300 \\cdot 300 \\",
|
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"gt_answers": "F = \\frac { L ^ { 1 } } { L ^ { 2 } } G = \\frac { 2 } { 3 } \\times 3 0 0 N = 2 0 0 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_5332.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 10x8x7z = 160 cm.",
|
|
"gt_answers": "0 \\times 8 \\times 2 = 1 6 0 c m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5333.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x - 1 = 0\\)",
|
|
"gt_answers": "( a + 2 ) x + 4 b = a - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5334.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
|
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"gt_answers": "4 . 5 \\times 2 0 0 0 0 0 0 0 = 9 0 0 0 0 0 0 0 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5335.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5336.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: \"a + b = c\".",
|
|
"gt_answers": "0 < a < 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5337.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "8 . 2 4 - 3 . 5 6 = 4 . 6 8 1 1 . 6 5 - 7 . 3 9 = 4 . 2 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_5338.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible for me to accurately transcribe it using LaTeX. However, I can provide a rough approximation of the formula using the English alphabet:\n\n\"A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z\"",
|
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"gt_answers": "x \\leq - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5339.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{3}x^3 + \\frac{1}{4}x^4 + \\frac{1}{5}x^5 + \\frac{1}{6}x^6 + \\frac{1}{7}x^7 + \\frac{1}{8}x^8 + \\frac{1}{9}x^9 + \\frac{1}{10}x^{10} + \\frac{1}{11}x^{11} + \\frac{1}{12}x^{12} + \\frac{1}{13}x^{13} + \\frac{1}{14}x^{14} + \\frac{1}{15}x^{15} + \\frac{1}{16}x^{16} + \\frac{1}{17}x^{17} + \\frac{1}{18}x^{18} + \\frac{1}{19}x^{19} + \\frac{1}{20}x^{20} + \\frac{1}{21}x^{21} + \\frac{1}{22}x^{22} + \\frac{1}{23}x^{23} + \\frac{1}{24}x^{24} + \\frac{1}{25}x^{25} + \\frac{1}{26}x^{26} + \\frac{1}{27}x^{27} + \\frac{1}{28}x^{28} + \\frac{1}{29}x^{29} + \\frac{1}{30}x^{30} + \\frac{1}{31}x^{31} + \\frac{1}{32}x^{32} + \\frac{1}{33}x^{33} + \\frac{1}{34}x^{34} + \\frac{1}{35}x^{35} + \\frac{1}{36}x^{36} + \\frac{1}{37}x^{37} + \\frac{1}{38}x",
|
|
"gt_answers": "\\sqrt { \\frac { 9 } { y } } + \\sqrt { y } = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5340.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ae11a + Ae11b + Ae11c + Ae11d + Ae11e + Ae11f + Ae11g + Ae11h + Ae11i + Ae11j + Ae11k + Ae11l + Ae11m + Ae11n + Ae11o + Ae11p + Ae11q + Ae11r + Ae11s + Ae11t + Ae11u + Ae11v + Ae11w + Ae11x + Ae11y + Ae11z + Ae11aa + Ae11ab + Ae11ac + Ae11ad + Ae11ae + Ae11af + Ae11ag + Ae11ah + Ae11ai + Ae11aj + Ae11ak + Ae11al + Ae11am + Ae11an + Ae11ao + Ae11ap + Ae11aq + Ae11ar + Ae11as + Ae11at + Ae11au + Ae11av + Ae11aw + Ae11ax + Ae11ay + Ae11az + Ae11ba + Ae11bb + Ae11bc + Ae11bd + Ae11be + Ae11bf + Ae11bg + Ae11bh + Ae11bi + Ae11bj + Ae11bk + Ae11bl + Ae11bm + Ae11bn + Ae11bo + Ae11bp + Ae11bq + Ae11br + Ae11bs + Ae11bt + Ae11bu + Ae11bv + Ae11bw + Ae11bx + Ae11by + Ae11bz + Ae11ca + Ae11cb + Ae11cc + Ae11cd + A",
|
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"gt_answers": "\\overrightarrow { A E } / / \\overrightarrow { A T }\n",
|
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"image_path": "./data/HME100K/test_images/test_5342.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\begin{equation}\n\\frac{2(13-8)}{3(24-13)} = \\frac{2(13-8)}{3(24-13)} = \\frac{2(5)}{3(11)} = \\frac{10}{33}\n\\end{equation}\n\nThe formula uses the following operations:\n\n* Multiplication: The first term is multiplied by 2, and the second term is multiplied by 3.\n* Division: The first term is divided by the second term.\n* Subtraction: The first term is subtracted from the second term.\n\nThe result is the final expression, which is the ratio of the first term to the second term.",
|
|
"gt_answers": "\\frac { 2 } { 3 } - \\frac { 1 } { 8 } = \\frac { 1 3 } { 2 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5344.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"DEG + CEF = 180\u00b0.\"",
|
|
"gt_answers": "\\frac { D E } { E G } = \\frac { C E } { E F }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5345.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: V = IR/Rs.",
|
|
"gt_answers": "I = \\frac { U _ { 1 } } { R _ { 1 } } = \\frac { 1 5 V } { 1 0 \\Omega } = 1 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5346.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_6 = \\frac{1}{6} \\left( \\frac{1}{2} \\left( \\frac{1}{3} \\left( \\frac{1}{4} \\left( \\frac{1}{5} \\left( \\frac{1}{6} \\left( \\frac{1}{7} \\left( \\frac{1}{8} \\left( \\frac{1}{9} \\left( \\frac{1}{10} \\left( \\frac{1}{11} \\left( \\frac{1}{12} \\left( \\frac{1}{13} \\left( \\frac{1}{14} \\left( \\frac{1}{15} \\left( \\frac{1}{16} \\left( \\frac{1}{17} \\left( \\frac{1}{18} \\left( \\frac{1}{19} \\left( \\frac{1}{20} \\left( \\frac{1}{21} \\left( \\frac{1}{22} \\left( \\frac{1}{23} \\left( \\frac{1}{24} \\left( \\frac{1}{25} \\left( \\frac{1}{26} \\left( \\frac{1}{27} \\left( \\frac{1}{28} \\left( \\frac{1}{29} \\left( \\frac{1}{30} \\left( \\frac{1}{31} \\left( \\frac{1}{32} \\left( \\frac{1}{33} \\left( \\frac{1}{34} \\left( \\frac{1}{35} \\left( \\frac{1}{36} \\left( \\frac{1}{37} \\left( \\frac{1}{38} \\left( \\frac{1}{39} \\left( \\frac{1}{40} \\left( \\frac{1}{41} \\left( \\frac{1}{42} \\left( \\frac{1}{43} \\left( \\frac{1}{44} \\left( \\frac{1}{45} \\left( \\frac{1",
|
|
"gt_answers": "C ^ { r } _ { 5 } ( \\frac { 1 } { x ^ { 2 } } ) ^ { r } = C _ { 5 } ^ { r } x ^ { - 2 r }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5347.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{1 + \\left(\\frac{1}{2}\\right)^2} = \\frac{1}{3}\n\\end{equation}\n\nThis formula can be simplified further to:\n\n\\begin{equation}\n\\frac{1}{3} = \\frac{1}{1 + \\left(\\frac{1}{2}\\right)^2}\n\\end{equation}\n\nThe equation is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "\\frac { x ^ { 2 } } { 9 } - \\frac { y ^ { 2 } } { 1 6 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5348.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3b^2 - 10b + 10 = 0\\)",
|
|
"gt_answers": "\\vert 3 b - 1 \\vert = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5349.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V = \\frac{I \\cdot R}{M \\cdot C} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot",
|
|
"gt_answers": "V _ { a } = \\frac { m - M } { M + m } V _ { a } = \\frac { 1 } { 9 } V _ { c }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5350.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/2(x + 1) - 1/2(x - 1) = 1/2(x^2 - 2x + 1) - 1/2(x^2 - 2x + 1) = 1/2(x^2 - 2x + 1) - 1/2(x^2 - 2x + 1) = 0.",
|
|
"gt_answers": "\\vert - \\frac { 7 } { 1 6 } \\vert = \\frac { 7 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5351.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(M = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "\\frac { x } { 2 } = \\frac { y } { 3 } = \\frac { z } { 4 } = m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5352.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(P(S_d \\mid S_s) = \\frac{P(S_d \\cap S_s)}{P(S_s)}\\)\n\nThis formula is used to calculate the probability of an event S_d occurring given that another event S_s has already occurred. The numerator represents the probability of both events occurring simultaneously, while the denominator represents the probability of the first event occurring alone.",
|
|
"gt_answers": "b = - 2 c _ { 2 } - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5354.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "- \\frac { \\sqrt { 3 } } { 2 } \\leq \\sin ( 2 x + \\frac { \\pi } { 3 } ) \\leq 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5355.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis is a simple algebraic equation that can be solved using the addition and subtraction operations.",
|
|
"gt_answers": "\\frac { 8 } { 1 2 } = \\frac { 4 } { 4 } = \\frac { 1 } { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5356.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AE + BE = 30m.\"",
|
|
"gt_answers": "A E = A B + B E = 3 0 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5358.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "x + y = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5359.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(b^2 + a^2 = c^2\\)\n\nThis is a quadratic equation, where the variables a, b, and c represent the coefficients of the quadratic polynomial. The equation states that the sum of the squares of the two sides of the equation is equal to the square of the third side.",
|
|
"gt_answers": "b ^ { 2 } > a ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5360.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 8x2 - 6x6 = 12.",
|
|
"gt_answers": "8 ) - ( 2 ) = ( 6 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5361.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula is a quadratic equation, which can be solved using the quadratic formula.",
|
|
"gt_answers": "\\frac { 1 } { 0 . 5 } = \\frac { 2 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5364.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. In this case, the variable is x, and the square of x is x^2. The other variable, y, is also squared, resulting in y^2. The equation is then combined with the equal sign, which states that the two expressions on either side of the equal sign are equal.",
|
|
"gt_answers": "x _ { 2 } = - \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5365.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 9-1/4.",
|
|
"gt_answers": "q = I \\cdot 1 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5366.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "y _ { 2 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5370.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = 2x^2 - 2x + 1\\)",
|
|
"gt_answers": "f ( a _ { n } ) = ( - 2 ) \\times 2 ^ { n - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5371.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 80x20000 = 255x50000.",
|
|
"gt_answers": "- 8 0 x + 2 0 0 0 = - 2 5 0 x + 5 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5372.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(100 - 99 = 1\\)",
|
|
"gt_answers": "= \\frac { 1 } { 1 0 0 } - 1 = - \\frac { 9 9 } { 1 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5373.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{1}{1",
|
|
"gt_answers": "y = \\frac { 8 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5375.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as HCl + NO2 + H2O = HNO3 + Cl2 + H2O.",
|
|
"gt_answers": "H C l + A g N O _ { 3 } = H N O _ { 3 } + A g C I \\downarrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_5376.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a(x) = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "a \\geq \\frac { 1 } { 2 } ( 2 0 0 - 2 a )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5377.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(3x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "B D = O D = \\frac { 1 } { 2 } B D , A C \\bot B D \\angle 4 = \\angle 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5378.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(V = \\frac{F \\cdot mg}{g} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{1000000} \\cdot \\frac{1000}{100000",
|
|
"gt_answers": "V = \\frac { m } { \\rho } = \\frac { 0 . 5 k g } { 1 . 0 \\times 1 0 ^ { 3 } k g / m ^ { 3 } } = 0 . 5 \\times 1 0 ^ { - 3 } k g / m ^ { 3 } .\n",
|
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"image_path": "./data/HME100K/test_images/test_5379.jpg",
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3\\cos(30^\\circ) + 2\\cos(60^\\circ) + 3\\cos(90^\\circ) = 10\\)",
|
|
"gt_answers": "\\vert - 3 \\vert - ( 3 - \\pi ) ^ { \\circ } - 2 \\sin 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5380.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"DEZ-DO.DB7\".",
|
|
"gt_answers": "D E ^ { 2 } = D O \\cdot D B\n",
|
|
"image_path": "./data/HME100K/test_images/test_5382.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 15x + 15 = 0\\)",
|
|
"gt_answers": "x = \\frac { \\sqrt { 3 } } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5383.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1110x = 570\u00b0.\"",
|
|
"gt_answers": "1 1 4 ^ { \\circ } \\times \\frac { 1 } { 2 } = 5 7 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5385.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\" in LaTeX format.",
|
|
"gt_answers": "y _ { 4 } = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5386.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 5y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, where the sum of their products is equal to 10.",
|
|
"gt_answers": "S = \\frac { 1 0 } { 9 } x - \\frac { 5 0 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5387.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(JF = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\",
|
|
"gt_answers": "\\downarrow F = \\downarrow P \\overline { S }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5388.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 + 100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 119 + 120 + 12",
|
|
"gt_answers": "\\frac { 1 } { R } = \\frac { 1 } { R _ { 1 } } + \\frac { 1 } { R _ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5389.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as y = 4x^2 - 5x + 10.",
|
|
"gt_answers": "\\frac { y - 1 } { 2 } - \\frac { 4 - 3 x } { 5 } = 2 \\times 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5390.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = \\frac{2x^2 + 3x + 4}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^2 + 2x + 3}{x^2 + 2x + 3} \\cdot \\frac{x^",
|
|
"gt_answers": "y = \\frac { 1 } { 2 } ( x ^ { 2 } - 2 x - 3 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5391.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\",
|
|
"gt_answers": "\\frac { E C } { C F } = \\frac { C B } { C A } = \\frac { A C } { C E }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5392.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 48y^2 = 1000\\)",
|
|
"gt_answers": "4 \\sqrt { 3 } \\times 4 \\sqrt { 3 } = 4 8 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5393.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\na^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 + h^2 + i^2 + j^2 + k^2 + l^2 + m^2 + n^2 + o^2 + p^2 + q^2 + r^2 + s^2 + t^2 + u^2 + v^2 + w^2 + x^2 + y^2 + z^2 = 100\n\\end{aligned}\n\\end{equation}\n\nThis formula represents the sum of the squares of the first 20 natural numbers, which is equal to 100.",
|
|
"gt_answers": "( a - b ) ^ { 2 } + 2 a b = a ^ { 2 } + b ^ { 2 } = 1 3 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_5394.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 100\\)",
|
|
"gt_answers": "p ( x = 2 ) = C _ { 3 } ^ { 2 } ( \\frac { 1 } { 5 } ) ^ { 2 } ( \\frac { 4 } { 5 } ) = \\frac { 1 2 } { 1 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5395.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"AC=12\".",
|
|
"gt_answers": "A C = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5396.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "C O = \\sqrt { A O ^ { 2 } - A C ^ { 2 } } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5397.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "( x - y ) ( x ^ { 2 } + x y + y ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5398.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\vert y = 3 \\vert y = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5399.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( x _ { 1 } - x _ { 2 } ) ^ { 2 } = ( x _ { 1 } + x _ { 2 } ) ^ { 2 } - 4 x _ { 1 } x _ { 2 } = ( 2 \\sqrt { 2 } ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5400.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 3(2x + 1) + 4(x + 1) = 12x + 16.",
|
|
"gt_answers": "7 3 x < 2 x + 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5401.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "a + b = 4 , a b = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5402.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 17 - 2 = 19.",
|
|
"gt_answers": "x > - \\frac { 1 9 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5403.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5x + 3 = 13.",
|
|
"gt_answers": "0 . 4 : \\frac { 3 } { 5 } = x : 1 \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5404.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
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"gt_answers": "\\cdot D E \\bot B E , D F \\bot A B\n",
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"image_path": "./data/HME100K/test_images/test_5405.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as: V1 = 3sh.",
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"gt_answers": "V = \\frac { 1 } { 3 } s h\n",
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"image_path": "./data/HME100K/test_images/test_5406.jpg",
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"model_name": "mPLUG"
|
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},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as follows:\n\n\\(81 \\cdot 10^{10} + 81 \\cdot 10^{11} + 81 \\cdot 10^{12} + 81 \\cdot 10^{13} + 81 \\cdot 10^{14} + 81 \\cdot 10^{15} + 81 \\cdot 10^{16} + 81 \\cdot 10^{17} + 81 \\cdot 10^{18} + 81 \\cdot 10^{19} + 81 \\cdot 10^{20} + 81 \\cdot 10^{21} + 81 \\cdot 10^{22} + 81 \\cdot 10^{23} + 81 \\cdot 10^{24} + 81 \\cdot 10^{25} + 81 \\cdot 10^{26} + 81 \\cdot 10^{27} + 81 \\cdot 10^{28} + 81 \\cdot 10^{29} + 81 \\cdot 10^{30} + 81 \\cdot 10^{31} + 81 \\cdot 10^{32} + 81 \\cdot 10^{33} + 81 \\cdot 10^{34} + 81 \\cdot 10^{35} + 81 \\cdot 10^{36} + 81 \\cdot 10^{37} + 81 \\cdot 10^{38} + 81 \\cdot 10^{39} + 81 \\cdot 10^{40} + 81 \\cdot 10^{41} + 81 \\cdot 10^{42} + 81 \\cdot 10^{43} + 81 \\cdot 10^{44} + 81 \\cdot 10^{45} + 81 \\cdot 10^{46} + 81 \\cdot 10^{47} + ",
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"gt_answers": "1 6 8 \\div 3 2 0 = \\frac { 1 6 8 } { 3 2 0 } = \\frac { 2 1 } { 4 0 }\n",
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"image_path": "./data/HME100K/test_images/test_5407.jpg",
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"model_name": "mPLUG"
|
|
},
|
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{
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|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1",
|
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"gt_answers": "S _ { \\Delta A O B } = \\vert S _ { \\Delta } O A D - S _ { \\Delta } O B D \\vert = \\frac { 1 } { 2 } ( x _ { 1 } - x _ { 2 } ) =\n",
|
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"image_path": "./data/HME100K/test_images/test_5408.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
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{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written as \"DL = 2 - B2.\"",
|
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"gt_answers": "\\frac { D E } { B C } = 2\n",
|
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"image_path": "./data/HME100K/test_images/test_5409.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"b^2 - 4ac = 0.\"",
|
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"gt_answers": "x = \\frac { 6 } { 9 }\n",
|
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"image_path": "./data/HME100K/test_images/test_5410.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
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{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x _ { 1 } = \\frac { \\sqrt { 5 } - 1 } { 2 } x _ { 2 } = \\frac { - \\sqrt { 5 } - 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5412.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{a(x^2 + bx + c)}{b^2 + cx + d}\\)\n\nThe variables a, b, c, and d are represented by the letters x, y, z, and w respectively.",
|
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"gt_answers": "( a + b ) \\times c = a \\times c + b \\times c\n",
|
|
"image_path": "./data/HME100K/test_images/test_5413.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x^2 + 3x - 4 = 0`.",
|
|
"gt_answers": "x + 2 = \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5414.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A) \\cdot P(B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(",
|
|
"gt_answers": "G E / / A B , P F / / A B\n",
|
|
"image_path": "./data/HME100K/test_images/test_5415.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2} + 3x + 5\\)",
|
|
"gt_answers": "y _ { 2 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5416.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.",
|
|
"gt_answers": "2 a - 2 b = 2 ( a - b )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5417.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(10 \\times 0.5 + 3 \\times 0.25 = 15.0 + 6.0 = 21.0\\)",
|
|
"gt_answers": "\\frac { 4 0 0 0 } { x } - \\frac { 4 0 0 0 } { 1 . 2 5 x } = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5419.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\text{ABDMN} &= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&= \\text{ANDM} + \\text{MA-1} \\\\\n&=",
|
|
"gt_answers": "\\frac { A ^ { \\prime } B } { A ^ { \\prime } N } \\cdot \\frac { D M } { M A ^ { \\prime } } = \\frac { D M } { M A } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5421.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "P A = B A - P B = 5 - \\frac { 2 5 } { 9 } = \\frac { 2 0 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5422.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nP(A \\land B) &= P(A) \\cdot P(B) \\\\\n&= 0.25 \\cdot 0.5 = 0.125\n\\end{aligned}\n\\end{equation}\n\nThe formula is a simple multiplication of the probabilities of events A and B, which are 0.25 and 0.5, respectively. The result is the probability of both events occurring, which is 0.125.",
|
|
"gt_answers": "P _ { 1 } = \\frac { 3 + \\sqrt { 1 3 } } { 2 } \\cdot P _ { 2 } = \\frac { 3 - \\sqrt { 1 3 } } { 2 } \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_5423.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\na^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 + h^2 + i^2 + j^2 + k^2 + l^2 + m^2 + n^2 + o^2 + p^2 + q^2 + r^2 + s^2 + t^2 + u^2 + v^2 + w^2 + x^2 + y^2 + z^2 = 100\n\\end{aligned}\n\\end{equation}\n\nThis formula represents the sum of the squares of the first 20 natural numbers, which is equal to 100.",
|
|
"gt_answers": "a ^ { 2 } + b ^ { 2 } < c ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5424.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "\\frac { x ^ { 2 } } { 2 } + y ^ { 2 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5425.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in Chinese.",
|
|
"gt_answers": "\\frac { 3 } { 4 } + ( 2 . 5 - \\frac { 1 } { 4 } ) + \\frac { 5 } { 1 2 } \\div 0 . 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5426.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x4 + 4x2 = 12\".",
|
|
"gt_answers": "S _ { \\Delta } C B D = 3 \\times 4 \\div 2 = 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_5427.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Lakhs = LEGGG60.\"",
|
|
"gt_answers": "\\angle A K H = \\angle E K G = 6 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5428.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\n\\(C_x = \\frac{1}{2} \\left(C_y + C_z\\right) + \\frac{1}{2} \\left(C_y - C_z\\right) + \\frac{1}{2} \\left(C_z - C_y\\right) + \\frac{1}{2} \\left(C_x - C_y\\right) + \\frac{1}{2} \\left(C_x - C_z\\right) + \\frac{1}{2} \\left(C_y - C_z\\right) + \\frac{1}{2} \\left(C_x - C_y\\right) + \\frac{1}{2} \\left(C_x - C_z\\right) + \\frac{1}{2} \\left(C_y - C_z\\right) + \\frac{1}{2} \\left(C_x - C_y\\right) + \\frac{1}{2} \\left(C_x - C_z\\right) + \\frac{1}{2} \\left(C_y - C_z\\right) + \\frac{1}{2} \\left(C_x - C_y\\right) + \\frac{1}{2} \\left(C_x - C_z\\right) + \\frac{1}{2} \\left(C_y - C_z\\right) + \\frac{1}{2} \\left(C_x - C_y\\right) + \\frac{1}{2} \\left(C_x - C_z\\right) + \\frac{1}{2} \\left(C_y - C_z\\right) + \\frac{1}{2} \\left(C_x - C_y\\right) + \\frac{1}{2} \\left(C_x - C_z\\right) + \\frac{1}{2} \\left(C_y - C_z\\right) + \\frac{1}{2} \\left(C_x - C_y\\right) + \\frac{1}{2} \\left(C_x - C_z\\right) + \\frac{1}{2} \\",
|
|
"gt_answers": "( x - \\frac { a } { 2 } ) ^ { 2 } + ( y - \\frac { b } { 2 } ) ^ { 2 } = \\frac { a ^ { 2 } } { 4 } + \\frac { b ^ { 2 } } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5429.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "y ^ { 2 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5430.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x2 + 2x1 = 12.",
|
|
"gt_answers": "1 2 \\times \\frac { 3 } { 8 } = \\frac { 9 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5431.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 4xy\\)",
|
|
"gt_answers": "- 4 \\times 3 = \\sqrt { 1 0 } \\times 4 = - \\sqrt { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5432.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(a^2 + b^2 - 2ab = (a + b)^2 - 2ab\\)",
|
|
"gt_answers": "- \\frac { 1 } { 2 } x - a = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5433.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Lead (Cd) + Cadmium (Cd) = 60%.\"",
|
|
"gt_answers": "\\angle E A D = \\angle A D F = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5434.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(x + 1) - 3(x - 2) = 0.",
|
|
"gt_answers": "y _ { 3 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5435.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/5 = 0.2.",
|
|
"gt_answers": "l y _ { 1 } = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5436.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V = \\frac{2\\pi R^2}{3} \\cdot \\left( \\frac{I}{m} \\right)^2 \\cdot \\left( \\frac{L}{2} \\right)^3 \\cdot \\left( \\frac{T}{2} \\right)^4 \\cdot \\left( \\frac{P}{2} \\right)^5 \\cdot \\left( \\frac{N}{2} \\right)^6 \\cdot \\left( \\frac{D}{2} \\right)^7 \\cdot \\left( \\frac{E}{2} \\right)^8 \\cdot \\left( \\frac{F}{2} \\right)^9 \\cdot \\left( \\frac{G}{2} \\right)^{10} \\cdot \\left( \\frac{H}{2} \\right)^{11} \\cdot \\left( \\frac{I}{2} \\right)^{12} \\cdot \\left( \\frac{J}{2} \\right)^{13} \\cdot \\left( \\frac{K}{2} \\right)^{14} \\cdot \\left( \\frac{L}{2} \\right)^{15} \\cdot \\left( \\frac{M}{2} \\right)^{16} \\cdot \\left( \\frac{N}{2} \\right)^{17} \\cdot \\left( \\frac{O}{2} \\right)^{18} \\cdot \\left( \\frac{P}{2} \\right)^{19} \\cdot \\left( \\frac{Q}{2} \\right)^{20} \\cdot \\left( \\frac{R}{2} \\right)^{21} \\cdot \\left( \\frac{S}{2} \\right)^{22} \\cdot \\left( \\frac{T}{2} \\right)^{23} \\cdot \\left( \\frac{U}{2} \\right)^{24} \\cdot \\left( \\frac{V}{2} \\right)^{25} \\cdot \\left( \\frac{W}{2} \\right)^{26} \\cdot \\left( \\frac{X}{2} \\right)^{27} \\cdot \\left( \\frac{Y}{2} \\right)^{28} \\cdot \\left( \\frac{Z}{",
|
|
"gt_answers": "\\frac { V } { V _ { m } } = \\frac { 1 0 . 0 8 L } { 2 2 . 4 2 / m o l } \\approx 0 . 4 5 m o l\n",
|
|
"image_path": "./data/HME100K/test_images/test_5438.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as y = 2x + 4.",
|
|
"gt_answers": "y = \\frac { 9 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5441.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the formula notation, which is a mathematical notation that represents a mathematical relationship between variables. The formula is written as RL = 12V - 12V/120000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "R _ { 2 } = \\frac { 1 2 V } { 1 A } = 1 2 \\Omega\n",
|
|
"image_path": "./data/HME100K/test_images/test_5442.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2}\\)",
|
|
"gt_answers": "y = \\frac { 1 7 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5443.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "2 0 x = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5445.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 4y^2 - 5y + 10 = 0.",
|
|
"gt_answers": "1 0 y - 5 y + 5 = 1 0 - 2 y + 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5446.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\frac { x } { x ^ { 2 } - 1 } = \\frac { 7 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5447.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"6x(6-2) = 6x(4) + 6x(-2) = 24 + 6x(-2) = 24 + 12 = 36.\"",
|
|
"gt_answers": "6 \\div 1 . 5 = 4 ( m ) ( 6 + 4 ) \\times 2 = 2 0 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5448.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3000 cm^2 = 3000 m^2\".",
|
|
"gt_answers": "3 0 m = 3 0 0 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5449.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(R = \\frac{1}{1 + \\left( \\frac{1}{2} \\right)^2} \\left( \\frac{1}{2} \\right)^2 = \\frac{1}{4} \\left( \\frac{1}{2} \\right)^4\\)",
|
|
"gt_answers": "I = I _ { 1 } + I _ { x } = 0 . 3 A + 0 . 6 A = 0 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5450.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 4\\)",
|
|
"gt_answers": "y _ { 1 } = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5451.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(A = 0.8 \\times 10^{8} \\times 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "A G = 0 . 8 \\times 1 . 2 = 0 . 9 6 \\approx 1 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5452.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 2 k - 1 } { 5 } \\leq \\frac { k + 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5453.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as:\n\n\\(a \\cdot c \\cdot s \\cdot n = a \\cdot c \\cdot sin(n) \\cdot n\\)\n\nThe formula is written in LaTeX format, with the variables a, c, s, and n enclosed in parentheses. The asterisk (*) is used to denote multiplication, and the sine function is written using the sin() function.",
|
|
"gt_answers": "a = \\frac { c \\sin A } { \\sin C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5454.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5.\"",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5456.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{26} \\times 3^{10} \\times 5^{3} \\times 7^{2} \\times 11^{1} \\times 13^{0} \\times 17^{1} \\times 19^{0} \\times 23^{1} \\times 29^{0} \\times 31^{1} \\times 37^{0} \\times 41^{1} \\times 43^{0} \\times 47^{1} \\times 53^{0} \\times 59^{1} \\times 65^{0} \\times 71^{1} \\times 77^{0} \\times 83^{1} \\times 89^{0} \\times 97^{1} \\times 103^{0} \\times 109^{1} \\times 115^{0} \\times 121^{1} \\times 127^{0} \\times 133^{1} \\times 139^{0} \\times 145^{1} \\times 151^{0} \\times 157^{1} \\times 163^{0} \\times 169^{1} \\times 175^{0} \\times 181^{1} \\times 187^{0} \\times 193^{1} \\times 199^{0} \\times 205^{1} \\times 211^{0} \\times 217^{1} \\times 223^{0} \\times 229^{1} \\times 235^{0} \\times 241^{1} \\times 247^{0} \\times 253^{1} \\times 259^{0} \\times 265^{1} \\times 271^{0} \\times 277^{1} \\times 283^{0} \\times 289^{1} \\times 295^{0} \\times 301^{1} \\times 307^{0}",
|
|
"gt_answers": "2 5 6 + 3 2 y + y ^ { 2 } + y ^ { 2 } - 1 0 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5458.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "( 4 k ^ { 2 } + 1 ) x ^ { 2 } + 8 \\sqrt { 3 } k ^ { 2 } x + 1 2 k ^ { 2 } - 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5459.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = mx + b\\)\n\nThis formula represents a linear equation, where y is the dependent variable, m is the slope, and b is the y-intercept.",
|
|
"gt_answers": "m ^ { 2 } y ^ { 2 } + 1 + 2 m y + 4 y ^ { 2 } - 4 = 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5462.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x + 17 = 19.\"",
|
|
"gt_answers": "x = \\frac { 5 } { 1 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5463.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as AC-JA+OC2.",
|
|
"gt_answers": "A C = \\sqrt { O A ^ { 2 } + D C ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5465.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "y _ { 3 } = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5466.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(10^{2} - 10^{1} + 10^{0} = 100\\)",
|
|
"gt_answers": "\\frac { 3 } { 1 0 } + \\frac { 1 } { 1 0 } = \\frac { 4 } { 1 0 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5467.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x + 1\\)",
|
|
"gt_answers": "( y - 1 5 ) ( y + 1 ) \\geq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5468.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as PG(110,10) = 110.",
|
|
"gt_answers": "P _ { 4 } ( . - 1 , 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5469.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis is a linear equation in two variables, where the variables are x and y. The equation states that the sum of the products of x and y is equal to 10.",
|
|
"gt_answers": "\\div \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5470.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 1/5x + 1/2.",
|
|
"gt_answers": "y = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5471.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1.6x300 = 450 cm^2.",
|
|
"gt_answers": "1 . 5 \\times 3 0 0 = 4 5 0 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5472.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n(0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
|
|
"gt_answers": "( 7 0 - y ) \\div 2 = 5 y\n",
|
|
"image_path": "./data/HME100K/test_images/test_5473.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a2 + b2 = c2.",
|
|
"gt_answers": "A O = \\frac { \\sqrt { 3 } } { 2 } a\n",
|
|
"image_path": "./data/HME100K/test_images/test_5474.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LFEC = 20\u00b0\".",
|
|
"gt_answers": "\\angle F E C = 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5476.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{x^2}{2} + 1\\)",
|
|
"gt_answers": "\\frac { 1 } { x - y } = v\n",
|
|
"image_path": "./data/HME100K/test_images/test_5477.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `LCAD + L3 = 180\u00b0`.",
|
|
"gt_answers": "\\angle C A D + \\angle 3 = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5478.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given by:\n\n\\(a^2 + b^2 - 2ab + c^2 = (a + b)^2 - 2ab + c^2\\)",
|
|
"gt_answers": "\\frac { - 2 - a } { 3 } - \\frac { ( - 1 ) - a } { 2 } = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5479.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which are not supported by LaTeX. However, I can provide a rough translation of the formula into English:\n\n\"The sum of the squares of the first 100 natural numbers plus the square of the sum of the first 100 natural numbers.\"",
|
|
"gt_answers": "\\overrightarrow { B N } = \\frac { 1 } { 2 } \\overrightarrow { A D } = \\frac { 1 } { 2 } \\overrightarrow { b } + D \\overrightarrow { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5480.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(3x + 1) - 3x - 1.",
|
|
"gt_answers": "- \\frac { 8 } { 3 } = \\frac { 4 } { 3 } + m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5481.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(V = \\frac{I \\cdot R}{2 \\cdot \\pi \\cdot f}\\)\n\nwhere:\n\n* V is the voltage (V)\n* I is the current (A)\n* R is the resistance (ohms)\n* f is the frequency (Hz)\n\nThis formula relates the voltage, current, resistance, and frequency of an alternating current (AC) circuit.",
|
|
"gt_answers": "S = v t = 1 5 0 0 m / s \\times 6 s = 9 0 0 0 m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5483.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(j_{a} = \\frac{1}{2} \\left( \\frac{1}{r_{a}} + \\frac{1}{r_{b}} \\right) \\left( \\frac{1}{r_{c}} + \\frac{1}{r_{d}} \\right) \\left( \\frac{1}{r_{e}} + \\frac{1}{r_{f}} \\right) \\left( \\frac{1}{r_{g}} + \\frac{1}{r_{h}} \\right) \\left( \\frac{1}{r_{i}} + \\frac{1}{r_{j}} \\right) \\left( \\frac{1}{r_{k}} + \\frac{1}{r_{l}} \\right) \\left( \\frac{1}{r_{m}} + \\frac{1}{r_{n}} \\right) \\left( \\frac{1}{r_{o}} + \\frac{1}{r_{p}} \\right) \\left( \\frac{1}{r_{q}} + \\frac{1}{r_{r}} \\right) \\left( \\frac{1}{r_{s}} + \\frac{1}{r_{t}} \\right) \\left( \\frac{1}{r_{u}} + \\frac{1}{r_{v}} \\right) \\left( \\frac{1}{r_{w}} + \\frac{1}{r_{x}} \\right) \\left( \\frac{1}{r_{y}} + \\frac{1}{r_{z}} \\right) \\left( \\frac{1}{r_{a}} + \\frac{1}{r_{b}} \\right) \\left( \\frac{1}{r_{c}} + \\frac{1}{r_{d}} \\right) \\left( \\frac{1}{r_{e}} + \\frac{1}{r_{f}} \\right) \\left( \\frac{1}{r_{g}} + \\frac{1}{r_{h}} \\right) \\left( \\frac{1}{r_{i}} + \\frac{1}{r_{j}} \\right) \\left( \\frac{1}{r_{k}} + \\frac{1}{r_{l}} \\right) \\left( \\frac{1",
|
|
"gt_answers": "a ^ { 2 } + b ^ { 2 } \\geq 2 a b = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5485.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 6 } { 3 - 2 } + \\frac { m } { 3 - 2 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5486.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(x^2 + 40x - 30y = 0\\)\n\nThis formula can be written using LaTeX as follows:\n\n\\(x^2 + 40x - 30y = 0\\)",
|
|
"gt_answers": "\\frac { 4 0 } { 3 0 } - \\frac { 2 1 } { 3 0 } = x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5487.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 4x + 3 = 0\\)",
|
|
"gt_answers": "x - \\frac { 3 } { 4 } = \\pm \\frac { \\sqrt { 3 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5489.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 2x + 40 = 0`.",
|
|
"gt_answers": "x = \\sqrt { 5 0 4 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5490.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 1.5x(1.25x-1.5) = 4.",
|
|
"gt_answers": "0 . 7 5 x - 1 . 2 5 x = 1 + \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5491.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: F = 1/2 * G * M * R^2.",
|
|
"gt_answers": "F = F _ { 1 } - F _ { 2 } = \\frac { 7 G M m } { 3 6 R ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5492.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\right) = \\frac{1}{4} \\).",
|
|
"gt_answers": "x ^ { - } = \\pm \\sqrt { \\frac { 2 } { a - 1 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5494.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"coef(3DEW3) = 1/2.\"",
|
|
"gt_answers": "C _ { \\Delta E D F } = 3 D E = 6 \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5495.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"O = 2x + 3f + 4g + 5h + 6i + 7j + 8k + 9l + 10m + 11n + 12o + 13p + 14q + 15r + 16s + 17t + 18u + 19v + 20w + 21x + 22y + 23z + 24a + 25b + 26c + 27d + 28e + 29f + 30g + 31h + 32i + 33j + 34k + 35l + 36m + 37n + 38o + 39p + 40q + 41r + 42s + 43t + 44u + 45v + 46w + 47x + 48y + 49z + 50a + 51b + 52c + 53d + 54e + 55f + 56g + 57h + 58i + 59j + 60k + 61l + 62m + 63n + 64o + 65p + 66q + 67r + 68s + 69t + 70u + 71v + 72w + 73x + 74y + 75z + 76a + 77b + 78c + 79d + 80e + 81f + 82g + 83h + 84i + 85j + 86k + 87l + 88m + 89n + 90o + 91p + 92q + 93r + 94s + 95t + 96u + 97v + 98w + 99x + 100y + 101z + 102a +",
|
|
"gt_answers": "\\sqrt { 2 x - 1 } \\geq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5496.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: LAB = 160\u00b0 - 30\u00b0 = 130\u00b0.",
|
|
"gt_answers": "\\angle A C B = \\angle A B C = \\frac { 1 8 0 ^ { \\circ } - 3 0 ^ { \\circ } } { 2 } = 7 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5497.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x^2 + 3x - 4 = 0.\"",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\angle B A C + \\frac { 1 } { 2 } \\angle A C D = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5498.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(2x + 3y = 10\\)\n\nThis is a simple equation that involves two variables, x and y, and a constant, 10. The equation states that the sum of the two variables is equal to 10.",
|
|
"gt_answers": "x _ { 1 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5499.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2 + d^2\\)\n\nThis formula is a Pythagorean theorem, which states that the sum of the squares of the lengths of two sides of a right triangle is equal to the square of the length of the third side. In this case, the three sides are represented by the variables a, b, and c, and the length of the third side is represented by d.",
|
|
"gt_answers": "b = \\frac { a \\sin B } { \\sin A } = \\sqrt { 3 } + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5500.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{3}{2} \\cdot \\frac{2}{3} \\cdot \\frac{1}{4} = \\frac{3}{8} \\cdot \\frac{2}{6} \\cdot \\frac{1}{4} = \\frac{3}{16} \\cdot \\frac{2}{12} \\cdot \\frac{1}{4} = \\frac{3}{48} \\cdot \\frac{2}{24} \\cdot \\frac{1}{4} = \\frac{3}{192} \\cdot \\frac{2}{120} \\cdot \\frac{1}{4} = \\frac{3}{768} \\cdot \\frac{2}{240} \\cdot \\frac{1}{4} = \\frac{3}{2880} \\cdot \\frac{2}{1200} \\cdot \\frac{1}{4} = \\frac{3}{17280} \\cdot \\frac{2}{12000} \\cdot \\frac{1}{4} = \\frac{3}{345600} \\cdot \\frac{2}{120000} \\cdot \\frac{1}{4} = \\frac{3}{3456000} \\cdot \\frac{2}{1200000} \\cdot \\frac{1}{4} = \\frac{3}{345600000} \\cdot \\frac{2}{120000000} \\cdot \\frac{1}{4} = \\frac{3}{34560000000} \\cdot \\frac{2}{12000000000} \\cdot \\frac{1}{4} = \\frac{3}{34560000000000} \\cdot \\frac{2}{12000000000000} \\cdot \\frac{1}{4} = \\frac{3}{345600000000000000} \\cdot \\frac{2}{12000000000",
|
|
"gt_answers": "x _ { 1 } = \\frac { 2 } { 5 } x _ { 2 } = \\frac { 3 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5501.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis is a simple algebraic equation that represents the relationship between two variables, x and y, and a constant, 10. The equation states that the sum of the products of x and y is equal to 10.",
|
|
"gt_answers": "c = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5502.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "y = - \\frac { 1 9 2 } { 3 5 } x + \\frac { 1 2 5 } { 7 } ( \\frac { 6 2 5 } { 2 3 4 } < x < \\frac { 2 5 } { 6 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5504.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "a + b = \\pm\n",
|
|
"image_path": "./data/HME100K/test_images/test_5505.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a negative sign, which can be represented in LaTeX as follows:\n\n\\(x = -1\\)",
|
|
"gt_answers": "x = \\frac { b } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5507.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x = \\frac { - 6 \\pm \\sqrt { b ^ { 2 } - 4 a c } } { 2 a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5508.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "5 0 0 0 0 0 \\times \\frac { 1 } { 1 0 0 0 } = 5 0 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5509.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a mathematical formula using LaTeX. The formula is:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": ": a = 4 b : 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_5511.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x + y = 2.\"",
|
|
"gt_answers": "x 1 = \\frac { 1 } { 2 } \\sqrt { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5512.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 9(x - 49) = 49(x - 9).",
|
|
"gt_answers": "g ^ { \\prime } = \\frac { 4 } { 9 } g\n",
|
|
"image_path": "./data/HME100K/test_images/test_5513.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(E = \\frac{F \\cdot B}{2} \\cdot \\cos \\theta\\)\n\nwhere E is the electric field strength, F is the force acting on the charge, B is the magnetic field strength, and \u03b8 is the angle between the electric and magnetic fields.",
|
|
"gt_answers": "\\angle E O B = \\frac { 1 } { 2 } \\angle A O B = 2 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5514.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as `x^2 + 3x + 2 = 0`.",
|
|
"gt_answers": "x = \\frac { 8 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5515.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x + 3 = 5.",
|
|
"gt_answers": "\\frac { 1 } { 5 } = \\frac { 1 \\times 4 } { 5 \\times 4 } = \\frac { 4 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5516.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Cota-4\" using LaTeX format.",
|
|
"gt_answers": "\\cot A = \\frac { 7 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5517.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 4x + 4 = 0\\)",
|
|
"gt_answers": "2 x = 4 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5518.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { ( 1 . 7 - 2 x ) \\times 1 0 } { 0 . 3 \\times 1 0 } = \\frac { x \\times 1 0 } { 0 . 7 \\times 1 0 } - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5519.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"33N + 39N = 72N.\"",
|
|
"gt_answers": "5 0 N l _ { 1 } = 3 0 N l _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5520.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = a^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "x _ { 1 } = \\frac { \\sqrt { a } } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5522.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 5x^2 - 3x + 1.",
|
|
"gt_answers": "y = - \\frac { 1 } { 5 } x ^ { 2 } + \\frac { 8 } { 5 } x - 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5523.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: y = 2x^2 - 4x + 2.",
|
|
"gt_answers": "y _ { 3 } = 2 , y _ { 4 } = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5524.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(m = \\frac{1}{2}mv^2 + mgx\\)\n\nwhere m is the mass of the object, v is its velocity, g is the gravitational constant, and x is the displacement of the object from its initial position.",
|
|
"gt_answers": "m ^ { 2 } + 1 = 2 m = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5525.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 9\\)",
|
|
"gt_answers": "x ^ { 2 } + 2 + \\frac { 1 } { x ^ { 2 } } = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5527.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so I cannot provide a LaTeX representation of it. However, the image shows a mathematical formula with a negative sign, which is typically written as a minus sign (-).",
|
|
"gt_answers": "x = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5528.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(P = \\frac{V^2}{2g}\\)\n\nThis formula relates pressure (P) to volume (V) and the acceleration due to gravity (g).",
|
|
"gt_answers": "v = \\frac { m } { \\rho } = \\frac { 2 k g } { 1 \\times 1 0 ^ { 3 } k g / m ^ { 3 } } = 2 \\times 1 0 ^ { - 3 } m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5529.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 13x + 20 = 30.",
|
|
"gt_answers": "x = \\frac { 2 0 } { 1 3 } - 1 3 x = - 2 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5530.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x _ { 3 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5531.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nNaCl + CO2 + H2O --> NaHCO3 + H2",
|
|
"gt_answers": "N a _ { 2 } C O _ { 3 } + H _ { 2 } S O _ { 4 } = N a _ { 2 } C O _ { 3 } + H _ { 2 } O + C O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_5532.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. In this case, the variable is x, and the square of x is x^2. The variable y is also involved in the equation, and its square is y^2. The equation states that the sum of the squares of these two variables is equal to 1.",
|
|
"gt_answers": "y _ { 4 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5533.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle A O C = 3 6 0 ^ { \\circ } - 1 5 0 ^ { \\circ } - 1 2 0 ^ { \\circ } = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5536.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\right) = \\frac{1}{4} \\).",
|
|
"gt_answers": "D E \\bot A C\n",
|
|
"image_path": "./data/HME100K/test_images/test_5537.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 6x^2 + 6z^2.",
|
|
"gt_answers": "y = 6 \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5538.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\frac { B E } { A D } = \\frac { E M } { A M } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5540.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(LB - 90) + 90 = 180.",
|
|
"gt_answers": "\\angle D = \\angle B = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5541.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(A + B - AC = AD\\)\n\nThis formula can be represented using the following LaTeX code:\n\n\\(A + B - AC = AD\\)\n\nThe formula is a simple algebraic equation that shows the relationship between the three variables A, B, and C. It states that the sum of A and B is equal to the difference between A and C, and the difference between B and C is equal to the sum of A and C.",
|
|
"gt_answers": "\\frac { A B } { A O } = \\frac { A D } { A C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5542.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows: \"mg = 1/2mv^2\".",
|
|
"gt_answers": "m g R = \\frac { 1 } { 2 } m V _ { 3 } ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5543.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/2(10 + 5) = 5.",
|
|
"gt_answers": "\\frac { 1 } { 1 0 } + \\frac { 2 } { 5 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5544.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows: `00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "( 4 0 + x - 3 0 ) ( 6 0 0 - 1 0 x ) = 1 0 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5545.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"5x + 1 = 10.\"",
|
|
"gt_answers": "x + y ^ { 1 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5546.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(4a^2 + 4b^2 - 4c^2 - 4d^2 = 0\\)\n\nThis is a quadratic equation in four variables, where a, b, c, and d are the unknowns.",
|
|
"gt_answers": "4 a ^ { 2 } - 4 \\times 2 ( a ^ { 2 } - 1 ) \\geq o\n",
|
|
"image_path": "./data/HME100K/test_images/test_5549.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "y = - \\frac { 1 } { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5550.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a + b = 4\\)\n\nThis formula represents the addition of two numbers, a and b, and the result is equal to 4.",
|
|
"gt_answers": "a = - \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5551.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"200 + 299 = 500.\"",
|
|
"gt_answers": "2 0 0 + 3 0 + 6 0 + 9 = 2 9 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5552.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(2x^2 + 3x + 4 = 5x^2 + 6x + 7\\)",
|
|
"gt_answers": "\\vert A B \\vert = \\sqrt { 1 + t ^ { 2 } } \\vert x _ { 1 } - x _ { 2 } \\vert = \\sqrt { 1 + t ^ { 2 } } \\cdot \\sqrt { ( x _ { 1 } + x _ { 2 } ) ^ { 2 } - 4 x _ { 1 } x _ { 2 } } = 2 ( t ^ { 2 } + 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5554.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 4x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 3 9 } { 2 8 } \\times \\frac { 4 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5556.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x ( x - a ) - 3 ( x - 1 ) = x ( x - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5557.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"PDF = DIC\" using LaTeX format.",
|
|
"gt_answers": "D _ { 1 } F = \\frac { 1 } { 2 } D _ { 1 } C\n",
|
|
"image_path": "./data/HME100K/test_images/test_5558.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(tan(x) = \\frac{sin(x)}{cos(x)}\\)",
|
|
"gt_answers": "\\tan C = \\frac { A F } { C F } = \\frac { B F } { C F } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5559.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 6/3 + 20/10 + 3/2.",
|
|
"gt_answers": "\\frac { 6 } { 2 0 } = \\frac { 6 \\div 2 } { 2 0 \\div 2 } = \\frac { 3 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5560.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(N = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) + \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{2} \\right) \\right) = \\frac{1}{4} + \\frac{1}{4} = \\frac{3}{4}\\)",
|
|
"gt_answers": "1 6 X ^ { 2 } - \\pi x = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5561.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 25\\)",
|
|
"gt_answers": "1 6 0 ^ { \\circ } - a = 2 \\cdot ( 9 0 ^ { \\circ } \\cdot 3 0 ^ { \\circ } ) + 1 6 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5562.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(20x^2 + 20y^2 - 20z^2 = 400\\)",
|
|
"gt_answers": "2 0 x = 2 . 5 - 1 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5563.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in a handwritten format, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a number 13 written in it.",
|
|
"gt_answers": "1 3 \u3001 - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5564.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 15\\)",
|
|
"gt_answers": "\\frac { 1 } { 4 } > \\frac { m } { 3 2 } \\textcircled { 1 } < 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5566.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = kx^2 + bx + c\\)",
|
|
"gt_answers": "l _ { A B } : y = k x + b 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5569.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\",
|
|
"gt_answers": "\\frac { O A } { O C } = \\frac { O C } { O B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5570.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "k _ { 0 A \\cdot } k _ { 1 } = - \\frac { \\sqrt { 3 } } { 2 } \\cdot \\frac { 2 b ^ { 2 } } { \\sqrt { 3 } \\cdot a ^ { 2 } } = \\frac { - b ^ { 2 } } { a ^ { 2 } } = - \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5571.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "1 0 . 1 - \\frac { 3 } { 2 5 } - \\frac { 3 } { 4 } = \\frac { 1 3 } { 1 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5572.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 4x + 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 4 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5573.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x5 = 15.",
|
|
"gt_answers": "\\frac { 3 } { 8 } \\times \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5574.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A + B = C + D\\)\n\nThis formula represents the addition of two numbers, A and B, to produce the sum C + D.",
|
|
"gt_answers": "1 ) \\Delta G = \\Delta H - T \\Delta S < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5576.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as tan(x) = sin(x)/cos(x).",
|
|
"gt_answers": "\\tan \\angle C B A = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5577.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\angle C = 9 0 ^ { \\circ } A D = A D\n",
|
|
"image_path": "./data/HME100K/test_images/test_5578.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + y^2 = 4.\"",
|
|
"gt_answers": "= x ^ { 3 } - 2 c x ^ { 2 } + c ^ { 2 } x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5579.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Soapn = SoAcin + SoPonin.\"",
|
|
"gt_answers": "S _ { \\Delta A P N } = S _ { \\Delta A C N } + S _ { \\Delta D C N }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5580.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 148 + 9 = 99.",
|
|
"gt_answers": "1 + 8 = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5582.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 20x - 100 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x _ { 2 } = \\frac { 1 0 } { 5 } = 2 0 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_5583.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "- 5 < - 2 . 5 < - 0 . 5 < \\frac { 1 } { 2 } < 2 < + 4 . 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5585.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m \\cdot n \\cdot \\sin(b) = m \\cdot n \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot \\sin(b) \\cdot \\cos(b) \\cdot",
|
|
"gt_answers": "S _ { \\Delta } A O B = - \\frac { m } { 3 } + \\frac { n } { 3 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5586.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = \\frac { 1 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5587.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(O_{c6}J_{33}t\\)",
|
|
"gt_answers": "O C = 6 \\sqrt { 1 3 } + y\n",
|
|
"image_path": "./data/HME100K/test_images/test_5589.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 + 123456789 +",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5590.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nMg(OH)2 + H2O = Mg(OH)3 + CO2 + H2",
|
|
"gt_answers": "\\mu g C O _ { 3 } + 2 H C l = \\mu g C l _ { 2 } + H _ { 2 } O + C O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_5591.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 65x9 - 7x19 - 3x39 = 139.",
|
|
"gt_answers": "\\frac { 6 5 } { x } = \\frac { 9 8 } { 1 9 . 6 g } x = 1 3 g\n",
|
|
"image_path": "./data/HME100K/test_images/test_5592.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(33k + 2k^2 = 88\\)",
|
|
"gt_answers": "- \\frac { 3 3 k } { 3 } + \\frac { 2 k } { 3 } = \\frac { 8 8 } { 6 } - \\frac { 6 9 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5593.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the image shows a mathematical formula with a negative sign in front of the expression.",
|
|
"gt_answers": "1 - p = \\pm \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5594.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{",
|
|
"gt_answers": "y = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5595.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\na(a+b) - (a+b) = a(a+b) - a(a+b) = 0",
|
|
"gt_answers": "\\frac { a } { 3 } - \\frac { a } { 3 } + 1 = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5596.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 5x + 6 = 15\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(x^2 + 5x + 6 = 15\\)",
|
|
"gt_answers": "1 . x ^ { 2 } \\cdot C _ { 6 } ^ { 4 } \\cdot + \\frac { 1 } { x ^ { 2 } } \\cdot x ^ { 4 } \\cdot E _ { 6 } ^ { 2 } = 1 5 + 1 5 = 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5597.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 15x + 15 = 0`.",
|
|
"gt_answers": "x = \\frac { 1 5 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5598.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3.21000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 . 2 \\div 1 0 0 = 0 . 0 3 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5599.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\nLBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd + LBd +",
|
|
"gt_answers": "\\angle B O D + \\angle D O C + \\angle B O A = 2 7 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5600.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(S_G = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { 8 a + 2 } { a } = 2 a = - \\frac { 1 } { 5 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_5601.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{a^2}{b^2} + \\frac{a^2}{c^2} + \\frac{a^2}{d^2} + \\frac{b^2}{c^2} + \\frac{b^2}{d^2} + \\frac{c^2}{d^2} = 1\n\\end{aligned}\n\\end{equation}\n\nThis formula represents the sum of the squares of the four sides of a square, where the sides are represented by the variables a, b, c, and d. The equation is equal to 1, which means that the sum of the squares of the sides of a square must always equal the square of the area of the square.",
|
|
"gt_answers": "( 1 ) . f ( x ) = 1 - \\frac { 9 } { x } = \\frac { x - a } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5602.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: `x^2 + 5x + 10 = 0`.",
|
|
"gt_answers": "x ^ { 2 } = \\frac { 5 } { m - 1 . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5603.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 25 km/h = 0.25 m/s.",
|
|
"gt_answers": "t = \\frac { s } { V } = \\frac { 2 5 k m } { 1 0 0 k m / h } = 0 . 2 5 h\n",
|
|
"image_path": "./data/HME100K/test_images/test_5604.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2D + 2D = 4D.",
|
|
"gt_answers": "D H = D G = \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5605.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: 9x9 - 20 = 27.",
|
|
"gt_answers": "\\frac { 1 } { 2 0 } \\times 9 = \\frac { 9 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5606.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n(3x + 4)(x + 180) = 3x^2 + 4x + 480\n\nThis formula can be rearranged to solve for x:\n\nx = (3x + 4)(180) - 480\n\nx = 3x(180) - 480\n\nx = 3x(90) - 480\n\nx = 270 - 480\n\nx = -210",
|
|
"gt_answers": "( 3 x + 1 6 ) ^ { \\circ } + ( 2 x + 1 4 ) ^ { \\circ } = 1 8 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5607.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x + 4 = 5\\)",
|
|
"gt_answers": "x ^ { 2 } = \\frac { 2 2 5 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5608.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "x ^ { 2 } + 4 x ^ { 2 } - 4 x + 1 + 6 x - 3 + x + 1 = 0 5 x ^ { 2 } + 3 x - 1 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5609.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(x + 1) - 4(x - 1) = 14 - 4x.",
|
|
"gt_answers": "k g = 1 3 4 \\times \\frac { 7 } { 2 0 } = 4 6 . 9 k g\n",
|
|
"image_path": "./data/HME100K/test_images/test_5611.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = 3x^2 + 2x + 1\\)",
|
|
"gt_answers": "x = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5612.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(L_{BG} = \\frac{BG}{100} \\cdot 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\angle B A C = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5614.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 245 - 9x30 - 8t7.",
|
|
"gt_answers": "4 5 - \\frac { 9 \\times 3 \\textcircled { < } } { 2 7 } < \\frac { 5 \\times 8 } { 4 0 } ^ { - } 1 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5615.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(n(n-1)(n-2) = n^3 - 3n^2 + 2n\\)",
|
|
"gt_answers": "\\vert n \\vert - 2 = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5616.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(k = \\frac{1}{2} \\pi r^2 \\rho g\\)\n\nwhere:\n\n* `k` is the spring constant,\n* `r` is the radius of the spring,\n* `g` is the gravitational constant, and\n* `\u03c1` is the density of the material the spring is made of.",
|
|
"gt_answers": "k ^ { \\prime } = k ^ { n }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5617.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"p = 5/12.\"",
|
|
"gt_answers": "P = \\frac { 5 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5618.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 423.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
|
|
"gt_answers": "4 2 3 . 9 \\times \\frac { 1 } { 3 } = 1 4 1 . 3 ( d m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5619.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\na^2 + b^2 + c^2 = a^2 + 2ab + b^2 + 2ac + c^2\n\\end{equation}\n\nThis formula is a generalization of the Pythagorean theorem, which states that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the hypotenuse. In this case, the sides of the triangle are represented by the variables a, b, and c, and the hypotenuse is represented by the variable a + b + c.",
|
|
"gt_answers": "a ^ { 2 } - \\frac { a } { b } + 2 + a\n",
|
|
"image_path": "./data/HME100K/test_images/test_5620.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 - 3x + 1 = 0.",
|
|
"gt_answers": "x = \\frac { 1 3 } { 7 - a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5621.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, where the sum of their values is equal to 10.",
|
|
"gt_answers": "\\frac { 1 } { 5 } = \\frac { 2 } { 1 0 } = \\frac { \\cdot 3 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5622.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2v3t - 24.4.",
|
|
"gt_answers": "2 V - 3 + V = 2 4 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5625.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(ADF = EF + DF\\)\n\nThis formula represents the total distance traveled by a vehicle, which is the sum of the distance traveled by the front wheels (EF) and the distance traveled by the rear wheels (DF).",
|
|
"gt_answers": "\\frac { A ^ { \\prime } D } { E C } = \\frac { D F } { F C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5626.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\" in LaTeX format.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5627.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x10^2 + x10^2 = 10^4.\"",
|
|
"gt_answers": "0 . 3 \\times 1 0 0 = 3 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5628.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = \\frac{1}{2}x^2 + 3x + 5\\)",
|
|
"gt_answers": "y = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5629.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x^2 - 5x + 1.",
|
|
"gt_answers": "\\frac { 3 } { 4 } x - \\frac { 1 } { 2 } x = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5630.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"a^2 + b^2 = c^2.\"",
|
|
"gt_answers": "a < 1 \\frac { 1 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5631.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\pi \\cdot r^2 \\cdot \\sin(2\\theta) \\cdot \\cos(2\\theta) \\cdot \\cos(3\\theta) \\cdot \\sin(3\\theta) \\cdot \\cos(4\\theta) \\cdot \\sin(4\\theta) \\cdot \\cos(5\\theta) \\cdot \\sin(5\\theta) \\cdot \\cos(6\\theta) \\cdot \\sin(6\\theta) \\cdot \\cos(7\\theta) \\cdot \\sin(7\\theta) \\cdot \\cos(8\\theta) \\cdot \\sin(8\\theta) \\cdot \\cos(9\\theta) \\cdot \\sin(9\\theta) \\cdot \\cos(10\\theta) \\cdot \\sin(10\\theta) \\cdot \\cos(11\\theta) \\cdot \\sin(11\\theta) \\cdot \\cos(12\\theta) \\cdot \\sin(12\\theta) \\cdot \\cos(13\\theta) \\cdot \\sin(13\\theta) \\cdot \\cos(14\\theta) \\cdot \\sin(14\\theta) \\cdot \\cos(15\\theta) \\cdot \\sin(15\\theta) \\cdot \\cos(16\\theta) \\cdot \\sin(16\\theta) \\cdot \\cos(17\\theta) \\cdot \\sin(17\\theta) \\cdot \\cos(18\\theta) \\cdot \\sin(18\\theta) \\cdot \\cos(19\\theta) \\cdot \\sin(19\\theta) \\cdot \\cos(20\\theta) \\cdot \\sin(20\\theta) \\cdot \\cos(21\\theta) \\cdot \\sin(21\\theta) \\cdot \\cos(22\\theta) \\cdot \\sin(22\\theta) \\cdot \\cos(23\\theta) \\cdot \\sin(23\\theta) \\cdot \\cos(24\\theta) \\cdot \\sin(24\\theta) \\cdot \\cos(25\\theta) \\cdot \\sin(25\\theta) \\cdot \\cos(26\\theta)",
|
|
"gt_answers": "C u S O _ { 4 } + 2 N a O H = N a _ { 2 } S O _ { 4 } + C u l ;\n",
|
|
"image_path": "./data/HME100K/test_images/test_5632.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "2 ( x ^ { 2 } - 4 ) = 2 ( x + 2 ) ( x - 2 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5633.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2.3456789 \\times 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725354028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253540288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535402884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725",
|
|
"gt_answers": "2 . \\frac { 3 } { 8 } : \\frac { 1 } { 4 } = \\frac { 1 } { 2 } : \\frac { 1 } { 3 } 3 . 1 8 : 0 . 2 =\n",
|
|
"image_path": "./data/HME100K/test_images/test_5634.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x4 - 3x3 - 3x2 - 3x1.",
|
|
"gt_answers": "\\cdot : 8 x = 3 \\times \\frac { 9 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5635.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 80 - 6i.",
|
|
"gt_answers": "B D = \\frac { 6 } { \\sqrt { 3 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5636.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 120/240 = 5/6.",
|
|
"gt_answers": "1 2 0 \\div 5 = 2 4 2 8 0 \\times 2 0 = 5 6 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5637.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written as follows:\n\n\\(x^2 + y^2 = d^2\\)\n\nThe formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is represented by the letter \"d,\" and the two sides are represented by the letters \"x\" and \"y.\"",
|
|
"gt_answers": "d d \\times d d\n",
|
|
"image_path": "./data/HME100K/test_images/test_5639.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(P(A \\land B) = P(A) \\cdot P(B) - P(A \\land B) = P(A) \\cdot P(B) - P(A) \\cdot P(B \\land C) + P(A \\land B \\land C) - P(A \\land B \\land C \\land D) + P(A \\land B \\land C \\land D \\land E) - P(A \\land B \\land C \\land D \\land E \\land F) + P(A \\land B \\land C \\land D \\land E \\land F \\land G) - P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H) + P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I) - P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I \\land J) + P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I \\land J \\land K) - P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I \\land J \\land K \\land L) + P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I \\land J \\land K \\land L \\land M) - P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I \\land J \\land K \\land L \\land M \\land N) + P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I \\land J \\land K \\land L \\land M \\land N \\land O) - P(A \\land B \\land C \\land D \\land E \\land F \\land G \\land H \\land I \\land J \\land K \\land L \\land M \\land N \\land O \\land P) + P(A \\land B \\land C \\land D \\land E",
|
|
"gt_answers": "P ( C ) = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5640.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { x - 3 } { 2 } = 2 - \\frac { 3 - x } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5642.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(H_2O + 2H^+ + 2e^- \\rightarrow 2H_2 + O_2\\)",
|
|
"gt_answers": "y _ { 1 } y _ { 2 } = x _ { 1 } + x _ { 2 } + 4 = \\frac { 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5644.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 1.5x2x0.5x4x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x0.625x2x",
|
|
"gt_answers": "1 . 5 \\times 1 . 2 \\times 0 . 4 = 0 . 1 2 ( m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5645.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a_1 + a_2 + a_3 + a_4 = a_1 + a_2 + a_3 + a_4\\)",
|
|
"gt_answers": "\\frac { a _ { 1 } } { a _ { 2 } } = \\frac { b _ { 1 } } { b _ { 2 } } = \\frac { c _ { 1 } } { c _ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5646.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 240 + 40x(26-10) + 5x(26-10)^2 + 6x(26-10)^3 + 7x(26-10)^4 + 8x(26-10)^5 + 9x(26-10)^6 + 10x(26-10)^7 + 11x(26-10)^8 + 12x(26-10)^9 + 13x(26-10)^10 + 14x(26-10)^11 + 15x(26-10)^12 + 16x(26-10)^13 + 17x(26-10)^14 + 18x(26-10)^15 + 19x(26-10)^16 + 20x(26-10)^17 + 21x(26-10)^18 + 22x(26-10)^19 + 23x(26-10)^20 + 24x(26-10)^21 + 25x(26-10)^22 + 26x(26-10)^23 + 27x(26-10)^24 + 28x(26-10)^25 + 29x(26-10)^26 + 30x(26-10)^27 + 31x(26-10)^28 + 32x(26-10)^29 + 33x(26-10)^30 + 34x(26-10)^31 + 35x(26-10)^32 + 36x(26-10)^33 + 37x(26-10)^34 + 38x(26-10)^35 + 39x(26-10)^36 + 40x(26",
|
|
"gt_answers": "2 4 0 + ( 2 4 0 \\times 0 . 5 ) x = ( 2 4 0 0 \\times 0 . 6 ) x + 1 4 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5647.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(a^2 + b^2 + c^2 + d^2 = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^2 + d^2 - 4ac - 4bc - 4ca - 4db) = 4(a^2 + b^2 + c^",
|
|
"gt_answers": "t x _ { 2 } = - 2 a . x _ { 1 } x _ { 2 } = a ^ { 2 } + 4 a - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5648.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(O_2 + 2H_2O \\rightarrow 2H_2O_2\\)",
|
|
"gt_answers": "\\frac { O E } { O O ^ { \\prime } } = \\frac { A E } { O ^ { \\prime } A ^ { \\prime } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5650.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 2x10^2.",
|
|
"gt_answers": "\\frac { 2 } { 3 } x = 1 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5651.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\cos \\alpha = \\cos ( \\pi - 2 \\beta ) = \\cos \\pi \\cos 2 \\beta + \\sin \\pi \\sin 2 \\beta = ( - 1 ) \\times ( 1 - 2 \\times \\frac { 1 6 } { 2 5 } ) + 0 = \\frac { 7 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5652.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x _ { 1 } = 3 x _ { 2 } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5653.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { x - 2 } { x } = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5654.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 69/9 = 30/20.",
|
|
"gt_answers": "\\frac { 6 9 } { 2 0 } = 3 \\frac { 9 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5655.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation. However, the image shows a mathematical formula with a number and a Chinese character, which could be a symbol or a letter.",
|
|
"gt_answers": "\\Rightarrow \\frac { 1 } { y } - \\frac { 1 } { x } = \\frac { 1 } { 3 0 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5656.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3 = C + 2.\"",
|
|
"gt_answers": "3 = c\n",
|
|
"image_path": "./data/HME100K/test_images/test_5657.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3.44 x 10^2.\"",
|
|
"gt_answers": "( 2 , 3 ) = 1 ( 3 , 4 ) = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5658.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(BP = \\frac{P_1 + P_2}{2}\\)\n\nwhere BP is the bipolarity, P1 and P2 are the polarities of the two electrodes, and the division sign is used to indicate the average of the two polarities.",
|
|
"gt_answers": "B F = B P - F P = \\sqrt { x ^ { 2 } - 8 x + 8 0 } - y\n",
|
|
"image_path": "./data/HME100K/test_images/test_5659.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1/900 = 0.001111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
|
|
"gt_answers": "9 \\div \\frac { 1 } { 1 0 0 } = 9 0 0 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5660.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_2H_5OH + 2NaOH \\rightarrow 2NaC_2H_5O + H_2O\\)",
|
|
"gt_answers": ": ( N H _ { 4 } ) = S O _ { 4 } + C a ( O H ) _ { 2 } = C a S O _ { 4 } + 2 H _ { 2 } O + 2 N H _ { 3 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_5661.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "m = - 2 \\sqrt { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5662.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as 1.22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222",
|
|
"gt_answers": "1 . 2 \\times 2 = 2 . 4 m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5663.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as y = 4x - 4.",
|
|
"gt_answers": "y = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5665.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(A + B = AB\\)\n\nThis formula represents the commutative property of addition, which states that the order of addition does not affect the result. In other words, the sum of two numbers is equal to the product of those two numbers, regardless of the order in which they are added.",
|
|
"gt_answers": "\\frac { O A } { A E } = \\frac { A C } { A B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5666.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 5x4 + 2x2 - 3x3.",
|
|
"gt_answers": "\\frac { 3 } { 2 } x - 4 ( h - 1 ) = - 4 - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5667.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a few Chinese characters, which could be related to a Chinese mathematical expression or a Chinese translation of a formula.",
|
|
"gt_answers": "\\frac { 1 } { 5 } + \\frac { 2 } { 2 5 } = \\frac { 7 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5668.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = \\sqrt{x^2 + y^2}\\)",
|
|
"gt_answers": "m a = 2 - x + \\frac { 4 x } { 8 - 2 x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5670.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x^2 + 3x - 4 = 0.",
|
|
"gt_answers": "x _ { 2 } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5672.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CMMD 2 DC'mN\".",
|
|
"gt_answers": "C ^ { \\prime } M + M D \\geq D C ^ { \\prime }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5673.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is written as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\text{AD/BE} & = \\frac{A \\cdot B}{A + B} \\\\\n& = \\frac{A \\cdot B}{A + B + C} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F + G} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F + G + H} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F + G + H + I} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F + G + H + I + J} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F + G + H + I + J + K} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F + G + H + I + J + K + L} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F + G + H + I + J + K + L + M} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F + G + H + I + J + K + L + M + N} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F + G + H + I + J + K + L + M + N + O} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P} \\\\\n& = \\frac{A \\cdot B}{A + B + C + D + E +",
|
|
"gt_answers": "A D / / B E\n",
|
|
"image_path": "./data/HME100K/test_images/test_5674.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\nCaCO3 + 2HCl --> CaCl2 + CO2 + H2O",
|
|
"gt_answers": "C a C O _ { 3 } + 2 H C l = C a C l _ { 2 } + H _ { 2 } O + C O _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_5675.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4x4 + 4x2 + 2x + 2 = 16.\"",
|
|
"gt_answers": "\\frac { 4 - 4 x + x ^ { 2 } } { 2 } + \\frac { x ^ { 2 } } { 2 } = \\frac { y ^ { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5676.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(C_i = \\frac{x_i^2}{2} + \\frac{y_i^2}{2} + \\frac{z_i^2}{2} + \\frac{w_i^2}{2} + \\frac{x_i^2}{2} + \\frac{y_i^2}{2} + \\frac{z_i^2}{2} + \\frac{w_i^2}{2} + \\frac{x_i^2}{2} + \\frac{y_i^2}{2} + \\frac{z_i^2}{2} + \\frac{w_i^2}{2} + \\frac{x_i^2}{2} + \\frac{y_i^2}{2} + \\frac{z_i^2}{2} + \\frac{w_i^2}{2} + \\frac{x_i^2}{2} + \\frac{y_i^2}{2} + \\frac{z_i^2}{2} + \\frac{w_i^2}{2} + \\frac{x_i^2}{2} + \\frac{y_i^2}{2} + \\frac{z_i^2}{2} + \\frac{w_i^2}{2} + \\frac{x_i^2}{2} + \\frac{y_i^2}{2} + \\frac{z_i^2}{2} + \\frac{w_i^2}{2} + \\frac{x_i^2}{2} + \\frac{y_i^2}{2} + \\frac{z_i^2}{2} + \\frac{w_i^2}{2} + \\frac{x_i^2}{2} + \\frac{y_i^2}{2} + \\frac{z_i^2}{2} + \\frac{w_i^2}{2} + \\frac{x_i^2}{2} + \\frac{y_i^2}{2} + \\frac{z_i^2}{2} + \\frac{w_i^2}{2} + \\frac{x_i^2}{2",
|
|
"gt_answers": "C _ { 1 } : y = - x ^ { 2 } - 2 x + 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5677.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"100 - 50 = 50\".",
|
|
"gt_answers": "\\frac { 1 0 0 } { 1 0 \\sqrt { 2 } } = 5 \\sqrt { 2 } m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5678.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\na(b(c(d(e(f(g(h(i(j(k(l(m(n(o))))))))))))))\n\\end{equation}\n\nThe expression is a nested sequence of functions, where each function is applied to the previous function's result. The first function is a, which is applied to the result of the second function, b, which is applied to the result of the third function, c, and so on. The last function is o, which is applied to the result of the last function, n.",
|
|
"gt_answers": "( a - b ) ( a + b + c ) = 0 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5679.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: `x^2 + 25x - 75 = 0`.",
|
|
"gt_answers": "\\frac { x - 4 } { 2 5 } = \\frac { 1 . 2 } { 7 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5682.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"LAOB = 60\u00b0\".",
|
|
"gt_answers": "\\angle A O B = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5683.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the half of the square of the half of a number.",
|
|
"gt_answers": "\\therefore M E / / A C\n",
|
|
"image_path": "./data/HME100K/test_images/test_5684.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(e^{i\\pi} = -1\\)",
|
|
"gt_answers": "= ( \\sqrt { 3 } ) ^ { 2 } + 1 = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5685.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x^2 - 4x + 12 = 0.",
|
|
"gt_answers": "\\frac { 4 0 - x ^ { 4 } } { 4 } = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5686.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2336.8`.",
|
|
"gt_answers": "7 x = 2 3 6 . 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5687.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "2 \\sqrt { 4 - a } + \\frac { 5 } { 3 } , \\sqrt { a - 4 } = b + 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5688.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 400x - 1000 = 0.\"",
|
|
"gt_answers": "\\frac { 2 3 } { 2 1 } x = x + 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5689.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: y = 3 - 12x.",
|
|
"gt_answers": "\\frac { y } { 3 } = 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5691.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"k-2\" using LaTeX format.",
|
|
"gt_answers": "k = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5692.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 3.97^2\\)",
|
|
"gt_answers": "x _ { 4 } = 5 . 9 7 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5694.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a negative sign in front of a number, which could be a negative number or a negative exponent.",
|
|
"gt_answers": "\\frac { 1 } { x } = \\frac { 1 } { 0 . 0 8 } \\therefore x = 0 . 0 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5695.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "x _ { 1 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5696.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(x^2 + y^2 = 1\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. The variable x represents the horizontal distance from the origin (0, 0) and y represents the vertical distance from the origin (0, 0). The equation states that the sum of the squares of these two variables is equal to 1.",
|
|
"gt_answers": "\\therefore c = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5697.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"28/8 = 3.5.\"",
|
|
"gt_answers": "b = \\frac { 5 8 } { 2 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5698.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 6x6 - 6 + 2 = 12.",
|
|
"gt_answers": "x - 6 x \\leq 6 - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5699.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(241 - 3b + b^2 = 0\\)\n\nThis formula can be written using LaTeX as follows:\n\n\\(241 - 3b + b^2 = 0\\)\n\nThe LaTeX code for this expression is:\n\n```\n241 - 3b + b^2 = 0\n```",
|
|
"gt_answers": "\\frac { 2 a + 1 } { 3 } - \\frac { 1 - b } { 6 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5700.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(P_{g} = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left",
|
|
"gt_answers": "B G = F G = x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5701.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(6x + 4y = 16\\)",
|
|
"gt_answers": "1 6 = 3 : 2 . 4 = 6 : 4 . 8 = \\frac { 5 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5702.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n(x^2 - 6x + 6) = 0\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\nx^2 - 6x + 6 = 0\n\\end{equation}\n\nThe LaTeX code for the equation is:\n\n\\begin{equation}\nx^2 - 6x + 6 = 0\n\\end{equation}\n\nThe equation is written in the form of an equation with two variables, x and y, and an expression involving the variables. The equation is also written in the form of an equation with an equal sign, which indicates that the two sides of the equation are equal.",
|
|
"gt_answers": "( x _ { 1 } - 2 ) ( x _ { 2 } - 6 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5703.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as sin(2 sin(Acos(B))).",
|
|
"gt_answers": "\\sin ( B + C ) = 2 \\sin A \\cos B\n",
|
|
"image_path": "./data/HME100K/test_images/test_5704.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 9x + 8 = 0.\"",
|
|
"gt_answers": "x ^ { 2 } + 9 + x ^ { 2 } - 6 x - 8 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5705.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 6x3 - 6 = 6(x3 - 1).",
|
|
"gt_answers": "\\frac { 6 x - 3 } { 6 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5706.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: ZnCl2 + H2O = Zn(OH)2 + Cl2.",
|
|
"gt_answers": "Z n + 2 H C l = Z n C l _ { 2 } + H _ { 2 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_5707.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LADC = 40\u00b0 + 10\u00b0\".",
|
|
"gt_answers": "\\angle A O C = 5 4 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5708.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 4x + 3 = 5x - 2.",
|
|
"gt_answers": "\\frac { 1 } { 3 - x } + \\frac { 4 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5709.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x^2 + 2x + 1 = 0\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\n3x^2 + 2x + 1 = 0\n\\end{equation}\n\nThe equation is written in the form of an equation with two variables, x and y, and an expression involving the variables. The equation is also written in the form of an equation with a single variable, x, and an expression involving the variable.",
|
|
"gt_answers": "( 1 ) - 3 x \\cdot ( 2 x ^ { 2 } + x - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5710.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(3x^2 + 2x - 1 = 0\\)\n\nThis formula can be written in LaTeX as:\n\n\\(3x^2 + 2x - 1 = 0\\)\n\nThe LaTeX code for this expression is:\n\n\\begin{equation}\n3x^2 + 2x - 1 = 0\n\\end{equation}\n\nThe LaTeX code for the entire image is:\n\n\\begin{figure}[ht]\n\\centering\n\\includegraphics[width=0.8\\textwidth]{formula.png}\n\\caption{Formula written in LaTeX}\n\\label{fig:formula}\n\\end{figure}",
|
|
"gt_answers": "\\frac { 1 2 5 } { 2 7 } = ( \\frac { 5 } { 3 } ) ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5711.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "5 a ( a - b ) ^ { 2 } - 1 0 ( a - b ) ^ { 3 } = ( a - b ) ^ { 2 } \\cdot ( 1 0 b - 5 a ) = 5 ( a - b ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5712.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 36.",
|
|
"gt_answers": "\\overline { \\frac { x } { 1 8 } = \\frac { 2 6 } { 3 1 6 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5713.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as `x^2 + 5x + 6 = 0`.",
|
|
"gt_answers": "x = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5714.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(BQ = \\sqrt{20 \\times 10 \\times 10} = 2000\\)",
|
|
"gt_answers": "B Q = A B \\times \\tan A = 2 0 \\times \\tan 6 0 ^ { \\circ } = 2 0 \\sqrt { 3 } (\n",
|
|
"image_path": "./data/HME100K/test_images/test_5715.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 4.565555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555",
|
|
"gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5716.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(J_{14} + J_{24} + J_{34} + J_{44} = 12\\)\n\nThe formula is a combination of four terms, each representing the sum of the four numbers in the image. The numbers are written as J14, J24, J34, and J44. The sum of these four terms is equal to 12.",
|
|
"gt_answers": "\\frac { \\sqrt { 1 2 + 4 } } { 1 2 - 4 } = \\frac { \\sqrt { 1 6 } } { 8 } = \\frac { 4 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5718.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x _ { 1 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5719.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\begin{equation}\n\\frac{AD}{DB} = \\frac{2}{4} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThe formula uses the variables AD and DB to represent the areas of two rectangles. The formula is then simplified by multiplying the numerator and denominator by the same fraction, which in this case is 1/4. The result is the final expression of the formula, which is 1/4.",
|
|
"gt_answers": "\\frac { D Q } { A D } = \\frac { 2 } { 4 } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5720.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\overrightarrow { P Q } = ( x _ { 2 } - x _ { 1 } , y _ { 2 } - y _ { 1 } ) = ( - 2 , - 3 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5721.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = 2\\sin(x) \\cos(x) = ",
|
|
"gt_answers": "\\frac { 1 } { 2 } - \\ln \\frac { 1 } { \\sqrt { 2 a } } \\geq 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5722.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 5 } { 9 } x = \\frac { 5 } { 6 } \\times \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5723.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/3 + 2/8 = 8/27.",
|
|
"gt_answers": "\\frac { 1 } { 2 } - \\frac { 1 } { 8 } = \\frac { 3 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5724.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 6x4 + 8x4 + 21x2 - 35x1.",
|
|
"gt_answers": "6 x + 9 = 8 4 x - 2 1 - 3 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5725.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(A + B + C = D + E + F\\)\n\nThe formula is written in the form of an equation, with the variables A, B, C, D, E, and F separated by the equal sign. The formula is also written in a way that it can be easily read and understood by those familiar with the LaTeX formula notation.",
|
|
"gt_answers": "A B / / C D , \\angle A = 1 0 0 ^ { \\circ } , \\angle C = 1 1 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5726.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 4x + 3 = 0`.",
|
|
"gt_answers": "\\frac { 5 x } { 3 } = 3 x - 4 - 1 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_5728.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "\\frac { x y + 3 x z - y z } { x y - 3 x ( z - y ) z } = \\frac { x _ { z } + y _ { z } + 3 x z - y _ { z } } { x _ { 8 } + y _ { z } - 3 x 8 - y _ { z } } = \\frac { 4 x z } { - 2 x z } = - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5729.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 60 - 20 = 40.",
|
|
"gt_answers": "\\frac { 6 6 } { x } = \\frac { 1 2 0 } { x } - 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_5731.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 + \\frac{1}{16}x^8 + \\frac{1}{32}x^{10} + \\frac{1}{64}x^{12} + \\frac{1}{128}x^{14} + \\frac{1}{256}x^{16} + \\frac{1}{512}x^{18} + \\frac{1}{1024}x^{20} + \\frac{1}{2048}x^{22} + \\frac{1}{4096}x^{24} + \\frac{1}{8192}x^{26} + \\frac{1}{16384}x^{28} + \\frac{1}{32768}x^{30} + \\frac{1}{65536}x^{32} + \\frac{1}{131072}x^{34} + \\frac{1}{262144}x^{36} + \\frac{1}{524288}x^{38} + \\frac{1}{1048576}x^{40} + \\frac{1}{2097152}x^{42} + \\frac{1}{4194304}x^{44} + \\frac{1}{8388608}x^{46} + \\frac{1}{16777216}x^{48} + \\frac{1}{33554432}x^{50} + \\frac{1}{67108864}x^{52} + \\frac{1}{134217728}x^{54} + \\frac{1}{268435456}x^{56} + \\frac{1}{536870912}x^{58} + \\frac{",
|
|
"gt_answers": "u _ { 3 } = u v\n",
|
|
"image_path": "./data/HME100K/test_images/test_5732.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2}",
|
|
"gt_answers": "2 2 6 \\times \\frac { 3 } { 5 } = 1 3 5 \\frac { 3 } { 5 } ( c m ) \\alpha 1 0 \\times \\frac { 5 } { 7 } = 1 5 0 ( c m ) \\cdot 1 3 5 \\frac { 2 } { 5 } c m < 1 5 0 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5733.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x = 1 0 - y\n",
|
|
"image_path": "./data/HME100K/test_images/test_5734.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "\\frac { 1 } { 2 } \\pi < B < \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_5735.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "\\therefore x = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5738.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: SGABD = BD + DE.",
|
|
"gt_answers": "\\frac { S _ { \\Delta A B D } } { S _ { \\Delta A D E } } = \\frac { B D } { D E } = \\alpha\n",
|
|
"image_path": "./data/HME100K/test_images/test_5739.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3x + 2y = 10\\)\n\nThis is a simple algebraic equation that can be solved using the addition and subtraction operations.",
|
|
"gt_answers": "\\frac { 8 } { 3 } > \\frac { 7 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5740.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/2(x + 15) = 10.",
|
|
"gt_answers": "\\frac { 2 } { 3 } = \\frac { 1 0 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5742.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"7x6 = 42.\"",
|
|
"gt_answers": "\\square \\div 7 = 7 \\cdots 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_5743.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\pi r^2 + 2\\pi r\\cos(\u03b8) + 2\\pi r\\sin(\u03b8) = 4\\pi r^2\\)\n\nThis formula represents the area of a circle with a radius of r, where \u03b8 is the angle between the radius vector and the x-axis.",
|
|
"gt_answers": "\\sin \\theta \\cos \\theta = 3 \\cos ^ { 2 } \\theta = \\frac { 3 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5744.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(24 + 52 - 42 = 54 - 42 = 12\\)",
|
|
"gt_answers": "\\frac { 5 7 } { 2 4 } > \\frac { 5 4 } { 2 4 } > \\frac { 5 2 } { 2 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5745.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 6x2 = 72 cm.",
|
|
"gt_answers": "6 \\times 6 \\times 2 = 7 2 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5746.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 5y^2 - 3xy - 5y + 3 = 0\\)",
|
|
"gt_answers": "3 x - 5 y = 1 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_5747.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `tan(x) = 2/x`.",
|
|
"gt_answers": "\\tan \\alpha = \\frac { 5 } { - 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5748.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 9x9-7=14.",
|
|
"gt_answers": "9 \\times 9 \\times 9 = 7 2 9 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5749.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(S_n = \\frac{1}{n} \\sum_{i=1}^n x_i^2\\)\n\nwhere `S_n` is the sum of the squares of the first `n` elements of the sequence `x_1, x_2, ..., x_n`.",
|
|
"gt_answers": "S n = n ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5750.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"13 PLBDO.\"",
|
|
"gt_answers": "B P \\bot B O\n",
|
|
"image_path": "./data/HME100K/test_images/test_5751.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2(3t + 1) - 3(t - 1) = 2t^2 - 3t - 3.",
|
|
"gt_answers": "\\cos \\frac { 2 } { 3 } \\pi = - \\frac { \\sqrt { 3 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5752.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as Ln(x) = 2x + 1.",
|
|
"gt_answers": "\\angle B O C = 1 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5753.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 50^2 + 80^2\\)",
|
|
"gt_answers": "9 0 x - 3 0 - 8 4 x + 8 4 = 1 2 6 x - 1 2 6 - 3 5 + 3 5 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5754.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 1937 - 2008 = 71 years.",
|
|
"gt_answers": "\\frac { 1 9 3 7 } { 2 0 0 5 } < \\frac { 1 9 4 0 } { 2 0 0 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5755.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = a + bx + cx^2 + dx^3 + ex^4 + fx^5\\)",
|
|
"gt_answers": "f ^ { \\prime } ( 1 ) = 1 - a\n",
|
|
"image_path": "./data/HME100K/test_images/test_5756.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis is a quadratic equation, which is a type of algebraic equation that involves the square of a variable. In this case, the variables are a, b, and c, and the equation states that the square of a plus the square of b equals the square of c.",
|
|
"gt_answers": "A . a b > 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5757.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"24/25\" using the Roman numeral system.",
|
|
"gt_answers": "1 2 \\times \\frac { 2 } { 8 } = \\frac { 2 4 } { 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5759.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 2x + 7.",
|
|
"gt_answers": "x _ { 2 } = \\frac { 4 \\sqrt { 1 7 } } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5760.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x10^2.",
|
|
"gt_answers": "x = \\frac { 3 } { 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5761.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 - 3x + 5 = 0\\)",
|
|
"gt_answers": ". x _ { 2 } = \\frac { 3 } { \\sqrt { 5 - \\sqrt { 2 } } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5762.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"d(x) = 2x^2 - 3x + 4.\"",
|
|
"gt_answers": "S _ { \\Delta D C O } = \\frac { 1 } { 2 } \\times C O \\times Q\n",
|
|
"image_path": "./data/HME100K/test_images/test_5763.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(k_1 + k_2 + k_3 = k_4\\)\n\nThis formula represents the relationship between four different constants, k1, k2, k3, and k4. The equation states that the sum of the first three constants (k1, k2, k3) is equal to the fourth constant (k4).",
|
|
"gt_answers": "x < \\frac { k - 3 } { k - 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5766.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is: (x + 2)(x + 3) = 10x^2 + 15x + 6.",
|
|
"gt_answers": "1 0 ( \\frac { 1 } { 5 x } - 2 ) = 2 5 ( \\frac { 8 } { 5 } x + \\frac { 3 } { 2 5 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5767.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Af = 1/2(1 + \u221a(1 - 4/9))\".",
|
|
"gt_answers": "A F = \\frac { \\sqrt { 7 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5768.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Peace + 15 = 17.\"",
|
|
"gt_answers": "\\angle E A C = 1 5 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5769.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2.4 + 0.07.",
|
|
"gt_answers": "O B = 0 . 7\n",
|
|
"image_path": "./data/HME100K/test_images/test_5770.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\nP = Fg / 19000a\n\nwhere P is the pressure, Fg is the gravitational force, and a is the acceleration due to gravity.",
|
|
"gt_answers": "P = \\frac { F } { S } = \\frac { G } { S } = \\frac { m g } { s } = \\frac { 2 k g \\cdot 9 . 8 N / k g } { 0 . 0 1 m ^ { 3 } } = 1 9 6 0 P a\n",
|
|
"image_path": "./data/HME100K/test_images/test_5771.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.",
|
|
"gt_answers": "B b \\times A x ^ { a } = \\frac { 1 } { 2 } \\times \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5772.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Bx-ay44.\"",
|
|
"gt_answers": "b x - a y = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5773.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n(400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "( 4 0 - 3 0 + x ) ( 6 0 0 - 1 0 x ) = 1 0 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5775.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/2(1/",
|
|
"gt_answers": "\\angle 1 = \\angle D B C + \\angle A B D = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5779.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as ABNCD.",
|
|
"gt_answers": "A B / / D C >\n",
|
|
"image_path": "./data/HME100K/test_images/test_5780.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `y = 2x^4 - 4x^2 + c`.",
|
|
"gt_answers": "y = x ^ { 2 } - 4 x + c ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5781.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3\\sqrt{2} - 2\\sqrt{3} = 3\\sqrt{2} - 2\\sqrt{3} \\cdot \\sqrt{2} = 3\\sqrt{2} - 2\\sqrt{3} \\cdot \\sqrt{3} = 3\\sqrt{2} - 2\\sqrt{6} = 3\\sqrt{2} - 2\\sqrt{6} \\cdot \\sqrt{2} = 3\\sqrt{2} - 2\\sqrt{6} \\cdot \\sqrt{3} = 3\\sqrt{2} - 2\\sqrt{6} \\cdot \\sqrt{6} = 3\\sqrt{2} - 2\\sqrt{12} = 3\\sqrt{2} - 2\\sqrt{12} \\cdot \\sqrt{2} = 3\\sqrt{2} - 2\\sqrt{12} \\cdot \\sqrt{3} = 3\\sqrt{2} - 2\\sqrt{12} \\cdot \\sqrt{6} = 3\\sqrt{2} - 2\\sqrt{12} \\cdot \\sqrt{12} = 3\\sqrt{2} - 2\\sqrt{24} = 3\\sqrt{2} - 2\\sqrt{24} \\cdot \\sqrt{2} = 3\\sqrt{2} - 2\\sqrt{24} \\cdot \\sqrt{3} = 3\\sqrt{2} - 2\\sqrt{24} \\cdot \\sqrt{6} = 3\\sqrt{2} - 2\\sqrt{24} \\cdot \\sqrt{12} = 3\\sqrt{2} - 2\\sqrt{24} \\cdot \\sqrt{24} = 3\\sqrt{2} - 2\\sqrt{48} = 3\\sqrt{2} - 2\\sqrt{48} \\cdot \\sqrt{2} = 3\\sqrt{2} - 2\\sqrt{48} \\cdot \\sqrt{3} = 3\\sqrt{2} - 2\\sqrt{48} \\cdot \\sqrt{6} = 3\\sqrt{2",
|
|
"gt_answers": "\\pm \\sqrt { a + b } = \\pm \\sqrt { \\frac { 1 4 } { 3 } - \\frac { 5 } { 3 } } = \\pm \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5783.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(x^2 + 10x - 100 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "( x - 2 0 ) ( x - 1 0 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5784.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2x + 3 = 6.",
|
|
"gt_answers": "t = \\frac { 6 } { V . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5785.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x^2 + 4x - 5 = 0.\"",
|
|
"gt_answers": "N _ { 2 } ( 8 - 4 \\sqrt { 5 } , 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5786.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { a } { \\sin A } = \\frac { b } { \\sin B } = \\frac { c } { \\sin C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5788.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\text{CF} &= \\frac{1}{2} \\left( \\text{AL} + \\text{AF} \\right) \\\\\n&= \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\text{AL} + \\text{AF} \\right) + \\frac{1}{2} \\left( \\text{AL} - \\text{AF} \\right) \\right) \\\\\n&= \\frac{1}{4} \\left( \\text{AL}^2 + \\text{AF}^2 + 2 \\text{AL} \\text{AF} \\right) \\\\\n&= \\frac{1}{4} \\left( \\text{AL}^2 + \\text{AF}^2 + 2 \\left( \\text{AL} \\text{AF} \\right) \\right) \\\\\n&= \\frac{1}{4} \\left( \\text{AL}^2 + \\text{AF}^2 + 2 \\left( \\text{AL} \\text{AF} \\right) \\right) \\\\\n&= \\frac{1}{4} \\left( \\text{AL}^2 + \\text{AF}^2 + 2 \\left( \\text{AL} \\text{AF} \\right) \\right) \\\\\n&= \\frac{1}{4} \\left( \\text{AL}^2 + \\text{AF}^2 + 2 \\left( \\text{AL} \\text{AF} \\right) \\right) \\\\\n&= \\frac{1}{4} \\left( \\text{AL}^2 + \\text{AF}^2 + 2 \\left( \\text{AL} \\text{AF} \\right) \\right) \\\\\n&= \\frac{1}{4} \\left( \\text{AL}^2 + \\text{AF}^2 + 2 \\left( \\text{AL} \\text{AF} \\right) \\right) \\\\\n&= \\frac{1}{4} \\left( \\text{AL}^2 + \\text{AF}^2 + 2 \\left( \\text{AL} \\text{AF} \\right) \\right) \\\\\n&= \\frac{1}{4} \\",
|
|
"gt_answers": "i A C = \\frac { C F } { A F } = \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5789.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2}",
|
|
"gt_answers": "\\angle D A C = 2 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5790.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1994-4=4988\".",
|
|
"gt_answers": "1 9 9 4 \\div 4 = 4 9 8 \\cdots 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5791.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2 + 2 = 4.",
|
|
"gt_answers": "= 2 3 2 + 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5792.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "D ( 4 . 1 ) E ( 3 . 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5793.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\n\\(f(x) = 3x^2 + 5x + 3\\)",
|
|
"gt_answers": "f ( \\frac { \\pi } { 2 } ) = 3 \\sin ( \\pi + \\frac { 5 \\pi } { 6 } ) = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5794.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{3}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{3}{8}\n\\end{equation}\n\nThe equation is a multiplication of three fractions, each with a denominator of 2. The result is a fraction with a denominator of 8.",
|
|
"gt_answers": "\\frac { \\sqrt { 3 } - \\vert a \\vert } { 2 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5795.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(3x + 5 - 6 = 10\\)",
|
|
"gt_answers": "1 - \\frac { 1 } { 5 } - \\frac { 3 } { 5 } = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5796.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"DE = BD + OD.\"",
|
|
"gt_answers": "\\frac { D E } { O D } = \\frac { B D } { D E }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5797.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x0.5 - 4 cm/h.",
|
|
"gt_answers": "2 \\times 1 0 \\div 5 = 4 ( k m / h )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5798.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression of the formula in the image is written as follows:\n\n\\(LC = y \\cdot LF\\)\n\nwhere LC represents the load current, y represents the load voltage, and LF represents the load resistance.",
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"gt_answers": "\\angle C O D = 4 \\angle E O D\n",
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"image_path": "./data/HME100K/test_images/test_5799.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 4x + 14 = 0\\)",
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"gt_answers": "x _ { 1 } = 2 \\sqrt [ 4 ] { 8 } - 1 \\approx 2 . 3 6 4\n",
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"image_path": "./data/HME100K/test_images/test_5800.jpg",
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"model_name": "mPLUG"
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},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
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"answer": "The expression in the image is written as: 2x + 3y = 7.",
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"gt_answers": "x = \\frac { 1 7 } { 5 }\n",
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"image_path": "./data/HME100K/test_images/test_5801.jpg",
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"model_name": "mPLUG"
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|
},
|
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
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"gt_answers": "1 8 0 0 > 1 5 0 0\n",
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"image_path": "./data/HME100K/test_images/test_5803.jpg",
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"model_name": "mPLUG"
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},
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{
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"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
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"gt_answers": "\\Delta A E H \\cong \\Delta C G F ( S A S )\n",
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"image_path": "./data/HME100K/test_images/test_5805.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x^2 + 3x + 4 = 0.",
|
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"gt_answers": "x ^ { 2 } = \\frac { 5 0 \\times ( 1 8 \\times 1 5 - 8 \\times 9 ) } { \\partial 6 \\times \\partial 4 \\times \\partial 7 \\times \\partial 3 }\n",
|
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"image_path": "./data/HME100K/test_images/test_5806.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2}{2} + \\frac{y^2}{2} + \\frac{z^2}{2} = \\frac{1}{2}\n\\end{equation}\n\nThis equation represents the formula for the volume of a cube, where x, y, and z are the lengths of the sides of the cube.",
|
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"gt_answers": "\\frac { 9 } { x + y } + \\frac { 6 } { x - y } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5807.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 4x + 9 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
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"gt_answers": "\\frac { 3 } { 4 } = \\frac { 1 } { 8 } = x : \\frac { 4 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5808.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(GH-TDC = \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{GH}{TDC} \\cdot \\frac{TDC}{GH} \\cdot \\frac{G",
|
|
"gt_answers": "G H = \\frac { 1 } { 6 } D C\n",
|
|
"image_path": "./data/HME100K/test_images/test_5809.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\sin(30^\\circ) + 2\\sin(60^\\circ) + 2\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) = 4\\sin(30^\\circ) + 4\\sin(60^\\circ) + 4\\sin(90^\\circ) =",
|
|
"gt_answers": "\\vert - 3 \\vert - ( 3 - \\pi ) ^ { \\circ } - 2 \\sin 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5810.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 8/7 - 3/4 = 14/14.",
|
|
"gt_answers": "x = 8 \\sqrt { 3 } - 1 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5811.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x^2 - 3x + 1 = 0`.",
|
|
"gt_answers": "6 . x + y = 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5812.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": ": \\Delta A E D \\sim \\Delta A D B\n",
|
|
"image_path": "./data/HME100K/test_images/test_5813.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"275 - 55 - 3 = 220.\"",
|
|
"gt_answers": "2 7 8 \\div 5 = 5 5 \\cdots 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5814.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( \\sqrt { 7 } ) ^ { 2 } = ( a - \\frac { 1 } { a } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5815.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\u3001 4 5 \\% \u3001 \\frac { ( 3 0 \\times 2 0 \\% ) ^ { 3 } } { ( 3 0 \\times 2 0 \\% ) ( 3 0 \\times 6 0 \\% ) ^ { 2 } } . N _ { 2 } + 6 C _ { 2 } H _ { 5 } O H = 2 N H _ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5816.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2^{20} + 2^{19} + 2^{18} + 2^{17} + 2^{16} + 2^{15} + 2^{14} + 2^{13} + 2^{12} + 2^{11} + 2^{10} + 2^{9} + 2^{8} + 2^{7} + 2^{6} + 2^{5} + 2^{4} + 2^{3} + 2^{2} + 2^{1} + 2^{0} = 10^{20} + 10^{19} + 10^{18} + 10^{17} + 10^{16} + 10^{15} + 10^{14} + 10^{13} + 10^{12} + 10^{11} + 10^{10} + 10^{9} + 10^{8} + 10^{7} + 10^{6} + 10^{5} + 10^{4} + 10^{3} + 10^{2} + 10^{1} + 10^{0} = 10^{20} + 10^{19} + 10^{18} + 10^{17} + 10^{16} + 10^{15} + 10^{14} + 10^{13} + 10^{12} + 10^{11} + 10^{10} + 10^{9} + 10^{8} + 10^{7} + 10^{6} + 10^{5} + 10^{4} + 10^{3} + 10^{2} + 10^{1} + 10^{0} = 10^{20} + 10^{19} + 10^{18} + 10^{17} + 10^{16} + 10^{1",
|
|
"gt_answers": "\\Delta = 3 6 - 4 ( 4 k + 1 ) = 3 6 - 1 6 k - 4 = 3 2 - 1 6 k\n",
|
|
"image_path": "./data/HME100K/test_images/test_5817.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 12 = 100.\"",
|
|
"gt_answers": "x = \\pm 1 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5818.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Labe = 30\u00b0.\"",
|
|
"gt_answers": "\\angle A B E = 3 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5819.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x + 2y = 10\\)",
|
|
"gt_answers": "= \\frac { 2 } { 3 } \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_5820.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(v = \\sqrt{2 \\cdot m \\cdot s}\\)\n\nThis formula relates the velocity (v) of an object to its mass (m) and the speed of light (c). The equation states that the velocity of an object is equal to the square root of the product of its mass and the speed of light.",
|
|
"gt_answers": "v = \\sqrt { 1 0 } m / s\n",
|
|
"image_path": "./data/HME100K/test_images/test_5821.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x^2 + 3x - 4 = 0.",
|
|
"gt_answers": "8 4 6 0 0 \\times 3 6 5 = 3 0 8 7 9 0 0 0 = 3 . 0 8 7 9 \\times 1 0 ^ { 2 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5822.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 14.",
|
|
"gt_answers": "\\frac { 5 } { 6 } - \\frac { 2 } { 9 } + \\frac { 5 } { 6 } = 1 \\frac { 4 } { 9 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5823.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 8n^2 + 4n + 1 = 4m^2 + 4m + 1, where n and m are integers.",
|
|
"gt_answers": "8 n m ^ { 2 } = 4 ( n + \\frac { 1 } { 2 } ) ^ { 2 } m ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5824.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(sin(x) = \\frac{sin(x)}{x} + \\frac{cos(x)}{x^2} + \\frac{sin(x)}{x^3} + \\frac{cos(x)}{x^4} + \\frac{sin(x)}{x^5} + \\frac{cos(x)}{x^6} + \\frac{sin(x)}{x^7} + \\frac{cos(x)}{x^8} + \\frac{sin(x)}{x^9} + \\frac{cos(x)}{x^{10}} + \\frac{sin(x)}{x^{11}} + \\frac{cos(x)}{x^{12}} + \\frac{sin(x)}{x^{13}} + \\frac{cos(x)}{x^{14}} + \\frac{sin(x)}{x^{15}} + \\frac{cos(x)}{x^{16}} + \\frac{sin(x)}{x^{17}} + \\frac{cos(x)}{x^{18}} + \\frac{sin(x)}{x^{19}} + \\frac{cos(x)}{x^{20}} + \\frac{sin(x)}{x^{21}} + \\frac{cos(x)}{x^{22}} + \\frac{sin(x)}{x^{23}} + \\frac{cos(x)}{x^{24}} + \\frac{sin(x)}{x^{25}} + \\frac{cos(x)}{x^{26}} + \\frac{sin(x)}{x^{27}} + \\frac{cos(x)}{x^{28}} + \\frac{sin(x)}{x^{29}} + \\frac{cos(x)}{x^{30}} + \\frac{sin(x)}{x^{31}} + \\frac{cos(x)}{x^{32}} + \\frac{sin(x)}{x^{33}} + \\frac{cos(x)}{x^{34}} + \\frac{sin(x)}{x^{35}} + \\frac{cos(x)}{x^{36}} + \\frac{sin(x)}{x^{37}} + \\frac{cos(x)}{x^{38}} + \\frac{sin(x",
|
|
"gt_answers": "\\sin \\angle D P O = \\frac { M O } { P O } = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5825.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 10x + 10 = 0\\)",
|
|
"gt_answers": "1 8 x + 9 0 + 6 x ^ { 2 } + 6 x - 1 2 = 5 x ^ { 2 } + 3 5 x + 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5826.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, but it can be represented in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{3} + \\frac{2}{3} + \\frac{3}{3} = 1\n\\end{aligned}\n\\end{equation}\n\nThis equation represents the sum of three terms, each of which is equal to one third.",
|
|
"gt_answers": "x - \\frac { 5 } { 1 2 } + \\frac { 5 } { 1 2 } = \\frac { 3 } { 8 } + \\frac { 5 } { 1 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5827.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z = 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26",
|
|
"gt_answers": "\\Delta A E C \\cong \\Delta M F C ( A \\cdot S . A )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5828.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "4 0 L = 4 0 d m ^ { 3 } = 4 0 0 0 0 c m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5829.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LGHD = 90^{\\circ} - 30^{\\circ} = 60^{\\circ}\\)",
|
|
"gt_answers": "\\angle G H D = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5831.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"8g = 800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "8 c m = 8 0 0 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5833.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V = \\frac{1}{2} \\pi r^2 \\left( \\frac{1}{2} \\left( \\frac{1}{r} \\right)^2 + \\frac{1}{r} \\right)\\)\n\nThis formula calculates the volume of a sphere using the formula for the area of a circle and the formula for the volume of a cylinder.",
|
|
"gt_answers": "\\sqrt { x ( x + y ) } \\div \\frac { \\vert y \\vert \\sqrt { x } } { \\sqrt { x + y } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5834.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(B_D = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2",
|
|
"gt_answers": "\\therefore \\widehat { B D } = \\widehat { C D }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5836.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `7.12x0.03`.",
|
|
"gt_answers": "1 . 7 2 - 7 . 1 x = 0 . 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5837.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "( 3 + 2 + 3 + 2 ) \\times 2 0 0 = 2 0 0 0 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5839.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 5x + 48 = 0.\"",
|
|
"gt_answers": "x = \\frac { 5 } { 4 8 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5841.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3xy + 4y^2 = 100\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\begin{equation}\n2x^2 + 3xy + 4y^2 = 100\n\\end{equation}\n\nThe equation is written in the form of an equation with two variables, x and y, and the expression is enclosed in the `\\( ... \\)` LaTeX command.",
|
|
"gt_answers": "1 2 ( 3 0 0 - 3 x ) + ( 1 2 - b )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5842.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(10^{10} \\cdot 10^{10} = 10^{20}\\)",
|
|
"gt_answers": "2 0 . 1 - 0 . 5 7 + 3 \\frac { 1 } { 4 } + 2 . 7 5 + ( - 5 \\frac { 1 } { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5843.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "O E \\bot D C\n",
|
|
"image_path": "./data/HME100K/test_images/test_5844.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"CADL = 48\u00b0.\"",
|
|
"gt_answers": "\\angle C D E = \\frac { 1 } { 2 } \\angle A D C = 4 8 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5845.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as:\n\n\\(RD = \\frac{AO}{OC}\\).",
|
|
"gt_answers": "\\frac { O D } { O E } = \\frac { O A } { O C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5846.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: `30x^2 + 23x + 10 = 0`.",
|
|
"gt_answers": "\\frac { 3 0 } { x } - \\frac { 3 2 } { x + 3 } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5847.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as \"7012 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "7 0 1 2 \\approx 7 0 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5849.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Sin(x) = 0.5 * (1 - cos(x))\".",
|
|
"gt_answers": "S _ { 1 } = S _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5850.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as yc = 8x.",
|
|
"gt_answers": "y _ { c } = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5853.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"45\u00b0-90\u00b0 = 45\u00b0\".",
|
|
"gt_answers": "\\angle D F B = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5854.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{BG}{BG + DE} = \\frac{BG}{BG + DE}\n\\end{equation}\n\nThis is a mathematical equation that states that the ratio of the blue and green areas of the image is equal to the ratio of the blue and green areas of the image.",
|
|
"gt_answers": "\\therefore \\frac { D E } { D O } = \\frac { B D } { D E }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5855.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V = \\frac{R_1 R_2}{R_1 + R_2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "I : \\frac { V } { R _ { 1 } + R _ { 2 } } = \\frac { 1 0 V } { 1 2 . 5 \\Omega } = 0 . 8 A .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5856.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(AC = \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot",
|
|
"gt_answers": "\\angle A D C = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5857.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"W = 2x + 3y + 48.\"",
|
|
"gt_answers": "W = - x ^ { 2 } + 7 x + 4 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5859.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 3y = 10.",
|
|
"gt_answers": "x = - \\frac { 6 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5860.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "x = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5861.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{",
|
|
"gt_answers": "= 1 + 2 y _ { 2 } = 1 - 3 .\n",
|
|
"image_path": "./data/HME100K/test_images/test_5863.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 15\\)",
|
|
"gt_answers": "y = - \\frac { 1 5 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5864.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "O P \\bot C D\n",
|
|
"image_path": "./data/HME100K/test_images/test_5865.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 10\\)\n\nThis formula can be represented using the LaTeX code:\n\n\\(x^2 + 2x + 3 = 10\\)\n\nThe LaTeX code uses the `\\( \\)` and `\\)` symbols to denote the beginning and end of the formula, respectively. The `\\( \\)` symbol is used to enclose the entire formula, while the `\\)` symbol is used to enclose the entire expression within the parentheses. The `x` and `3` variables are written using the `\\(x\\)` and `\\(3\\)` symbols, respectively, to denote that they are variables. The `+` symbol is written using the `\\+` symbol, and the `=` symbol is written using the `\\=` symbol.",
|
|
"gt_answers": "\\frac { 2 } { 3 } \\times \\frac { 1 } { 4 } = \\frac { 2 } { 1 2 } = \\frac { 1 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5866.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"P(E|W) = P(W|E)P(E) / P(W).\"",
|
|
"gt_answers": "P = \\frac { W } { t } , W = V I t , I = \\frac { V } { R }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5867.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(Z_{EG} = 180^{\\circ} - 90^{\\circ} - 60^{\\circ} = 90^{\\circ} - 60^{\\circ} - 90^{\\circ} = 0^{\\circ}\\)",
|
|
"gt_answers": "\\angle E K G = 1 8 0 ^ { \\circ } - 9 0 ^ { \\circ } - 3 0 ^ { \\circ } = 6 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5868.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(cos(x) + sin(x) = 1\\)",
|
|
"gt_answers": "\\cos x \\in [ \\frac { 1 } { 2 } , 1 ]\n",
|
|
"image_path": "./data/HME100K/test_images/test_5869.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 2x + 2 = 2(x^2 + x + 1)\\)",
|
|
"gt_answers": "\\frac { 1 } { x } - ( - 2 ) = 2 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5870.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{2x^2 + 3x + 4}{x^2 + 2x + 3}\n\\end{aligned}\n\\end{equation}",
|
|
"gt_answers": "x ^ { 2 } - 2 x - 1 = ( x - 1 - \\sqrt { 2 } ) ( x - 1 + \\sqrt { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5871.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(V_{out} = I_{in} \\times R_{total} \\times 0.002000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "I _ { 1 } = \\frac { V } { R _ { 1 } } = \\frac { 1 2 V } { 2 0 \\Omega } = 0 . 6 A\n",
|
|
"image_path": "./data/HME100K/test_images/test_5872.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(R = \\frac{V_1}{I_1} = \\frac{V_2}{I_2} = \\frac{V_3}{I_3} = \\frac{V_4}{I_4} = \\frac{V_5}{I_5} = \\frac{V_6}{I_6} = \\frac{V_7}{I_7} = \\frac{V_8}{I_8} = \\frac{V_9}{I_9} = \\frac{V_{10}}{I_{10}} = \\frac{V_{11}}{I_{11}} = \\frac{V_{12}}{I_{12}} = \\frac{V_{13}}{I_{13}} = \\frac{V_{14}}{I_{14}} = \\frac{V_{15}}{I_{15}} = \\frac{V_{16}}{I_{16}} = \\frac{V_{17}}{I_{17}} = \\frac{V_{18}}{I_{18}} = \\frac{V_{19}}{I_{19}} = \\frac{V_{20}}{I_{20}} = \\frac{V_{21}}{I_{21}} = \\frac{V_{22}}{I_{22}} = \\frac{V_{23}}{I_{23}} = \\frac{V_{24}}{I_{24}} = \\frac{V_{25}}{I_{25}} = \\frac{V_{26}}{I_{26}} = \\frac{V_{27}}{I_{27}} = \\frac{V_{28}}{I_{28}} = \\frac{V_{29}}{I_{29}} = \\frac{V_{30}}{I_{30}} = \\frac{V_{31}}{I_{31}} = \\frac{V_{32}}{I_{32}} = \\frac{V_{33}}{I_{33}} = \\frac{V_{34}}{I_{34}} = \\frac{V_{35}}{I_{35}} = \\frac{V_{36}}{I_{36}} = \\frac{V_{3",
|
|
"gt_answers": "R = \\frac { U } { I }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5873.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\nPd = 2.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "\\frac { P D } { D C } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5875.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1",
|
|
"gt_answers": "5 0 \\times 1 0 \\times 2 0 = 1 0 0 0 0 ( c m ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5876.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 1/2 + 1/3 = 1/6.",
|
|
"gt_answers": "y _ { 1 } = \\frac { 1 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5878.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"L2 = LABC\" using LaTeX format.",
|
|
"gt_answers": "\\angle 2 = \\frac { 1 } { 2 } \\angle A B C\n",
|
|
"image_path": "./data/HME100K/test_images/test_5879.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LEGK = 3BGGE.\"",
|
|
"gt_answers": "\\angle E G K = \\frac { 1 } { 2 } \\angle B G E\n",
|
|
"image_path": "./data/HME100K/test_images/test_5882.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(30\\sin(x) + 50\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) + 30\\cos(x) = 50\\sin(x) +",
|
|
"gt_answers": "B O = \\frac { 1 } { 2 } B D = 1 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_5883.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: y = 2x^2 - 3x + 1.",
|
|
"gt_answers": "y _ { 2 } = - \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5884.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a plus sign and two numbers, which could be written in LaTeX as follows:\n\n\\(x + 2\\)",
|
|
"gt_answers": "\\frac { 1 2 ( x + 1 ) \\vert } { 3 } - 2 ( x + 2 ) =\n",
|
|
"image_path": "./data/HME100K/test_images/test_5885.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a letter \"B\" in it, which could be a reference to the letter \"B\" in the Korean alphabet.",
|
|
"gt_answers": "B _ { 2 } = \\frac { \\pi } { 2 } + B _ { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5886.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "U _ { r } = \\sqrt { P \\cdot R _ { 1 } } = \\sqrt { 4 W \\times 1 \\Omega } = 2 V\n",
|
|
"image_path": "./data/HME100K/test_images/test_5887.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as y = 2x + 35.",
|
|
"gt_answers": "x = \\frac { 2 } { 3 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5889.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: Cp = Cb + Cp0.",
|
|
"gt_answers": "\\frac { C D } { C P } = \\frac { C P } { C B }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5890.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"1x3 + 2x2 - 3x + 4 = 10.\"",
|
|
"gt_answers": "1 \\times ( - 3 ) = \\frac { c } { a }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5891.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 3x9 - 21.",
|
|
"gt_answers": "\\frac { 3 } { 7 } \\times 9 = \\frac { 2 7 } { 6 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5892.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)\n\nThe formula is written using the LaTeX equation editor, which is a standard notation for mathematical expressions.",
|
|
"gt_answers": "x - \\frac { 1 } { 2 } [ \\frac { 1 } { 2 } x - \\frac { 1 } { 2 } ] = \\frac { 2 } { 3 } x + \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5893.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Korean, and it is not possible to provide a LaTeX representation of it without knowing the exact Korean characters. However, the image shows a mathematical formula with a few numbers and letters, which could be a representation of a mathematical expression in any language.",
|
|
"gt_answers": "\\frac { x + 1 } { 2 } - \\frac { 3 x - 1 } { 4 } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5894.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = c^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is represented by the letter \"c,\" the side opposite the right angle is represented by \"a,\" and the side adjacent to the right angle is represented by \"b.\"",
|
|
"gt_answers": "x _ { 1 } = \\frac { \\sqrt { 3 a + 3 } } { a + 1 } , x _ { 2 } = - \\frac { \\sqrt { 3 a + 3 } } { a + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5895.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{x} + \\frac{1}{x^2} + \\frac{1}{x^3} = \\frac{1}{x} + \\frac{1}{x^2} + \\frac{1}{x^3} + \\frac{1}{x^4} + \\frac{1}{x^5} + \\frac{1}{x^6} + \\frac{1}{x^7} + \\frac{1}{x^8} + \\frac{1}{x^9} + \\frac{1}{x^{10}} + \\frac{1}{x^{11}} + \\frac{1}{x^{12}} + \\frac{1}{x^{13}} + \\frac{1}{x^{14}} + \\frac{1}{x^{15}} + \\frac{1}{x^{16}} + \\frac{1}{x^{17}} + \\frac{1}{x^{18}} + \\frac{1}{x^{19}} + \\frac{1}{x^{20}} + \\frac{1}{x^{21}} + \\frac{1}{x^{22}} + \\frac{1}{x^{23}} + \\frac{1}{x^{24}} + \\frac{1}{x^{25}} + \\frac{1}{x^{26}} + \\frac{1}{x^{27}} + \\frac{1}{x^{28}} + \\frac{1}{x^{29}} + \\frac{1}{x^{30}} + \\frac{1}{x^{31}} + \\frac{1}{x^{32}} + \\frac{1}{x^{33}} + \\frac{1}{x^{34}} + \\frac{1}{x^{35}} + \\frac{1}{x^{36}} + \\frac{1}{x^{37}} + \\frac{1}{x^{38}} + \\frac{1}{x^{39}} + \\frac{1}{x^{40}} + \\frac{1}{x^{41}} + \\frac{1}{x^{42}} + \\frac{1}{x^{43}} +",
|
|
"gt_answers": "\\frac { x + 1 } { ( x + 1 ) ( x - 1 ) } - \\frac { 1 } { 3 x } = \\frac { 1 } { 3 ( x - 1 ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5896.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"S(s-a) = S(s-b) + S(a-b).\"",
|
|
"gt_answers": "S _ { \\Delta } A C B = \\frac { 1 } { 2 } \\cdot A C \\cdot C B\n",
|
|
"image_path": "./data/HME100K/test_images/test_5897.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 60/4 + 3cm = 33cm.",
|
|
"gt_answers": "6 0 \\div 4 \\div 5 = 3 ( c m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5898.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(A + B + C = 3\\)",
|
|
"gt_answers": "\\frac { 1 } { a } + = \\frac { 1 } { b } = \\frac { 1 } { c } = \\frac { 1 } { 6 \\sqrt { 3 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5899.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(29.669 \\times 26.286 = 799.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
|
|
"gt_answers": "2 9 6 - 2 6 . 8 = 2 6 9 . 2 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5900.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1.54 x 1.75 x 1.01 x 1.54 x 1.75 x 1.01.",
|
|
"gt_answers": "1 . 5 x + 1 = 1 . 5 \\times 1 0 2 + 1 = 1 5 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5902.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x + 2 = 10.\"",
|
|
"gt_answers": "t = \\frac { 5 \\sqrt { 3 } } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5903.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: sin(9) = 3/5.",
|
|
"gt_answers": "\\sin \\theta = \\frac { y } { r } = - \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5904.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Japanese characters, so it is not possible to write it out in LaTeX format. However, the image shows a mathematical formula with a negative sign in front of the expression, which is typically written as `-x`.",
|
|
"gt_answers": "x = \\frac { 5 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5905.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(f(x) = \\frac{x^2 + y^2}{2} + 3xy + 4\\)",
|
|
"gt_answers": "6 0 y + 1 5 y + 1 5 0 = 2 y ^ { 2 } + 2 0 y\n",
|
|
"image_path": "./data/HME100K/test_images/test_5907.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows: `280 cm^2 = 280 cm^2`.",
|
|
"gt_answers": "( 1 0 \\times 5 + 1 0 \\times 6 + 5 \\times 6 ) \\times 2 = 2 8 0 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5908.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "F = P S = 2 . 7 \\times 1 0 ^ { 3 } P a \\times 1 \\times 1 0 ^ { 3 } m ^ { 2 } = 1 . 7 N \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_5909.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `2x + 3 = 47 - 13`.",
|
|
"gt_answers": "\\frac { 1 } { 2 } x = 4 7 - 1 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5910.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = \\frac{1}{2} \\left( \\frac{1}{x} + \\frac{1}{x^2} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^3} + \\frac{1}{x^4} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^5} + \\frac{1}{x^6} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^7} + \\frac{1}{x^8} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^9} + \\frac{1}{x^{10}} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^{11}} + \\frac{1}{x^{12}} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^{13}} + \\frac{1}{x^{14}} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^{15}} + \\frac{1}{x^{16}} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^{17}} + \\frac{1}{x^{18}} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^{19}} + \\frac{1}{x^{20}} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^{21}} + \\frac{1}{x^{22}} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^{23}} + \\frac{1}{x^{24}} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^{25}} + \\frac{1}{x^{26}} \\right) + \\frac{1}{2} \\left( \\frac{1}{x^{27}} + \\frac{1}{x^{28}} \\right) + \\frac{1}{2} \\left(",
|
|
"gt_answers": "f ( x ) _ { \\min } = f ( \\frac { 1 } { \\sqrt { 2 a } } ) = \\frac { 1 } { 2 } - \\ln ( \\frac { 1 } { \\sqrt { 2 a } } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5911.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, and it is not possible to accurately transcribe it using LaTeX. However, the image shows a mathematical formula with a circle and a triangle, which could be related to trigonometry or geometry.",
|
|
"gt_answers": "\\frac { 4 } { 5 } \\textcircled { > } \\frac { 5 } { 7 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5913.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"9x + 3 = 12.\"",
|
|
"gt_answers": "9 \\times \\frac { 1 } { 3 } = 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5914.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x + 1 = 3.",
|
|
"gt_answers": "3 - \\frac { 2 x - 1 } { 5 } = \\frac { x + 1 } { \\cdot 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5915.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 16x20 - 10x10 - 20x10 - 10x10 - 16x20.",
|
|
"gt_answers": "7 0 \\times 1 6 + 1 2 0 0 = 2 3 2 0 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5916.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"19x2 + 4 = 100\".",
|
|
"gt_answers": "y = - \\frac { 1 9 } { 2 } \\times \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5918.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "\\{ a \\vert 0 < a < 1 r i g h t \\}\n",
|
|
"image_path": "./data/HME100K/test_images/test_5920.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "6 \\times \\frac { 1 } { 4 } T = 2 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5921.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(SABBACBADDE4\\)",
|
|
"gt_answers": "S _ { \\Delta A B C } = \\frac { 1 } { 2 } \\times B C \\times A D = 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5922.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\na^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 + h^2 + i^2 + j^2 + k^2 + l^2 + m^2 + n^2 + o^2 + p^2 + q^2 + r^2 + s^2 + t^2 + u^2 + v^2 + w^2 + x^2 + y^2 + z^2 = 100\n\\end{aligned}\n\\end{equation}\n\nThis equation represents the sum of the squares of the first 20 natural numbers, which is equal to 100.",
|
|
"gt_answers": "a ^ { 2 } + b ^ { 2 } \\geqslant \\frac { ( a + b ) ^ { 2 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5923.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "3 0 \\times 1 0 = 3 0 0 ( c m ^ { 3 } ) = 3 0 0 ( m L\n",
|
|
"image_path": "./data/HME100K/test_images/test_5924.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(L_a = 40 \\text{ cm} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2",
|
|
"gt_answers": "a = 1 2 0 ^ { \\circ } \\angle A O C = 4 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5925.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 5\\)",
|
|
"gt_answers": "3 x + 1 = 5 x - 4 + 2 \\sqrt { 5 x - 4 } + 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5926.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3x^2 + 2x - 1 = 0\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x = \\frac { 7 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5927.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 2y = 10.\"",
|
|
"gt_answers": "1 = \\frac { 2 } { \\frac { 1 } { V _ { 1 } } + \\frac { 1 } { V _ { 2 } } } = \\frac { 2 V _ { 1 } V _ { 2 } } { V _ { 1 } + v _ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5928.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\times 2^{20} \\",
|
|
"gt_answers": "1 0 \\times 5 \\times 2 + 6 \\times 5 \\times 2 + 1 0 \\times 6 \\times 2 = 2 8 0 ( c m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5929.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as `x^2 + 40x + 5 = 0`.",
|
|
"gt_answers": "x = 4 0 \\times \\frac { 8 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5930.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a negative sign in front of a number, which is a common feature of many mathematical expressions.",
|
|
"gt_answers": "\\frac { 3 } { 1 6 } + \\frac { 5 } { 1 6 } - \\frac { 1 } { 1 6 } = \\frac { 7 } { 1 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5931.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "[ \\frac { 1 } { 5 } ( \\frac { x + 2 } { 3 } + 4 ) + 6 ] + 5 6 = 6 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5932.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Kababefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabefcabef",
|
|
"gt_answers": "\\Delta A B E \\cong \\Delta B C F ( A S A )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5933.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis is a linear equation in two variables, where x and y represent the unknown quantities. The equation states that the sum of the products of x and y is equal to 10.",
|
|
"gt_answers": "\\angle C = \\pi - \\frac { \\pi } { 3 } - \\frac { \\pi } { 4 } = \\frac { 5 } { 1 2 } \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_5934.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(y = 3x^2 + 2x + 1\\)",
|
|
"gt_answers": "y = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5938.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n2(x + 15) = 30\n\nThe formula is written using the LaTeX math notation, which is a standard way of writing mathematical expressions in a text document.",
|
|
"gt_answers": "\\frac { 2 } { C _ { 6 } ^ { 2 } } = \\frac { 2 } { 1 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5939.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(E = mc^2\\)\n\nThis formula is the famous equation of mass-energy equivalence, which states that the energy (E) of an object is equal to its mass (m) multiplied by the speed of light squared (c^2).",
|
|
"gt_answers": "u _ { 1 } = u - u _ { 2 } = 6 V - 2 V = 4 V\n",
|
|
"image_path": "./data/HME100K/test_images/test_5941.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as follows:\n\n\\(x^2 + y^2 = m^2 + 4xy + 4y^2\\)\n\nThis formula can be written in LaTeX as follows:\n\n\\(x^2 + y^2 = m^2 + 4xy + 4y^2\\)\n\nThe LaTeX code for the formula is as follows:\n\n\\begin{equation}\nx^2 + y^2 = m^2 + 4xy + 4y^2\n\\end{equation}",
|
|
"gt_answers": "x _ { 1 } = \\frac { \\sqrt { m ^ { 2 } + 1 } } { m ^ { 2 } + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5943.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + 2x + 3 = 5\\)\n\nThis is a quadratic equation in the variable x.",
|
|
"gt_answers": "x _ { 1 } = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5944.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}\n\\end{equation}\n\nThis is a simple algebraic expression that represents the multiplication of two fractions, each with a denominator of 2. The result is a fraction with a denominator of 4.",
|
|
"gt_answers": "A C / / B D\n",
|
|
"image_path": "./data/HME100K/test_images/test_5945.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 24 - 33 + 44 = 117.",
|
|
"gt_answers": "\\frac { 2 4 } { 3 2 } = \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5946.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(k_b = \\frac{1}{298.15 \\times 10^3 \\times T} \\times \\left( \\frac{V_m}{R} \\right)^2 \\times \\left( \\frac{P_m}{R} \\right) \\times \\left( \\frac{T_m}{R} \\right) \\times \\left( \\frac{T_m}{T} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right) \\times \\left( \\frac{T_m}{T_0} \\right)",
|
|
"gt_answers": "\\frac { 3 1 } { 3 } k = - \\frac { 2 9 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5947.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 60x - 20.",
|
|
"gt_answers": "\\frac { 1 } { x + y } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5948.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 3 = 0\\)",
|
|
"gt_answers": "( x + 3 + x ) ^ { 2 } - ( 2 x + 3 + x ) = 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5949.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\therefore x = - \\frac { b } { 2 a } = - \\frac { \\frac { 3 } { 2 } } { - 1 } = \\frac { 3 } { 2 . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5951.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\pi r^2 = 1256 cm^2\\)",
|
|
"gt_answers": "1 6 4 c m ^ { 3 } = \\overline { 1 2 5 6 ( c m } ^ { 3 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5952.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(x^2 + y^2 = 100\\)\n\nThis formula represents the relationship between the x and y coordinates of a point on a circle, where the circle has a radius of 100 units.",
|
|
"gt_answers": "\\sin \\angle A x = \\frac { 2 } { 5 } \\sqrt { 5 } = \\frac { C H } { O C }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5953.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(f(x) = \\frac{x^2 + 2x + 1}{x^2 - 2x + 1}\\)",
|
|
"gt_answers": "f ^ { \\prime } ( x ) = 2 a x - \\frac { 1 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5954.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m = \\frac{4}{3} \\left( \\frac{n}{2} \\right)^2 + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\left( \\frac{n}{2} \\right) + \\frac{4}{3} \\",
|
|
"gt_answers": "( m + n ) ^ { 2 } - 4 m n = ( m - n ) ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5955.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3x^2 + 2x + 1}{x^2 + 2x + 1} = \\frac{3",
|
|
"gt_answers": "y = \\frac { 1 } { 3 } x ^ { 2 } + \\frac { 3 } { 3 } x - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_5956.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The formula in the image is written as:\n\n\\(BdA = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { G F } { B D } = \\frac { A F } { A D . }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5957.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(3x^2 + 5x - 6 = 0\\)",
|
|
"gt_answers": "( 5 ) \\frac { 3 } { 5 } - x = \\frac { 1 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5958.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "\\frac { 1 } { 2 } : \\frac { 2 } { 7 } = \\frac { 2 } { 3 } : x\n",
|
|
"image_path": "./data/HME100K/test_images/test_5960.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\pi r^2 = 4\\pi r^2 - 2\\pi r^2 \\cos(2\\theta)\\)",
|
|
"gt_answers": "\\angle D A E = 1 0 8 ^ { \\circ } - 7 2 ^ { \\circ } = 3 6 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5961.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, so it is not possible to provide a LaTeX representation of it. However, the image shows a mathematical formula with a negative sign in front of a number, which could be a negative exponent or a negative number.",
|
|
"gt_answers": "t = \\frac { 3 2 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5963.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1/",
|
|
"gt_answers": "\\frac { 1 \\times 5 } { 5 \\times 5 } = \\frac { 5 } { 2 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5964.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "x _ { 2 } = \\frac { - 1 - \\sqrt { 5 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5965.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 13\\)",
|
|
"gt_answers": "x = \\frac { 2 } { 1 3 } \\div 4\n",
|
|
"image_path": "./data/HME100K/test_images/test_5966.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x _ { 1 } = - \\frac { \\sqrt { 2 b + 2 } } { b + 1 } , x _ { 2 } = \\frac { \\sqrt { 2 b + 2 } } { b + 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5967.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2^{2x} + 2^{2x-1} + 2^{2x-2} + 2^{2x-3} + 2^{2x-4} + 2^{2x-5} + 2^{2x-6} + 2^{2x-7} + 2^{2x-8} + 2^{2x-9} + 2^{2x-10} + 2^{2x-11} + 2^{2x-12} + 2^{2x-13} + 2^{2x-14} + 2^{2x-15} + 2^{2x-16} + 2^{2x-17} + 2^{2x-18} + 2^{2x-19} + 2^{2x-20} + 2^{2x-21} + 2^{2x-22} + 2^{2x-23} + 2^{2x-24} + 2^{2x-25} + 2^{2x-26} + 2^{2x-27} + 2^{2x-28} + 2^{2x-29} + 2^{2x-30} + 2^{2x-31} + 2^{2x-32} + 2^{2x-33} + 2^{2x-34} + 2^{2x-35} + 2^{2x-36} + 2^{2x-37} + 2^{2x-38} + 2^{2x-39} + 2^{2x-40} + 2^{2x-41} + 2^{2x-42} + 2^{2x-43} + 2^{2x-44} + 2^{2x-45} + 2^{2x-46} + 2^{2x-47} + 2^{2x-48} + 2^{2x-49} + 2^{2x-5",
|
|
"gt_answers": "2 + 3 + ( - 1 ) + 0 + ( - 3 ) + 1 + ( - 2 ) + 3 + 2 + 3 = 8\n",
|
|
"image_path": "./data/HME100K/test_images/test_5968.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x + 4 = 12\\)",
|
|
"gt_answers": "3 2 5 - 1 8 7 . 5 \\div ( 1 2 5 - 7 5 ) = 2 . 7 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5969.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(3x + 2y = 10\\)\n\nThis is a linear equation in two variables, where the variables are x and y. The equation states that the sum of the products of x and y is equal to 10.",
|
|
"gt_answers": "x = \\frac { 1 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5970.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2(x + 1) - 3(x - 2) = 0.",
|
|
"gt_answers": "y _ { 3 } = \\frac { 2 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5971.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the LaTeX formula notation. The formula is:\n\n\\(500 - 914 + 1366 = 1970\\)",
|
|
"gt_answers": "5 0 0 - 9 = 4 9 1 4 9 1 \\times 1 5 = 7 3 6 5\n",
|
|
"image_path": "./data/HME100K/test_images/test_5972.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Lang-LMBc\".",
|
|
"gt_answers": "\\angle A N C = \\angle M B C (\n",
|
|
"image_path": "./data/HME100K/test_images/test_5973.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(e^{x} = \\sum_{n=0}^{\\infty} \\frac{x^n}{n!} \\tag{1}\\\\)\n\nThis formula represents the exponential function, which is a special case of the power function. It is a continuous function that maps the real number line to the real number line, and it is defined as the limit of the sequence of powers of a real number x. The power function is defined as \\(f(x) = x^n\\) for any positive integer n, and the exponential function is defined as \\(f(x) = e^x\\) for any real number x.\n\nIn the image, the expression is written using the summation symbol \\(\\sum\\) to represent the infinite sum of the powers of x, and the factorial symbol \\(n!\\) is used to represent the factorial of the integer n. The summation symbol is followed by the variable x, and the factorial symbol is followed by the variable n. The expression is then written in the form of an equation, with the equal sign between the two terms.",
|
|
"gt_answers": "x _ { 1 } = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5974.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"H2O + 326.04 g/mol = 2H2O + 4 g/mol.\"",
|
|
"gt_answers": "\\Delta H = 3 2 6 0 . 4 k J / m o l\n",
|
|
"image_path": "./data/HME100K/test_images/test_5975.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(a^2 + b^2 = c^2\\)",
|
|
"gt_answers": "\\frac { 1 } { a - 1 } + \\frac { 1 } { a ^ { 2 } - 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5977.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as:\n\n\\(x^2 + 5x + 10 = 15x + 10\\)\n\nThis formula can be rewritten as:\n\n\\(x^2 + 5x + 10 = (x + 5)(x + 1)\\)\n\nThe formula can also be written as:\n\n\\(x^2 + 5x + 10 = (x + 5)(x + 1) = x^2 + 5x + 10 + 5x + 10 = 2x^2 + 15x + 10\\)\n\nThis formula can be simplified further by factoring out the common factor of (x + 5) from both sides of the equation:\n\n\\(x^2 + 5x + 10 = (x + 5)(x + 1) = (x + 5)(x + 1) = x^2 + 5x + 10 + 5x + 10 = 2x^2 + 15x + 10\\)\n\nThis simplified formula can be written as:\n\n\\(x^2 + 5x + 10 = 2x^2 + 15x + 10\\)\n\nThe formula can also be written as:\n\n\\(x^2 + 5x + 10 = 2x^2 + 15x + 10 = 2x^2 + 15x + 10 = 2x^2 + 15x + 10\\)\n\nThis formula can be written as:\n\n\\(x^2 + 5x + 10 = 2x^2 + 15x + 10 = 2x^2 + 15x + 10 = 2x^2 + 15x + 10\\)\n\nThis formula can be written as:\n\n\\(x^2 + 5x + 10 = 2x^2 + 15x + 10 = 2x^2 + 15x + 10 = 2x^2 + 15x + 10\\)\n\nThis formula can be written as",
|
|
"gt_answers": "\\frac { x + 1 } { x ( x - 1 ) } - \\frac { 1 } { 3 x } = \\frac { x + 5 } { 3 ( x - 1 ) }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5978.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2x^2 + 3x - 4 = 0\\)",
|
|
"gt_answers": "w = \\frac { 3 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5979.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "( a + b ) \\times c = a \\times c + b \\times c\n",
|
|
"image_path": "./data/HME100K/test_images/test_5980.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 2H2O + CO2 = CaCO3 + H2O.",
|
|
"gt_answers": "C a 0 + H _ { 2 } O = C a ( O H ) _ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5981.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2x^2 + 3x + 4 = 0.",
|
|
"gt_answers": "\\sqrt { 4 \\frac { 2 } { 3 } } = 2 \\sqrt { \\frac { 2 } { 3 } } = 2 \\sqrt { \\frac { 2 \\times 3 } { 3 \\times 3 } } = 2 \\sqrt { \\frac { 6 } { 9 } } = 6 \\sqrt { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5982.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m_1^2 + m_2^2 = m_1^2 + m_2^2 + 2m_1m_2\\cdot\\cos(90^\\circ - \\theta)\\)\n\nThis formula is used to calculate the sum of the squares of two masses, where the angle between them is given by theta.",
|
|
"gt_answers": "m ^ { 2 } + ( - \\frac { 2 } { 3 } m + 3 ) ^ { 2 } = 9\n",
|
|
"image_path": "./data/HME100K/test_images/test_5983.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "3 \\times 1 x < - 1 , . x > 2 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5984.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: AD = AG + CF.",
|
|
"gt_answers": "\\frac { A D } { D G } = \\frac { A F } { C F }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5985.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ln(400) - Ln(40) = 360\".",
|
|
"gt_answers": "4 x ^ { 2 } + 1 8 x + 9 - 2 x - 3 - x = 4 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5986.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "2 5 V + 3 V = 6 . 7 5 V\n",
|
|
"image_path": "./data/HME100K/test_images/test_5987.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as Fi = 3000N.",
|
|
"gt_answers": "F _ { 1 } = 3 0 0 N\n",
|
|
"image_path": "./data/HME100K/test_images/test_5989.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "\\frac { 1 } { x - y } = b\n",
|
|
"image_path": "./data/HME100K/test_images/test_5990.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1}{2} \\cdot \\left( \\frac{1",
|
|
"gt_answers": "0 2 3 < 1 0 3 2 < 1 2 0 3 < 1 2 3 0 < 1 3 0 2 < 1 3 7 0 < 2 0 1 3 < 2 0 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_5992.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 3x + 4 = 10\\)",
|
|
"gt_answers": "3 . x > 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_5993.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2x + 5y = 400.",
|
|
"gt_answers": "\\frac { 2 \\times 4 5 + x ( 4 5 + 5 5 ) = 4 0 0 } { 1 0 0 x = 3 1 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5994.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{b^2}{a^2} + \\frac{c^2}{b^2} + \\frac{d^2}{c^2} = 1\n\\end{equation}\n\nThis equation represents the Pythagorean theorem, which states that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the hypotenuse.",
|
|
"gt_answers": "b ^ { 2 } - 4 a c = ( k + 4 ) ^ { 2 } - 4 \\times 1 \\times ( - 1 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_5995.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2a^2 + b^2 = c^2.\"",
|
|
"gt_answers": "2 a + b = \\frac { 7 } { 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5997.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"0.02222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222",
|
|
"gt_answers": "0 x = 1 y = \\pm 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_5998.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(2x^2 + 3x + 4 = 10\\)\n\nThis is a quadratic equation in the variable x, with the coefficients 2, 3, and 4. The solution to this equation is x = 5.",
|
|
"gt_answers": "\\frac { x } { 1 5 } = \\frac { 1 . 5 } { 0 . 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_5999.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + 2x + 1 = 0\\)",
|
|
"gt_answers": "0 . 5 2 8 + 1 . 4 7 2 = 2 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_6000.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"JT + \u03c0 = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821484810973749673362491475866923437593259480732427752699882073716793176637938183593751055527487093856482114527372456730917936563781835277742643383279502884197169399375105820974944592307816406286208998628034825342117067982148481097374967336249147586692343759325948073242775269988207371679317663793818359375105552748709385648211452737245673091793656378183527774264338327950288419716939937510582",
|
|
"gt_answers": "\\pi + \\sqrt { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6001.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"U(x) = 1/2 x^2 + 1/4 x^4 + 1/8 x^6 + 1/16 x^8 + 1/32 x^10 + 1/64 x^12 + 1/128 x^14 + 1/256 x^16 + 1/512 x^18 + 1/1024 x^20 + 1/2048 x^22 + 1/4096 x^24 + 1/8192 x^26 + 1/16384 x^28 + 1/32768 x^30 + 1/65536 x^32 + 1/131072 x^34 + 1/262144 x^36 + 1/524288 x^38 + 1/1048576 x^40 + 1/2097152 x^42 + 1/4194304 x^44 + 1/8388608 x^46 + 1/16777216 x^48 + 1/33554432 x^50 + 1/67108864 x^52 + 1/134217728 x^54 + 1/268435456 x^56 + 1/536870912 x^58 + 1/1073741824 x^60 + 1/2147483648 x^62 + 1/4294967296 x^64 + 1/8589934592 x^66 + 1/17179565600 x^68 + 1/34359736968 x^70 + 1/6871947673",
|
|
"gt_answers": "u = \\frac { 1 } { x \\div y }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6002.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\sqrt{2} = 2\\sqrt{\\sqrt{2}\\sqrt{2}} = 2\\sqrt{2^2} = 2\\sqrt{4} = 2 \\times 2 = 4\\)",
|
|
"gt_answers": "1 0 = \\frac { 1 } { 2 } \\cdot \\sqrt { 5 0 } \\cdot h\n",
|
|
"image_path": "./data/HME100K/test_images/test_6004.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Cn + Cl = Ca + b mol L.\"",
|
|
"gt_answers": "C _ { ( N a ^ { + } ) } = C _ { ( A ^ { - } ) } = \\frac { b } { 2 } m o l / L\n",
|
|
"image_path": "./data/HME100K/test_images/test_6005.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(5 \\times 4a = 20a\\)\n\nThe formula is written using the LaTeX equation editor, which is a standard notation for mathematical expressions. The equation consists of the variables 5, 4, and a, and the operator \"times\" (multiplication). The result of the multiplication is 20a, which is the desired answer.",
|
|
"gt_answers": "= - \\frac { 5 } { 4 } a\n",
|
|
"image_path": "./data/HME100K/test_images/test_6007.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows:\n\n\\(O_B = O_A + O_B\\)\n\nThis formula represents the relationship between the output (O) of a system and the output (O) of another system. The subscripts A and B refer to the two systems. The equation states that the output of the second system is equal to the sum of the outputs of the first and second systems.",
|
|
"gt_answers": "\\frac { O B \\cdot Q I } { 2 } = O B \\cdot O A\n",
|
|
"image_path": "./data/HME100K/test_images/test_6008.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"4a^2 = 4a^4.\"",
|
|
"gt_answers": "9 + a ^ { 2 } = 4 a ^ { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6009.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"x^2 + 2x + 1 = 0.\"",
|
|
"gt_answers": "x _ { 1 } = \\frac { 1 } { b }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6010.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "\\frac { b } { a } = \\frac { 2 - 9 } { a } \\times \\frac { 2 } { 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6011.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 0\\)",
|
|
"gt_answers": "( 2 x + y ) ( x - 3 y ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_6012.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1",
|
|
"gt_answers": "( x - \\frac { 2 - \\sqrt { 6 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6013.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "x + \\frac { \\pi } { 4 } = \\frac { 2 } { 4 } + 2 k \\pi\n",
|
|
"image_path": "./data/HME100K/test_images/test_6014.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ci-Pi-P3\" using the LaTeX formula notation.",
|
|
"gt_answers": "( 1 - P ) ^ { 7 } p ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6016.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"44-B\".",
|
|
"gt_answers": "4 4 \u3001 B\n",
|
|
"image_path": "./data/HME100K/test_images/test_6017.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(5\\times 6 + 7\\times 8 + 9\\times 10 + 11\\times 12 + 12\\times 13 + 13\\times 14 + 14\\times 15 + 15\\times 16 + 16\\times 17 + 17\\times 18 + 18\\times 19 + 19\\times 20 + 20\\times 21 + 21\\times 22 + 22\\times 23 + 23\\times 24 + 24\\times 25 + 25\\times 26 + 26\\times 27 + 27\\times 28 + 28\\times 29 + 29\\times 30 + 30\\times 31 + 31\\times 32 + 32\\times 33 + 33\\times 34 + 34\\times 35 + 35\\times 36 + 36\\times 37 + 37\\times 38 + 38\\times 39 + 39\\times 40 + 40\\times 41 + 41\\times 42 + 42\\times 43 + 43\\times 44 + 44\\times 45 + 45\\times 46 + 46\\times 47 + 47\\times 48 + 48\\times 49 + 49\\times 50 + 50\\times 51 + 51\\times 52 + 52\\times 53 + 53\\times 54 + 54\\times 55 + 55\\times 56 + 56\\times 57 + 57\\times 58 + 58\\times 59 + 59\\times 60 + 60\\times 61 + 61\\times 62 + 62\\times 63 + 63\\times",
|
|
"gt_answers": "\\frac { ( 5 + 6 ) ( 5 - 6 ) } { 5 + 6 } + \\cdots +\n",
|
|
"image_path": "./data/HME100K/test_images/test_6019.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: AC = BC - 2.",
|
|
"gt_answers": "\\frac { A C } { B C } = 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_6021.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + y^2 = 1\\)",
|
|
"gt_answers": "0 = 1 - \\frac { m x } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6023.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 17000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
|
"gt_answers": "= ( 1 9 6 0 P a - 1 0 1 8 p a ) \\times \\frac { 4 k g } { 1 9 6 0 P a } = 1 . 8 k g\n",
|
|
"image_path": "./data/HME100K/test_images/test_6025.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 120 - 96 = 24.",
|
|
"gt_answers": "\\frac { 3 } { 4 } \\cdot 1 2 0 = 9 0 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6026.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: \"I = 1/2 (a + b)2 - 3ab + c2.\"",
|
|
"gt_answers": "A E + D E = \\frac { 1 } { 2 } C \\Delta A B E = 3 5 ( m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_6028.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ACLBGACBC90m\".",
|
|
"gt_answers": "A C \\bot B C \\therefore A C = \\sqrt { A B ^ { 2 } - B C ^ { 2 } } = 9 c m\n",
|
|
"image_path": "./data/HME100K/test_images/test_6029.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3A-4\".",
|
|
"gt_answers": "3 a = - \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6030.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{2x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{2x^2 + 3x + 4}{x^2 + 2x + 3}\n\\end{equation}\n\nThis is a simple algebraic equation that can be solved by factoring out the common factor of \"x^2 + 2x + 3\" from both sides of the equation. The result is:\n\n\\begin{equation}\n\\frac{2x^2 + 3x + 4}{x^2 + 2x + 3} = \\frac{2x^2 + 3x + 4}{x^2 + 2x + 3}\n\\end{equation}\n\nThis is the same expression as the original equation.",
|
|
"gt_answers": "\\frac { 5 - 4 y } { 2 } x ^ { 2 } + 1 \\times 2 = - 2 \\times 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_6032.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is given as follows:\n\n\\(y = \\frac{1}{2} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac{1}{4} \\left( \\frac",
|
|
"gt_answers": "b ^ { 2 } + c ^ { 2 } = 4 ^ { 2 } + 5 ^ { 2 } = ( \\sqrt { 4 1 } ) ^ { 2 } = a ^ { 2 } .\n",
|
|
"image_path": "./data/HME100K/test_images/test_6033.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} + \\frac{1}{32} + \\frac{1}{64} + \\frac{1}{128} + \\frac{1}{256} + \\frac{1}{512} + \\frac{1}{1024} + \\frac{1}{2048} + \\frac{1}{4096} + \\frac{1}{8192} + \\frac{1}{16384} + \\frac{1}{32768} + \\frac{1}{65536} + \\frac{1}{131072} + \\frac{1}{262144} + \\frac{1}{524288} + \\frac{1}{1048576} + \\frac{1}{2097152} + \\frac{1}{4194304} + \\frac{1}{8388608} + \\frac{1}{16777216} + \\frac{1}{33554432} + \\frac{1}{67108864} + \\frac{1}{134217728} + \\frac{1}{268435456} + \\frac{1}{536870912} + \\frac{1}{1073741824} + \\frac{1}{2147483648} + \\frac{1}{4294967296} + \\frac{1}{8589934592} + \\frac{1}{17179869184} + \\frac{1}{34359738368} + \\frac{1}{68719476736} + \\frac{",
|
|
"gt_answers": "\\vert - 4 \\vert + \\vert + 7 \\vert + \\vert - 9 \\vert + \\vert + 8 \\vert + \\vert + 6 \\vert + \\vert - 4 \\vert + \\vert - 3 \\vert = 4 \\vert ( k m )\n",
|
|
"image_path": "./data/HME100K/test_images/test_6034.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"LPAPE-LAPRPB\".",
|
|
"gt_answers": "\\angle P A C = \\angle A P B + \\angle P B D\n",
|
|
"image_path": "./data/HME100K/test_images/test_6035.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(LORB = \\frac{L}{D} \\cdot AQQ\\)\n\nThe formula is a ratio of the length of the line (L) to the diameter of the circle (D) multiplied by the area of the circle (AQQ).",
|
|
"gt_answers": "\\therefore \\angle O Q A = \\angle O C A Q = 6 2 ^ { \\circ }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6036.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(23\\text{e-3} \\cdot 3600 \\cdot 60 \\cdot 60 \\cdot 24 \\cdot 365 = 1.08648 \\times 10^{18}\\)",
|
|
"gt_answers": "x = \\frac { 2 3 - 3 P ^ { 1 } } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6037.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: 24/44 = 5/9.",
|
|
"gt_answers": "y = \\frac { 4 } { x }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6039.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3 = 5\" in LaTeX format.",
|
|
"gt_answers": "= \\frac { 1 } { 2 } A O \\cdot C M\n",
|
|
"image_path": "./data/HME100K/test_images/test_6040.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in the form of a mathematical formula, which is a combination of letters, numbers, and symbols. The formula is written in a black box, and the letters and numbers are written in a white font. The formula is likely a mathematical equation or a formula for calculating a value.",
|
|
"gt_answers": "( 3 ) p \\frac { 1 } { 5 } \\times p _ { 6 } ^ { 6 } = 5 \\times 6 \\times 5 \\times 4 \\times 1 \\times 2 \\times 1 = 3 6 0 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_6041.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"Ez a ZnE\" in the Hungarian language.",
|
|
"gt_answers": "e \\geq \\frac { c } { a } \\geq \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6042.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as follows: 2(x + y) - 2(x - y) = 0.",
|
|
"gt_answers": "y ^ { 2 } - 2 0 y + 1 0 0 - 4 y - 2 0 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_6043.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(m\\cdot s^2\\cdot h^2\\cdot d^2\\)",
|
|
"gt_answers": "N a _ { 2 } C O _ { 3 } + H _ { 2 } S O _ { 4 } = N a _ { 2 } S O _ { 4 } + H _ { 2 } O + C O _ { 3 } \\uparrow\n",
|
|
"image_path": "./data/HME100K/test_images/test_6044.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 700\\)",
|
|
"gt_answers": "h ( x ) = \\frac { 2 I n x } { x ^ { 2 } } ( x > 0 )\n",
|
|
"image_path": "./data/HME100K/test_images/test_6045.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 3x2.133333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
|
|
"gt_answers": "x \\div 3 \\times 3 = 2 . 1 \\times 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_6049.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 200 - 200/200 = 0.",
|
|
"gt_answers": "\\frac { 1 0 } { 2 0 0 } = \\frac { 1 } { 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6050.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(A = \\frac{4}{3} \\cdot \\frac{3}{4} \\cdot \\frac{4}{5} \\cdot \\frac{5}{6} \\cdot \\frac{6}{7} \\cdot \\frac{7}{8} \\cdot \\frac{8}{9} \\cdot \\frac{9}{10} \\cdot \\frac{10}{11} \\cdot \\frac{11}{12} \\cdot \\frac{12}{13} \\cdot \\frac{13}{14} \\cdot \\frac{14}{15} \\cdot \\frac{15}{16} \\cdot \\frac{16}{17} \\cdot \\frac{17}{18} \\cdot \\frac{18}{19} \\cdot \\frac{19}{20} \\cdot \\frac{20}{21} \\cdot \\frac{21}{22} \\cdot \\frac{22}{23} \\cdot \\frac{23}{24} \\cdot \\frac{24}{25} \\cdot \\frac{25}{26} \\cdot \\frac{26}{27} \\cdot \\frac{27}{28} \\cdot \\frac{28}{29} \\cdot \\frac{29}{30} \\cdot \\frac{30}{31} \\cdot \\frac{31}{32} \\cdot \\frac{32}{33} \\cdot \\frac{33}{34} \\cdot \\frac{34}{35} \\cdot \\frac{35}{36} \\cdot \\frac{36}{37} \\cdot \\frac{37}{38} \\cdot \\frac{38}{39} \\cdot \\frac{39}{40} \\cdot \\frac{40}{41} \\cdot \\frac{41}{42} \\cdot \\frac{42}{43} \\cdot \\frac{43}{44} \\cdot \\frac{44}{45} \\cdot \\frac{45}{46} \\cdot \\frac{46}{47} \\cdot \\frac{47}{48} \\cdot \\",
|
|
"gt_answers": "\\frac { a } { \\frac { \\sqrt { 7 } } { 4 } } = \\frac { c } { \\frac { 3 \\sqrt { 7 } } { 8 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6053.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\ny = 4x + 100x^2 + 40x^3 + 10x^4 + 4x^5 + 10x^6 + 4x^7 + 10x^8 + 4x^9 + 10x^{10} + 4x^{11} + 10x^{12} + 4x^{13} + 10x^{14} + 4x^{15} + 10x^{16} + 4x^{17} + 10x^{18} + 4x^{19} + 10x^{20} + 4x^{21} + 10x^{22} + 4x^{23} + 10x^{24} + 4x^{25} + 10x^{26} + 4x^{27} + 10x^{28} + 4x^{29} + 10x^{30} + 4x^{31} + 10x^{32} + 4x^{33} + 10x^{34} + 4x^{35} + 10x^{36} + 4x^{37} + 10x^{38} + 4x^{39} + 10x^{40} + 4x^{41} + 10x^{42} + 4x^{43} + 10x^{44} + 4x^{45} + 10x^{46} + 4x^{47} + 10x^{48} + 4x^{49} + 10x^{50} + 4x^{51} + 10x^{52} + 4x^{53} + 10x^{54} + 4x^{55} + 10x^{56} + 4x^{57} + 10x^{58} + 4x^{59} + 10x^{60} + 4",
|
|
"gt_answers": "y = \\frac { 3 } { 4 } + \\frac { 1 } { 4 } \\cos 4 x\n",
|
|
"image_path": "./data/HME100K/test_images/test_6054.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(x^2 + 4x + 5 = 0\\)",
|
|
"gt_answers": "x _ { 4 } = - \\sqrt { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6055.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2m - 6n = 200.\"",
|
|
"gt_answers": "2 m - 1 = 0 , n - 3 = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_6056.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"ACI BDB.\"",
|
|
"gt_answers": "A C \\bot B D\n",
|
|
"image_path": "./data/HME100K/test_images/test_6057.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"3x2 + 2x + 1 = 7\".",
|
|
"gt_answers": "3 \\sqrt { 3 } \\times 3 \\sqrt { 3 } = 2 7 ( m ^ { 2 } )\n",
|
|
"image_path": "./data/HME100K/test_images/test_6058.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(a^2 + b^2 = 1416 - 8 \\cdot 13\\)",
|
|
"gt_answers": "a ^ { 2 } = 1 + 1 6 - 8 \\times \\frac { 1 } { 2 } = 1 3\n",
|
|
"image_path": "./data/HME100K/test_images/test_6059.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"m2 + m4 = 1.\"",
|
|
"gt_answers": "m ^ { 2 } - 4 = - 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_6060.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a=a+b.",
|
|
"gt_answers": "a > \\frac { 1 } { 2 } a\n",
|
|
"image_path": "./data/HME100K/test_images/test_6061.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as: \"sapoc = 4x^2y.\"",
|
|
"gt_answers": "\\cdot S _ { \\Delta } P D C = \\frac { 1 } { 2 } \\times 4 \\times y\n",
|
|
"image_path": "./data/HME100K/test_images/test_6062.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(T = \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac",
|
|
"gt_answers": "x - 2 = - \\frac { 4 } { k }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6064.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\begin{equation}\n\\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\left(",
|
|
"gt_answers": "x ^ { 2 } - x - \\frac { 3 } { 4 } < 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_6065.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in Chinese characters, which are not supported by LaTeX. However, the image shows a mathematical formula with the letters \"x\" and \"y\" and the symbol \"=\". The formula could be written in LaTeX as follows:\n\n\\begin{equation}\nx + y = 2\n\\end{equation}\n\nThis is a simple algebraic equation that represents the addition of two numbers, where x and y are the unknown variables.",
|
|
"gt_answers": "x + \\frac { 3 } { 4 } = \\pm \\frac { 3 } { 4 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6067.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 30/20 = 1.5.",
|
|
"gt_answers": "\\frac { 3 0 + 2 0 + 1 5 } { 1 0 0 } = 6 5 \\%\n",
|
|
"image_path": "./data/HME100K/test_images/test_6069.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(y = 0.082 + 0.022x^2 + 0.008x^3 + 0.004x^4 + 0.002x^5 + 0.001x^6 + 0.0005x^7 + 0.0003x^8 + 0.0002x^9 + 0.0001x^{10} + 0.00005x^{11} + 0.0003x^{12} + 0.0002x^{13} + 0.0001x^{14} + 0.00005x^{15} + 0.0003x^{16} + 0.0002x^{17} + 0.0001x^{18} + 0.00005x^{19} + 0.0003x^{20} + 0.0002x^{21} + 0.0001x^{22} + 0.00005x^{23} + 0.0003x^{24} + 0.0002x^{25} + 0.0001x^{26} + 0.00005x^{27} + 0.0003x^{28} + 0.0002x^{29} + 0.0001x^{30} + 0.00005x^{31} + 0.0003x^{32} + 0.0002x^{33} + 0.0001x^{34} + 0.00005x^{35} + 0.0003x^{36} + 0.0002x^{37} + 0.0001x^{38} + 0.00005x^{39} + 0.0",
|
|
"gt_answers": "0 . 0 8 = 0 . 0 8 1 0 . 2 : 2 . 5 = 4 : 5 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_6070.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 1x12 + 3x13 + 1x14 = 12x13 + 3x14.",
|
|
"gt_answers": "\\frac { 7 } { 1 2 } \\times \\frac { 1 } { 3 } = \\frac { 7 \\times 1 } { 1 2 \\times 3 } = \\frac { 7 } { 3 6 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6071.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(2^{24} + 2^{25} + 2^{26} + 2^{27} + 2^{28} + 2^{29} + 2^{30} + 2^{31} + 2^{32} + 2^{33} + 2^{34} + 2^{35} + 2^{36} + 2^{37} + 2^{38} + 2^{39} + 2^{40} + 2^{41} + 2^{42} + 2^{43} + 2^{44} + 2^{45} + 2^{46} + 2^{47} + 2^{48} + 2^{49} + 2^{50} + 2^{51} + 2^{52} + 2^{53} + 2^{54} + 2^{55} + 2^{56} + 2^{57} + 2^{58} + 2^{59} + 2^{60} + 2^{61} + 2^{62} + 2^{63} + 2^{64} + 2^{65} + 2^{66} + 2^{67} + 2^{68} + 2^{69} + 2^{70} + 2^{71} + 2^{72} + 2^{73} + 2^{74} + 2^{75} + 2^{76} + 2^{77} + 2^{78} + 2^{79} + 2^{80} + 2^{81} + 2^{82} + 2^{83} + 2^{84} + 2^{85} + 2^{86} + 2^{87} + 2^{88} + 2^{89} + 2^{90} + 2^{91} + 2^{92} + 2^{93} + 2^{94",
|
|
"gt_answers": "- \\frac { 1 } { 5 } , - \\sqrt [ 3 ] { \\alpha 7 } , - 5 . 1 \\alpha 3 4 5 \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_6072.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as t^2 - 100 = 0.",
|
|
"gt_answers": "t = \\frac { n } { 1 2 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6073.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"a = 4 + 5\".",
|
|
"gt_answers": "x = \\frac { 4 } { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6074.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is:\n\n\\(m \\cdot m \\cdot m = m^3\\)",
|
|
"gt_answers": "m ^ { 2 } + m - \\frac { 3 } { 4 } = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_6075.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x",
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"gt_answers": "2 x + 1 0 0 = 2 \\times 1 2 0 0 + 1 0 0 = 2 5 0 0\n",
|
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"image_path": "./data/HME100K/test_images/test_6076.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
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"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(2\\left(10^{4} + 10^{3} + 10^{2} + 10^{1} + 10^{0}\\right) = 2\\left(10^{5} + 10^{4} + 10^{3} + 10^{2} + 10^{1}\\right) = 2\\left(10^{6} + 10^{5} + 10^{4} + 10^{3} + 10^{2}\\right)\\)",
|
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"gt_answers": "\\cos ( \\alpha + \\beta - \\alpha + \\beta ) = \\cos 2 \\beta = - \\frac { 3 } { 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6078.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(CO_2 + H_2O + O_2 = CO_2 + 2H_2O + O_2\\)\n\nThis formula represents the chemical reaction between carbon dioxide (CO2), water (H2O), and oxygen (O2) to produce carbon dioxide (CO2), water (H2O), and oxygen (O2).",
|
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"gt_answers": "C a C O _ { 3 } + 2 H C l = C a C l _ { 2 } + H _ { 2 } O + C O _ { 2 } \\uparrow \\cdot\n",
|
|
"image_path": "./data/HME100K/test_images/test_6079.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"2x + 3y = 10.\"",
|
|
"gt_answers": "b _ { 1 } + b _ { 2 } + \\cdots + b _ { n } = 2 ^ { n + 1 } - 2\n",
|
|
"image_path": "./data/HME100K/test_images/test_6081.jpg",
|
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"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as 0.025 = 32/100.",
|
|
"gt_answers": "8 \\div 0 . 2 5 = 3 2\n",
|
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"image_path": "./data/HME100K/test_images/test_6082.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(BP = \\sqrt{2 \\pi \\left( \\frac{1}{2} \\left( \\frac{1}{2} \\right) \\right)} = \\sqrt{\\frac{1}{4}} \\approx 0.707106875\\)",
|
|
"gt_answers": "B P = \\sqrt { 9 + ( 1 - y ) ^ { 2 } }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6083.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 2x + 2 = 4.",
|
|
"gt_answers": "\\frac { 8 } { 1 1 } \\div 2 \\textcircled { < } \\frac { 8 } { 1 1 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6084.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n\\(2x + 3y = 10\\)\n\nThis formula represents the relationship between two variables, x and y, where the sum of their values is equal to 10.",
|
|
"gt_answers": "\\frac { x } { 1 5 } = \\frac { 1 . 5 } { 0 . 5 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6086.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as \"BeEF = EFBe.\"",
|
|
"gt_answers": "\\frac { B E } { E F } = \\frac { E G } { B E }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6087.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(x^2 + y^2 = 25\\)",
|
|
"gt_answers": "\\overrightarrow { x } = 1 . 6 m ^ { 3 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6088.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows:\n\n(x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + 8)^(1/2) = (x^2 + 4x + ",
|
|
"gt_answers": "( x ^ { 2 } + 4 x ) ( x ^ { 2 } + 4 x + 8 ) = 0\n",
|
|
"image_path": "./data/HME100K/test_images/test_6089.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as follows: 2x3 - 12.6.",
|
|
"gt_answers": "x = \\frac { 2 . 4 \\times 3 } { 1 2 } = 0 . 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_6090.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using the chemical formula notation, which is a standard way to represent chemical compounds. The formula is written as Fe(CuSO4)3(OH)2.",
|
|
"gt_answers": "F e + C u S O _ { 4 } = F e S O _ { 4 } + C u\n",
|
|
"image_path": "./data/HME100K/test_images/test_6091.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written using LaTeX format as follows:\n\n\\(t^2 + s^2 = r^2\\)\n\nThis formula represents the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is represented by the letter \"r,\" the side opposite the right angle is represented by the letter \"t,\" and the side adjacent to the right angle is represented by the letter \"s.\"",
|
|
"gt_answers": "t = \\frac { S } { V }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6092.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as Fe2+ + Cu2+ + F- + Cl- = Fe3+ + CuCl2.",
|
|
"gt_answers": "F e + C u S O _ { 4 } = F e S O _ { 4 } + + C u\n",
|
|
"image_path": "./data/HME100K/test_images/test_6093.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(y = 2x^2 + 3x + 4\\)",
|
|
"gt_answers": "y = x \\pm \\sqrt { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6094.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in HTML format, which is not a standard mathematical notation. To write it out in LaTeX format, we can use the following code:\n\n\\begin{code}\n\\begin{equation}\n\\begin{aligned}\n\\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2}",
|
|
"gt_answers": "\\Delta = 3 6 m + 1 6\n",
|
|
"image_path": "./data/HME100K/test_images/test_6095.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression of the formula in the image is written as: 5x3 - 3x5 = 15x2.",
|
|
"gt_answers": "\\frac { 5 } { 6 } = \\frac { 5 \\times 5 } { 6 \\times 5 } = \\frac { 2 5 } { 3 0 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6096.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written as a mathematical formula using LaTeX. The formula is written in the form of a line with a negative sign (-) in front of it. The formula is followed by a line with a positive sign (+) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a negative sign (-) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a positive sign (+) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a negative sign (-) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a positive sign (+) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a negative sign (-) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a positive sign (+) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a negative sign (-) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a positive sign (+) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a negative sign (-) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a positive sign (+) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a negative sign (-) and a number. The number is written in superscript format, indicating that it is a power of 2. The formula is then followed by a line with a positive sign (+) and a number. The number is",
|
|
"gt_answers": "\\frac { C G } { A G } = 1\n",
|
|
"image_path": "./data/HME100K/test_images/test_6097.jpg",
|
|
"model_name": "mPLUG"
|
|
},
|
|
{
|
|
"question": "Please write out the expression of the formula in the image using LaTeX format.",
|
|
"answer": "The expression in the image is written in LaTeX format as follows:\n\n\\(k = \\frac{1}{2} \\pi r^2 \\mu\\)\n\nwhere `k` is the spring constant, `r` is the radius of the spring, `\u03bc` is the viscosity of the fluid, and `\u03c0` is the constant pi.",
|
|
"gt_answers": "k _ { o y } = 2 \\therefore k m _ { 3 } = - \\frac { 1 } { 2 }\n",
|
|
"image_path": "./data/HME100K/test_images/test_6098.jpg",
|
|
"model_name": "mPLUG"
|
|
}
|
|
] |