[
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by: $ $\\frac{x^2 - 5x + 4}{x - 2} = 2x - 5 + 4$ $\\frac{x - 2}{x - 2} = 1$ The image represents the quadratic formula with the coefficients of the quadratic equation, a and b, as the roots, and the constant term c as the y-intercept.",
        "gt_answers": "\\frac { 5 } { 1 4 } = \\frac { 1 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_2.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\begin{aligned} \\text{a + b} &= \\text{c}\\end{aligned}$$This equation states that the sum of `a` and `b` is equal to `c`.",
        "gt_answers": "- 2 x ^ { 4 } - x ^ { 2 } + 5 = ( - x ^ { 2 } + 1 ) ( x + a ) + b = x ^ { 2 } + a x + 3 x - 3 a - b\n",
        "image_path": "./data/HME100K/test_images/test_3.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format.\n\nThe formula is a geometric sequence with first term 2 and common ratio 5, which means that the second term is 5 times the first term, the third term is 5 times the second term, and so on. To find the 10th term in the sequence, we can use the formula:\n\nan = a1 \\* r^(n-1)\nwhere an is the nth term in the sequence, a1 is the first term, and r is the common ratio. Plugging in",
        "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",
        "image_path": "./data/HME100K/test_images/test_5.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula using LaTeX format is:\n\n$$\\frac{1}{3x^{2}+2x+1}$$\n\nWhere x is the variable.",
        "gt_answers": ": x _ { 1 } = - \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_6.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{5\\times 6}{7\\times 8}$$This can be simplified to$$\\frac{5}{7}\\times \\frac{6}{8}$$or$$\\frac{5\\times 6}{7\\times 8}= \\frac{5}{7}\\times \\frac{6}{8}= \\frac{5}{7\\times 8}= \\frac{10}{7\\times 8}= \\frac{1}{0.75}$$This is equivalent to $\\frac{1}{0.75",
        "gt_answers": "7 5 \\div ( 7 5 + 2 5 ) = 7 5 \\div 1 0 0 = 7 5 \\%\n",
        "image_path": "./data/HME100K/test_images/test_7.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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 + 2y - 3z = 10x + 4y - 6z = 10x + 6y - 9z = 10x + 2y - 3z = 10x + 2y - 3z = 10x + 4y - 6z = 10x + 6y - 9z = 10x + 2y - 3z = 10x + 2y - 3z = 10x",
        "gt_answers": "y = 3 . y = - 1\n",
        "image_path": "./data/HME100K/test_images/test_8.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the expression in the image:\n\n$$\\frac{x^2 - 4x + 3}{x - 1} = \\frac{x - 1}{x^2 - 4x + 3}$$\n\nThis is an algebraic expression that represents a rational function with the form $\\frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials with integer coefficients.",
        "gt_answers": "x _ { 1 } = - 6 x _ { 2 } = 4\n",
        "image_path": "./data/HME100K/test_images/test_9.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{5\\times 3}{2}\\times 2 = \\frac{3\\times 2}{1}\\times 2 = \\frac{6}{2} = 3$$\n\nwhere the variable `x` represents the number 2 and the constant `n` represents the number 3.",
        "gt_answers": "2 3 . 5 + \\frac { 1 } { 2 } x = 1 3 + x\n",
        "image_path": "./data/HME100K/test_images/test_10.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $x^2 + 5x - 6$.\n\nHere's how to derive it:\n\n1. Start by identifying the variable, x, and the constant terms, 5 and 6.\n2. Multiply the variable and the first constant term: x(5) = 5x\n3. Add the constant terms: 5x + 6 = 11x\n4. Multiply the variable and the second constant term: x(6) = 6x\n5. Add the two expressions:",
        "gt_answers": "\\frac { 9 } { 1 0 } \\div \\frac { 3 } { 5 } = \\frac { ( 9 ) } { ( 1 0 ) } \\textcircled { \\times } \\frac { ( 5 ) } { ( 3 ) } = ( \\frac { 2 } { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_13.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$x + 2 = 5$\n\nThis is because the image shows a number line with the number 5 on it, and the number 2 to the right of the 5. This means that x + 2 = 5.",
        "gt_answers": "= \\frac { ( 7 + 1 8 ) + ( 9 - 1 4 ) i } { 5 } = \\frac { 2 5 - 5 i } { 5 } = 5 - i\n",
        "image_path": "./data/HME100K/test_images/test_14.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle is given by:\n\nA = l \\* w,\n\nwhere l is the length and w is the width.\n\nGiven the image, the length of the rectangle is 4 cm and the width is 3 cm.\n\nTherefore, the area of the rectangle is:\n\nA = 4 cm \\* 3 cm = 12 cm\u00b2\n\nor 12 cm\u00b2 = 4 cm \\* 3 cm\n\nTherefore, the area of the rectangle is 12 cm\u00b2.",
        "gt_answers": "\\angle C P Q = \\angle B = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_16.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is of a function that is undefined at the origin, and is given by the equation y = 4x^2 + 9x + 3.\n\nIn LaTeX format, the equation can be written as:\n\n\\begin{align}\ny &= 4x^2 + 9x + 3 \\\n\\end{align}\n\nThis equation describes a parabola that opens upwards and has its vertex at the origin. The equation is symmetric about the y-axis, meaning that it is unchanged when reflected across the y-axis.",
        "gt_answers": "a - 4 b = - 1\n",
        "image_path": "./data/HME100K/test_images/test_17.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{center}\n\\frac{a^2 + b^2}{2ab}\n\\end{center}\n\nwhere a and b are the lengths of the sides of the triangle in the image.",
        "gt_answers": "a \\neq \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_18.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$ $\\text{Imaginary part of the complex number} z = a + bi$\n\nwhere $a$ and $b$ are real numbers.",
        "gt_answers": "a \\bot b\n",
        "image_path": "./data/HME100K/test_images/test_19.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$ \\frac{4}{\\sqrt{12}} = \\frac{4}{2} \\Rightarrow 2 = 2 $$",
        "gt_answers": "\\frac { O E } { A C } = \\frac { O B } { A B }\n",
        "image_path": "./data/HME100K/test_images/test_20.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by: $3x - 2y + 4 = 0$",
        "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",
        "image_path": "./data/HME100K/test_images/test_21.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:$$\\frac{a}{b}+\\frac{c}{d}=\\frac{a\\cdot b+c\\cdot d}{b\\cdot d}$$This formula can be used to find the ratio of the area of a rectangle with a length of $a$ and width of $b$ to the area of a rectangle with a length of $c$ and width of $d$.",
        "gt_answers": "y = \\frac { 7 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_23.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can follow these steps:\n\n1. Select the image and right-click on it to copy it to the clipboard.\n2. Open a text editor or LaTeX editor, such as Overleaf, and paste the image into a new document.\n3. Select the image and apply the LaTeX command to display it in math mode. The command for the image is \\frac12.\n4. To write out the formula in LaTeX format, we can use the following code:\n\n\\begin{align\\*}\n\\frac12",
        "gt_answers": "( - 1 + 0 ) ^ { 2 } = ( - 1 ) ^ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_24.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle is given by:A=lw, where l is the length and w is the width. To find the area of the rectangle in the given image, we need to first determine the length and width of the rectangle. We can do this by measuring the distance from the left edge of the image to the right edge of the image, and the distance from the top edge of the image to the bottom edge of the image. The length of the rectangle is given by the first measurement, and the width of the rectangle is given by the second measurement. Once we have determined the length and width",
        "gt_answers": "x _ { 3 } = \\frac { - 5 + \\sqrt { 4 1 } } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_25.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{F}(x) = \\frac{2x^2}{5} - \\frac{x^4}{20}$$\n\nIn LaTeX format, this can be written as:\n\n$$\\text{F}(x) = \\frac{2x^2}{5} - \\frac{x^4}{20}$$",
        "gt_answers": "b ^ { 2 } \\dot { = } a ^ { 2 } + c ^ { 2 } - 2 a c \\cdot \\cos B\n",
        "image_path": "./data/HME100K/test_images/test_26.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided as it is not displayed in my viewport. Can you please provide a different image or text that I can work with?",
        "gt_answers": "1 0 \\sqrt { 1 0 x - x ^ { 2 } } = 1 4\n",
        "image_path": "./data/HME100K/test_images/test_27.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "5 . 5 - 2 . 5 ) x + 4 8 \\times 5 . 5 = 4 8 0\n",
        "image_path": "./data/HME100K/test_images/test_28.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$\\frac{x^2}{x+4}$$\n\nwhere $x$ is an integer variable.",
        "gt_answers": "4 . 5 8 5 > 4 . 6 5 > 4 . 5 6 > 4 . 5 0 6\n",
        "image_path": "./data/HME100K/test_images/test_29.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$ 2 \\cdot ( 2 + \\frac{3}{5} ) = 2 \\cdot ( 5 + \\frac{2}{3} ) = 2 \\cdot ( 5 + \\frac{2}{3} ) + \\frac{1}{2} = 10 + \\frac{1}{2} = 5.5 $$",
        "gt_answers": "\\angle D O E = \\angle D B E = \\angle A E B = 7 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_30.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{x^2+y^2}{2}=\\sqrt{x^2+y^2}$$\nThis formula is the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.",
        "gt_answers": "x = \\frac { 1 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_31.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Cost of each item} = \\frac{2}{x + 2} + 1$$\n\nwhere x is the number of items.",
        "gt_answers": "\\frac { 1 } { 3 } \\times \\frac { 1 } { 4 } = \\frac { 1 } { 1 2 } = 1 2 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_32.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\nx = 2(4 + 3y)b\n\nThis can be written in LaTeX format as:\n\nx = 2(4 + 3y)\\*b\n\nThe variable x represents the number of people in the group. The variable y represents the number of people in the classroom. The variable b represents the number of people who like to play sports. The equation states that the number of people in the group is twice the number of people in the classroom who like to play sports, plus three times the number of people in the class",
        "gt_answers": "\\frac { 2 x - 6 } { 2 } = 6\n",
        "image_path": "./data/HME100K/test_images/test_33.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a linear equation. The equation can be written as: x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y = 4x + y",
        "gt_answers": "y = \\frac { x ( x - 2 ) } { ( x - 1 ) ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_34.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n\\begin{center}\n\\frac{x^2+y^2}{r^2}=\\frac{r^2+x^2+y^2}{r^2}\n\\end{center}\n\nwhere $x$ and $y$ are the coordinates of the point on the unit circle and $r$ is the radius of the circle.",
        "gt_answers": "x _ { 1 } = \\frac { 1 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_35.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression shown in the image is: 3(x+y)-1.5xy+0.5xy2.\n\nTo write this formula in LaTeX format, you can use the following code:\n\n$$ 3(x + y) - 1.5xy + 0.5xy^2 $$\nThis will produce the formula with the correct mathematical notation, including the parentheses and the subscripts.",
        "gt_answers": "y _ { 1 } = 0 , y _ { 2 } = \\frac { 8 } { 3 } \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_36.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a line of best fit for the given data points. To write the equation in LaTeX format, we can use the following code:\n\n![](https://i.imgur.com/image.png)\n\nwhere the variable x is the x-coordinate of each point, y is the y-coordinate of each point, and a and b are the y-intercepts of the line.",
        "gt_answers": "( 2 ) \\vert A B \\vert = \\vert - 1 - 5 \\vert = 6\n",
        "image_path": "./data/HME100K/test_images/test_39.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the expression in the image:\n\n\\begin{center}\n\\begin{equation}\n2 + 2 = 4\n\\end{equation}\n\\end{center}\n\nThis equation is written in LaTeX, which is a mathematical typesetting language. The equation shows that 2 + 2 is equal to 4. The equals sign (=) is used to indicate that the two sides of the equation are equal. The LaTeX code for the equation is simple and easy to read, making it a useful tool for mathematical expression.",
        "gt_answers": "\\frac { 4 x } { 3 } + \\frac { 3 } { 2 } > - \\frac { x } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_40.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a diagram of a right triangle with sides of 3 and 4, with the hypotenuse marked as 5. The length of the altitude from the hypotenuse to the base is 8. The length of the altitude from the base to the opposite side of the right angle is 6. The length of the altitude from the base to the point on the hypotenuse opposite the right angle is 10. The length of the altitude from the base to the point on the hypotenuse adjacent to the right angle is 12.\n\nTo solve for x, we",
        "gt_answers": "( \\frac { ( 2 \\times 4 ) } { 8 } + 1 3 = 2 1 > 2 0 )\n",
        "image_path": "./data/HME100K/test_images/test_41.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:",
        "gt_answers": "n = \\frac { 1 } { 2 } \\div \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_42.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation for the moment of inertia of a rod with respect to its rotation axis. The moment of inertia is given by the product of the cross-sectional area of the rod and its perpendicular distance from the rotation axis. The perpendicular distance is given by the formula d = r^2 - (h/2)^2, where r is the radius of the rod and h is its height. The cross-sectional area of the rod is given by the formula A = pi \\* r^2, where pi is the mathematical constant approximately equal to 3.14",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\frac{3x + 4y + 5z}{2x + 3y + 6z}$$\n\nIn this formula, the variable x represents the length of a rectangle's base, the variable y represents the height of a rectangle's base, and the variable z represents the thickness of a rectangle's base. The denominator 2x + 3y + 6z represents the total area of the base of the rectangle. The numerator 3x + 4y + 5z",
        "gt_answers": "x = 2 ( \\frac { 5 x - 1 7 } { 4 } )\n",
        "image_path": "./data/HME100K/test_images/test_44.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x = 2y + 3z.\n\nNote: The above expression assumes that the variables x, y, and z are independent and follow the normal distribution with mean 2, variance 3, and correlation coefficient 1.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula on the image:\n\n$ \\frac{b}{a} = \\frac{a}{b} = \\frac{64}{120} = \\frac{1}{5} $\n\nwhere $a$ and $b$ are the lengths of the two sides of the triangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: 5x + 3y = 10.",
        "gt_answers": "\\frac { 1 } { 3 } \\times \\frac { 1 } { 3 } = \\frac { 1 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_47.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the expression:\n\n\\begin{align\\*}\nx^2 + y^2 &= r^2 \\\n&= (x + y)^2 \\\n&= (r \\* cos(theta))^2 + (r \\* sin(theta))^2 \\\n&= r^2 \\* cos^2(\\theta) + r^2 \\* sin^2(\\theta) \\\n&= (r \\* sqrt(2))^2 \\\n&= 2 \\* r^2 \\\n&= 4 \\\n&= 6 \\\n\\end{align",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick, red] (0,0) -- (1,0) node[midway, above] {$a$};\n\\draw[thick, blue] (1,0) -- (2,0) node[midway, above] {$b$};\n\\draw[thick, green] (2,0) -- (3,0) node[midway, above] {$c$};\n\\draw[thick, yellow] (3,0) -- (",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\frac{5+3\\sqrt{5}}{2}=\\frac{11+3\\sqrt{5}}{2}$$\n\nThis can be simplified by canceling out the common factors of 5:\n\n$$\\frac{5+3\\sqrt{5}}{2}=\\frac{11}{2}$$\n\nSo the image shows that $\\frac{5+3\\sqrt{5}}{2}=\\frac{11}{2}$ is equivalent to $\\frac{11}{2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{aligned}\ny &= 2x^2 + 2x - 1 \\\n&= (2x + 1)(x + 1) - 1 \\\n&= (2x + 1)x - 2 \\\n&= 2x^2 + 2x - 2\n\\end{aligned}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle with length l and width w is given by A = lw.",
        "gt_answers": "1 + a ^ { 2 } b ^ { 2 } - a ^ { 2 } - b ^ { 2 } > 0\n",
        "image_path": "./data/HME100K/test_images/test_52.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: $\\frac{25}{50} + \\frac{10}{20} = \\frac{35}{60}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$2x^2 + 2x - 3 = 0$\n\\end{center}\n\nThe solutions to this equation are x = 1 and x = - 1.",
        "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": "MiniGPT4"
    },
    {
        "question": "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 + 4x - 5 $.\n\nThis formula can be derived by substituting the variables in the given equation into the formula for the quadratic function: $ y = ax^2 + bx + c $. The values of a, b, and c in the given equation are 3, 4, and - 5, respectively. Substituting these values into the formula, we get:\n\n$ 3(2x)^2 + 4(2x) - 5 = 3(4x",
        "gt_answers": "A H = 3 k B H = 4 k\n",
        "image_path": "./data/HME100K/test_images/test_55.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$ E = mc^2 $\n\nwhere E is the energy of the object, m is its mass, and c is the speed of light in a vacuum.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{4\\sqrt{2}}{4\\sqrt{2}+8\\sqrt{4}+4\\sqrt{3}}-\\frac{1}{\\sqrt{2}+1}$\n\nThis expression is derived from the given image by identifying the variables and using algebra to solve for the value of the expression. The variables in the expression are the measurements of the sides of the rectangle.",
        "gt_answers": "\\frac { 2 x } { 3 } = \\frac { 4 x - 8 } { 9 } - 5\n",
        "image_path": "./data/HME100K/test_images/test_62.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula using LaTeX format is:\n\n\u222b\u2061 \u222b\u2061 x f(x) dx\u222b\u2061 \u222b\u2061 x f(x) dx=\u222b\u2061\u222b\u2061 \u222b\u2061 \u222b\u2061 \u222b\u2061 \u222b\u2061\u222b\u2061 \u222b\u2061 \u222b\u2061 x f(x) dxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdxdx",
        "gt_answers": "x = - \\frac { 6 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_64.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=1]\n\\draw (0,0) -- (1,1) -- (1,0) -- cycle;\n\\draw (1,0) -- (0,1) -- (1,1) -- cycle;\n\\draw (0,0) -- (1,1) -- (1,0) -- cycle;\n\\filldraw (0,0) circle (2pt) node[below left] {$ a $};\n\\filldraw",
        "gt_answers": "( x + 1 ) ^ { 2 } - 4 = ( x + 1 ) ( x - 1 )\n",
        "image_path": "./data/HME100K/test_images/test_65.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a formula in LaTeX format that describes the area of a rectangle with a width of x and a height of y:\n\n$$A = \\frac{xy}{4}$$\n\nThis formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.\n\nGiven the width x and height y of the rectangle, we can substitute these values into the formula to find the area:\n\n$$A = \\frac{x",
        "gt_answers": "x ^ { 2 } + a x ^ { 2 } + a ^ { 2 } x - a x ^ { 2 } - a ^ { 2 } x - a\n",
        "image_path": "./data/HME100K/test_images/test_66.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the sum of the quantities of the substances in the reaction, represented by the chemical equation:$$ \\ce{H2O2 + 2O2 -> 2H2O}$$The subscripts indicate the number of each substance in the reaction, with the coefficients indicating the stoichiometry of each substance. The coefficients are given as numbers, with the first number indicating the number of moles of the substance and the second number indicating the number of moles of the other substance. The coefficients are also colored red to distinguish them from the numbers indicating the subscripts. The formula",
        "gt_answers": "3 6 0 0 0 c m ^ { 3 } = 3 6 d m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_67.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ \\frac{\\text{2}}{\\text{2} - \\text{3}}$$This formula is a fraction with numerator 2 and denominator 2 - 3, which gives a value of 1 when substituted into the formula.",
        "gt_answers": "x - y = - \\frac { 1 1 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_68.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is 10 - (2x + 4y).\n\nThis can be written as:\n\n$$\\begin{aligned} 10 - (2x + 4y) \\ &= 10 - 2x - 4y \\\\ &= 10 - 2x - 4y \\end{aligned}$$\n\nThe image shows the formula being evaluated for the values x = 3 and y = 4, with the result being written as the sum of the values on the right-hand side of the equation.",
        "gt_answers": "0 . 5 < 0 . 5 0 1 < 0 . 5 1 < 0 . 5 1 1\n",
        "image_path": "./data/HME100K/test_images/test_70.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a fraction representation of a fraction with a numerator of 8 and a denominator of 2. The fraction is simplified to 4/2, which is equivalent to 2.",
        "gt_answers": "\\frac { 8 } { 8 } - \\frac { 7 } { 8 } = \\frac { 1 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_71.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\begin{aligned}3x+2y&=-1\\\n\\begin{cases}3x+2y&=-1\\\n3x+2y&=5\\\n\\begin{cases}3x+2y&=5\\\n3x+2y&=7\\\n\\begin{cases}3x+2y&=7\\\n3x+2y&=-3\\\n\\begin{cases}3x+2y&=-3\\\n3x+2y&=-5\\\n\\begin{cases}3",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{100 - 20\\times 4 + 30}{50 + 20} = \\boxed{\\frac{70}{70}}$$",
        "gt_answers": "9 x - 5 , 2 = 2 1 . 8\n",
        "image_path": "./data/HME100K/test_images/test_73.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a ratio expression, which can be expressed as:W = a \\* m / nwhere a, m, and n are the lengths of the sides of a triangle. The image shows that the ratio of the base to the height is 4:1, or 4/1.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the expression in the image:\n\n$$\\frac{a}{b}$$\n\nwhere $a$ and $b$ are constants.",
        "gt_answers": "x _ { 1 } = \\sqrt { 2 } x _ { 2 } = - \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_75.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length $l$ and width $w$ is:\n\nA = lwA = lwA = (l x w)A = (l x w)where $A$ is the area of the rectangle.",
        "gt_answers": "\\therefore F 1 8 0\n",
        "image_path": "./data/HME100K/test_images/test_76.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2} x^2 - \\frac{1}{4} x^4$\n\nThis is a quadratic equation with a constant term of $\\frac{1}{2}$ and a quadratic term of $x^2$. The coefficient of the quadratic term is $\\frac{1}{4}$ and the constant term is $\\frac{1}{2}$.",
        "gt_answers": "1 0 0 = 2 0 0 k + b\n",
        "image_path": "./data/HME100K/test_images/test_77.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is not visible, as the image is not displayed. Please provide the image so I can determine the formula.",
        "gt_answers": "x _ { 3 } = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_78.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$c\\_0 = \\frac{P\\_0 - P\\_1}{\\sqrt{x\\_1^2 + (y\\_1 - y\\_0)^2}}$\n\\end{center}\n\nwhere $P\\_0$ and $P\\_1$ are the y-coordinates of the two points, and $x\\_1$ and $y\\_1$ are the x-coordinates of the point that lies on the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius $r$ is given by $A = \\pi r^2$. In the image, we can see the formula written out as $A = \\pi r^2$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image:\n\n$$\\frac{x + 3}{2x - 5} = \\frac{x + 3}{2x - 5}$$",
        "gt_answers": "\\frac { x ^ { 2 } + 1 } { x + 1 } - \\frac { 2 } { x + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_81.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the volume of a cylinder can be written as:\n\nV = \u222b\u03c0r^2hdr\n\nwhere V is the volume, r is the radius, h is the height, and dr is an infinitesimal volume element. This equation can be derived using the definition of a cylinder as the set of all points (x, y, z) that satisfy the equation x^2 + y^2 = r^2, where r is the radius of the cylinder. The volume of the cylinder can then be calculated as the integral of the area of a cross-sectional",
        "gt_answers": "3 0 - 3 = 2 7 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_82.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the given image using LaTeX format, we can use the following equation:\n\n$$\\begin{aligned} x = \\frac{a + 3b + 5c}{6} \\end{aligned}$$\n\nwhere a, b, and c are the numbers given in the image, which are 2, 5, and 8, respectively.\n\nPlugging these values into the equation, we get:\n\n$$\\begin{aligned} x = \\frac{2 + 3(5) + 5(8)}{6} \\end{aligned}$$",
        "gt_answers": "3 y - 2 = 9 - 6 \\sqrt { y + 3 } + y + 3\n",
        "image_path": "./data/HME100K/test_images/test_83.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$\\frac{x^2+y^2}{2}=\\sqrt{3x^2+3y^2}$\n\nThe equation is a quadratic formula in the form of $\\frac{ax^2+bx+c}{a}$ where $a=\\frac{1}{2}$, $b=0$, and $c=0$ and it represents a parabola with vertex at the origin and passing through the point $(0,2)$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$E = mc^2$$\n\nwhere E is the energy of the object, m is its mass, and c is the speed of light in a vacuum.",
        "gt_answers": "v = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_86.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{500 \\* 1.50}{15}$$\n\nThis formula calculates the cost per kilogram of meat for a specific customer order. It uses the cost per kilogram of meat ($500) and the additional charge for the meat (1.50), and divides them by the number of kilograms in the customer's order (15). The result is the cost per kilogram of meat for the specific customer order.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 3x + 2y = 10. This is a linear equation that represents the line shown in the image, with the point (2, 3) on the line. The equation can be used to determine the value of the constant c in the equation, which is 10 - 3x - 2y.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written on the whiteboard is the formula for the derivative of y with respect to x. The formula is dy/dx = 5x - 3y.",
        "gt_answers": "5 \\times 3 \\times 4 = 6 0 ( d m ) ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_89.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\begin{align\\*} x &= \\frac{b - \\sqrt{b^2 - 4ac}}{2a} \\\n\\end{align\\*}$$",
        "gt_answers": "a m + b n > a n + b m > 0\n",
        "image_path": "./data/HME100K/test_images/test_90.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```scss\n\n\\documentclass{article}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{equation}\n\\frac{3600 \\times 30}{600} = 90\n\\end{equation}\n\\end{document}\n```",
        "gt_answers": "2 x = 8\n",
        "image_path": "./data/HME100K/test_images/test_91.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation shown in the image is the product of the given expression: x + 5y. This can be represented in LaTeX format as follows:\n\nx + 5y = 4x + 15y\n\nwhere x and y are variables representing the number of items in the first and second piles, respectively.",
        "gt_answers": "x = \\frac { 5 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_92.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\begin{aligned}\\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} = \\frac{9}{16}\\end{aligned}$$",
        "gt_answers": "\\frac { 1 } { 4 } \\div \\frac { 3 } { 2 } = \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_93.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is: (x + y + z) \\* (2x - 3y + 4z) + 6x + 4y + 8z.",
        "gt_answers": "3 x _ { ( g ) } + y _ { ( g ) } \\rightleftharpoons 2 z ( g )\n",
        "image_path": "./data/HME100K/test_images/test_94.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written as follows:\n\n\\begin{center}\n2x^2 + 2 = 6x - 2x^2\n\\end{center}\n\nwhere x is a variable.",
        "gt_answers": "x + 1 = \\pm \\frac { 4 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_95.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the product of two binomials, (x + 2) and (y - 3), which are added to give the expression: xy - 5. This is a binomial product that can be written as: (xy) - 5.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n5x^2 + (2x - 5)y^2 = 36x^2 + 10xy^2 + 4y^2\n\\end{center}\n\nThis formula is a quadratic equation in the variables x and y, with coefficients given by the numbers in the image. It can be used to solve for the values of x and y that satisfy the equation, or to analyze the behavior of the equation for different values of x and y.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the derivative of the function f(x) = x2, which can be written as d/dx f(x) = 2x.\n\nIn LaTeX format, this can be written as:\n\n$$\\frac{d}{dx} f(x) = \\frac{d}{dx} x^2 = 2x$$\n\nThe expression can also be simplified to:\n\n$$\\frac{d}{dx} x^2 = 2x$$",
        "gt_answers": "- 1 0 - \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_98.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the formula in the image:\n\n\\begin{equation}\n2x^2 + 2y^2 = 25\n\\end{equation}\n\nThe equation is a quadratic equation in two variables, x and y. The left-hand side of the equation is the sum of the squares of x and y, which is 2x^2 + 2y^2. The right-hand side of the equation is the constant value 25.",
        "gt_answers": "\\frac { 1 } { 2 } x = \\frac { 2 } { 3 } \\times 6\n",
        "image_path": "./data/HME100K/test_images/test_101.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\text{ImageContent}$.",
        "gt_answers": "1 0 a + 1 5 0 - 1 5 a \\geq\n",
        "image_path": "./data/HME100K/test_images/test_102.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image using LaTeX format is:\n\n$$ 4 \\sin(x) + 3 \\cos(x) = 5 $$\n\nwhere $x$ is an angle in radians.",
        "gt_answers": "B D ^ { 2 } - A B ^ { 2 } - A D ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_103.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression that represents the integral of the exponential function f(x) = e^x, from x = 0 to x = 1, with respect to dx. The expression is written in LaTeX format as follows: $\\int\\_0^1 e^x dx = \\int\\_0^1 \\left(1 + x\\right) dx = \\int\\_0^1 dx = \\frac{1}{2}$.",
        "gt_answers": "( 1 ) a ^ { x } _ { 2 } = a _ { 1 } + ( 2 - 1 ) d\n",
        "image_path": "./data/HME100K/test_images/test_105.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given formula:\n\n$$\\frac{x^{2}+3x-5}{x-2}=\\frac{a}{b}$$\n\nThe given formula is a rational expression with a numerator of $x^{2}+3x-5$ and a denominator of $x-2$. The fraction is in the form $\\frac{a}{b}$, where $a$ and $b$ are constants.\n\nTo solve this equation, we can substitute the values of $x$ that make the denominator zero, which will give us the solutions to the equation",
        "gt_answers": "2 ^ { 2 } + b ^ { 2 } = a ^ { 2 } + b ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_106.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by the equation:y = 2x^2 + 5x - 7.\n\nThe equation represents a parabolic function with the vertex at the origin and the maximum value of 10 at the point (3,5). The axis of symmetry is the x-axis.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with width w and height h is:\n\nA = wh\n\nwhere A is the area and w and h are the width and height, respectively.",
        "gt_answers": "\\frac { x } { 3 } + \\frac { a + x } { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_110.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is given by:\n\ngiven that x and y are the number of girls and boys in a class, respectively, and the teacher has a ratio of 3:5, then the total number of students in the class is given by:\n\nx + y = 3(5x) + 5y = 3(5x + 5y) = 15x + 30y\n\nTherefore, the number of girls in the class is given by:\n\ngirls = x = 5y - 30y = 5y -",
        "gt_answers": "a = - 7 - ( 2 , s )\n",
        "image_path": "./data/HME100K/test_images/test_111.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that.\n\nThe expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{\\text{d}\\sigma}{\\text{d}t} = \\frac{k}{V} $$\n\nwhere $\\sigma$ is the entropy of the system, $k$ is the Boltzmann constant, and $V$ is the volume of the system.\n\nNote that this equation assumes that the system is in thermodynamic equilibrium and that the entropy change of the system is proportional to the heat transferred to or from the system. This equation can be used to calculate",
        "gt_answers": "\\angle B O C = 1 2 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_112.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression of the formula in the image:\n\n\\begin{equation}\na + 2b = 6\n\\end{equation}",
        "gt_answers": "a _ { 2 } = 3 b _ { 2 } = 6\n",
        "image_path": "./data/HME100K/test_images/test_113.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is:\n\nA = (1/2)bh, where b is the base length, h is the height, and A is the area.\n\nUsing the image provided, we can calculate the area of each triangle by finding the base and height of each triangle, and then plugging the values into the formula.\n\nFor the first triangle, the base is 10 cm and the height is 5 cm, so the area is:\n\nA = (1/2)bh = (1/2)(10)(5) = 12",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is:$$x = \\frac{2y}{y+3}$$This equation is derived from the given image by considering the number of people in each group and the total number of people in all groups. The x-coordinate of each group is equal to the number of people in that group, and the y-coordinate is equal to the sum of the x-coordinates of all groups. The equation represents the ratio of the number of people in each group to the total number of people in all groups.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{a}{b} = \\frac{c}{d}$$Where `a`, `b`, `c`, and `d` are variables.",
        "gt_answers": "l = R + R \\sin 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_116.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I'm unable to see the image provided as it's not accessible. Can you please provide a different image or format that I can use to answer your question?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:",
        "gt_answers": "a n c = 0\n",
        "image_path": "./data/HME100K/test_images/test_118.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a rectangle with a width of 5 and a height of 7 is:5*7=35.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by: A = l \\* w, where l is the length and w is the width. In the image, l is 10 and w is 5. Therefore, the area of the rectangle is 10 \\* 5 = 50.\n\nThe formula for the area of a square is given by: A = s^2, where s is the side length. In the image, s is 5. Therefore, the area of the square is 5^2 = 25.\n\nThe formula for the area of a triangle",
        "gt_answers": "x = \\frac { B E } { A B } = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_120.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Could you please provide the image so that I can help you with the LaTeX format?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{400 \\times \\left(100 + \\frac{10}{4}\\right)}{350 - 200}$$which can be simplified as:$$\\frac{400 \\times 100 + 400 \\times \\frac{10}{4}}{350 - 200}$$or$$400\\times 100 + 200\\times \\frac{10}{4}$$\n\nNote that the fraction $\\frac{10",
        "gt_answers": "\\frac { m ^ { 2 } + 4 } { m ^ { 2 } - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_122.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n\\begin{align}\nx = \\frac{3y+5z}{2}\n\\end{align}\n\nwhere $x$ and $y$ are variables and $z$ is a constant.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\begin{aligned} y &= 2\\sqrt{x^2 + 3x - 2} \\\n\\end{aligned}$$\n\nThis formula represents the equation of a parabolic arch with center at the origin and a radius of 2. The variable x represents the horizontal position along the arch and y represents the vertical position.",
        "gt_answers": "x _ { 1 } = n + 2 , x _ { 2 } = 2 ( n + 1 )\n",
        "image_path": "./data/HME100K/test_images/test_125.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$x = \\frac{b}{2a}$\n\nThis formula can be used to solve for the x-intercept of the parabola $y = ax^2 + bx + c$. The x-intercept is the value of x that makes the parabola $y = 0$. In this case, the x-intercept is given by the formula:\n\n$x = \\frac{b}{2a}$\n\nTo use this formula, we plug in the values for a and b from the given formula for y:",
        "gt_answers": "- x = m + 1 , y = - m - 3\n",
        "image_path": "./data/HME100K/test_images/test_126.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by:\n\n$$4x^2+12x+8=0$$\n\nSolving for x, we get:\n\n$$x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}$$\n\nwhere a=1, b=12, and c=8. Therefore,\n\n$$x=\\frac{-12\\pm\\sqrt{12^2-4\\times1\\times8}}{2\\times1}=\\frac{-12\\pm\\sqrt{144-32}}{2\\",
        "gt_answers": "\\frac { 4 \\times 1 2 } { 4 8 } + \\frac { ( 8 - 4 ) } { 4 } \\times 3 = 6 0\n",
        "image_path": "./data/HME100K/test_images/test_127.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is x^2 - x^2 = x^2. The x^2 term cancels out, leaving only x^2.",
        "gt_answers": "\\frac { 3 } { 2 } = \\frac { 2 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_128.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\frac{a + 3}{b + 2} \\times \\frac{b - 2}{c + 1} = \\frac{a + 3}{c + 1}$$\n\nThis is a cross product of two fractions. The first fraction is $\\frac{a + 3}{b + 2}$, which represents a glass of water with ice cubes in it, and the second fraction is $\\frac{b - 2}{c + 1}$, which represents a glass of water with one ice",
        "gt_answers": "x = \\frac { 2 4 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_129.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by $A = \\pi r^2$, where $\\pi$ is the constant ratio of the circumference of a circle to its diameter, and $r$ is the radius of the circle.\n\nThe formula can be derived from the definition of the area of a circle. The area of a circle is the amount of space inside the circle, and it can be calculated by multiplying the radius of the circle by itself. The formula for the area of a circle is derived from this definition by using the constant ratio of the circumference of a circle to its diameter.",
        "gt_answers": "x = \\frac { 2 4 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_130.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} & 2x + 4y = 12 \\ \\ \\Rightarrow \\ \\ 2x + 4y - 12 = 0 \\ \\ \\Rightarrow \\ \\ x = \\frac{12 - 4y}{2} \\ \\ \\Rightarrow \\ \\ x = \\frac{8y}{2} \\ \\ \\Rightarrow \\ \\ x = y + \\frac{8}{2} \\end{aligned}$$\n\nThis is the equation of a line in the form y = mx +",
        "gt_answers": "2 L i O H + C O _ { 2 } = L i _ { 2 } C O _ { 3 } + H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_131.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: 2 + 3 = 5.",
        "gt_answers": "\\therefore D P = \\frac { - 3 + \\sqrt { 6 9 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_132.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{3x^2+2x-5}{x^2-5x+2}$.",
        "gt_answers": "\\sin \\alpha x = \\alpha\n",
        "image_path": "./data/HME100K/test_images/test_133.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as: f(x) = 5x + 2.",
        "gt_answers": "3 x - \\frac { 3 } { 4 } = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_134.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression that is written in LaTeX format:$$5\\times 5+6\\times 2+3=21$$\n\nThis is an equation that shows the result of multiplying 5 by 5, adding 6 times 2, and adding 3. The answer is 21.",
        "gt_answers": "\\frac { 2 7 } { 2 } - 6 + 3 \\sqrt { 3 } + \\frac { 9 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_135.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following equation:\n\n\\frac{mg}{r} = \\frac{v^2}{r} + \\frac{GM}{r^2}\n\nWhere m is the mass of the object, g is the acceleration due to gravity, v is the velocity of the object, r is the distance from the center of the Earth to the object, and GM is the gravitational constant.",
        "gt_answers": "y ( 2 y + x ) = 0 \\cdot \\therefore y\n",
        "image_path": "./data/HME100K/test_images/test_136.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\begin{aligned}\n\\frac{1}{2} + \\frac{1}{4} &= \\frac{5}{8} \\\n\\frac{2}{3} - \\frac{1}{4} &= \\frac{1}{12}\n\\end{aligned}\n```",
        "gt_answers": "1 0 0 y \\times 2 \\times 2 = 1 0 0 x \\times 1 \\times 1\n",
        "image_path": "./data/HME100K/test_images/test_137.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{x+y-2}{2x+3y-7}$$\n\nwhere $x$ and $y$ are the variables in the equation.",
        "gt_answers": "y = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_139.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not clear without additional context or information. Can you please provide more information or context about the formula?",
        "gt_answers": "k \\geq 0 . k \\geq \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_140.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by the equation: $ \\frac{1}{1+e^{-x}} $.",
        "gt_answers": "A D \\bot B C\n",
        "image_path": "./data/HME100K/test_images/test_141.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\begin{center}\n\\begin{tabular}{|c|c|}\n    \\hline\n    $i^2$ & $i$ is an imaginary number \\\\\n    \\hline\n    $i^3$ & $i$ is an imaginary number \\\\\n    \\hline\n    $i^4$ & $i$ is an imaginary number \\\\\n    \\hline\n\\end{tabular}\n```",
        "gt_answers": "2 t - \\frac { 2 5 } { 2 4 } )\n",
        "image_path": "./data/HME100K/test_images/test_143.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{cos}(x) = \\frac{e^2}{2\\sqrt{e^4 + 1}}$$\n\nIn the image, the formula is given as $\\text{cos}(x) = \\frac{e^2}{2\\sqrt{e^4 + 1}}$.",
        "gt_answers": "I _ { 1 } : I _ { 2 } = 3 : 1\n",
        "image_path": "./data/HME100K/test_images/test_144.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$\\frac{a}{b} = \\frac{c}{d}$$\n```\nIn this formula, $a$ and $b$ are integers with $b$ positive, and $c$ and $d$ are integers. The fraction bar separates the numerator and denominator of the fraction.",
        "gt_answers": "\\cdot E G = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_145.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$a^2 + b^2 = c^2$\n\nwhere a, b, and c are variables.",
        "gt_answers": "F e + H _ { 2 } S O _ { 4 } = F e S O _ { 4 } + H _ { 2 } \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_146.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: $\\frac{5}{x}+\\frac{2}{x^2}$$\\frac{4}{x}+\\frac{3}{x^2}$$\\frac{3}{x}+\\frac{5}{x^2}$$\\frac{2}{x}+\\frac{4}{x^2}$The formula is a quadratic function with the variable x. The coefficient of x^2 is 4 and the constant term is 5.",
        "gt_answers": "x = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_148.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\nThe expression for the given image is:\n\n$$\\text{y} = \\frac{5}{4}$$\n```",
        "gt_answers": "( y - 2 ) ( y + 1 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_149.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{4x^2+4y^2+4z^2}{2}=\\frac{4x^2+4y^2+4z^2}{2}=\\frac{4x^2+4y^2+4z^2}{2}=\\frac{4x^2+4y^2+4z^2}{2}=\\frac{4x^2+4y^2+4z^2}{2}=\\frac{4x^2+4y^2+4z^2}{2",
        "gt_answers": "4 - 2 h = \\sqrt { h ^ { 2 } + r ^ { 2 } } . \\textcircled { 1 }\n",
        "image_path": "./data/HME100K/test_images/test_151.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for an equilateral triangle is $\\sqrt{3}r$.\n\nIn LaTeX format, this would be written as:\n\n\\begin{equation}\n\\sqrt{3}r\n\\end{equation}\n\nWhere $r$ is the length of the sides of the triangle.",
        "gt_answers": "\\sqrt { x + 4 5 } - 2 x + 1 = 0\n",
        "image_path": "./data/HME100K/test_images/test_153.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} x &= \\frac{1}{2} \\cdot \\frac{1}{4} + \\frac{1}{2} \\cdot \\frac{1}{8} + \\frac{1}{2} \\cdot \\frac{1}{16} + \\frac{1}{2} \\cdot \\frac{1}{32} \\\n\\end{aligned}$$\n\nThis formula calculates the sum of the first four terms of the geometric sequence with a common ratio of $\\frac{1}{2",
        "gt_answers": "\\frac { 1 } { 4 } x + \\frac { 3 } { 1 0 } y = 1\n",
        "image_path": "./data/HME100K/test_images/test_154.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 20\\*0.2+30\\*0.15+10\\*0.1+5\\*0.05. This formula calculates the number of apples and oranges needed to make a pie with a crust made of flour, sugar, and water, and a filling made of apples and oranges.\n\nNote: the formula does not include the amount of water needed to make the crust. To calculate the amount of water needed, you can use the following formula:\n\nWater needed = (",
        "gt_answers": "x = \\frac { 3 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_155.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{P(A) = \\frac{N(A)}{N(A) + \\frac{N(B)}{2}}}$$\n\nwhere $N(A)$ is the number of people who prefer A, $N(B)$ is the number of people who prefer B, and $N(A)+N(B)/2$ is the total number of people who prefer either A or B.",
        "gt_answers": "( 8 9 9 9 ) < ( 9 0 0 1 ) < ( 9 8 9 9 ) < ( 9 9 9 9 )\n",
        "image_path": "./data/HME100K/test_images/test_156.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 1/x \\* logx(y) \\* 1/y.\n\nHere's the LaTeX code for the expression:\n\n$ \\frac{1}{x} \\times \\log\\_x(y) \\times \\frac{1}{y}$\n\nNote: The logarithm function is written as log\\_x(y), where x is the variable being logarithmed and y is the value being logarithmed to.",
        "gt_answers": "\\angle P F E = 1 8 0 ^ { \\circ } - \\angle 1 - 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_158.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{center}\na + b = 2b\n\\end{center}\n\nThe image shows that the sum of two numbers is equal to twice the second number. In LaTeX format, this can be written as:\n\n\\begin{center}\na + b = 2b\n\\end{center}\n\nNote that the plus sign is used to represent addition, and the equal sign is used to indicate equality.",
        "gt_answers": "S _ { \\Delta } A F C = \\frac { 1 } { 2 } A F \\cdot B C = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_159.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the expression of the formula in the image using LaTeX format:\n\n$$3x + 5y = 30$$\n\nThe image shows a line in the Cartesian plane with slope 3 and intercept 30, and another line with slope 5 and intercept 50. The point of intersection of the two lines is (3, 35).",
        "gt_answers": "6 0 \\times \\frac { 3 } { 4 } = \\frac { 6 0 \\times 3 } { 4 } = \\frac { 1 8 0 } { 4 } = 4 5\n",
        "image_path": "./data/HME100K/test_images/test_161.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n$$ \\frac{3(x + 5)}{x^2 - 10} $$",
        "gt_answers": "1 4 0 ^ { \\circ } - 5 m + 5 m - 5 0 ^ { \\circ } = 9 0\n",
        "image_path": "./data/HME100K/test_images/test_163.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$2x^2 + 4x - 5 = 0$\n\nwhere $x$ is the variable being solved for.",
        "gt_answers": "x > - \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_164.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for finding the derivative of a function f(x) with respect to x. The formula is: \u231f(f(x)) = \u2202f(x)/\u2202x, which can be written as \u2202f(x)/\u2202x = \u231f(f(x)).",
        "gt_answers": "\\frac { x + 2 } { 3 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_165.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you would use the following equation:$$x = \\frac{1}{a} \\sqrt{y^2 + (b - 1)^2}$$where x is the result, a is the coefficient of x^2, and b is the coefficient of x. In the image, a = 10 and b = 20. Therefore, the expression is:$$x = \\frac{1}{10} \\sqrt{y^2 + (20 - 1)^2} = \\frac{1}{10}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is $\\frac{3x+5}{x-2}$.",
        "gt_answers": "I = \\frac { Q } { t } = \\frac { 2 } { 4 } = 0 . 5\n",
        "image_path": "./data/HME100K/test_images/test_167.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick] (0,0) -- (2,0) node[midway, right] {$x$};\n\\draw[thick] (0,0) -- (0,2) node[midway, above] {$y$};\n\\filldraw (1,0) circle[radius=2pt] node[midway, left] {$A$};\n\\filldraw (0,1) circle[radius=2pt] node[midway,",
        "gt_answers": "\\angle A O F = \\angle 3 = 4 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_168.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{1}{2}(x + 3y) = 5$$",
        "gt_answers": "( 4 2 \\div 2 ) + 2 = 2 3 ( m )\n",
        "image_path": "./data/HME100K/test_images/test_169.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:$$\\frac{x^2 - 4x + 3}{x - 2}$$In this expression, the numerator is the difference of the squares of x and 4x minus 3, while the denominator is the difference of x and 2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{align}\n\\frac{x+2y+3z}{x-y-z}=5\n\\end{align}\n\nwhere x, y, and z are variables.",
        "gt_answers": "n ( n + 2 ) + 1 = ( n + 1 ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_171.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 2(x + y) + 3x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This image shows a formula written in LaTeX format, with the variable x represented by the symbol d, the variable y represented by the symbol c, the variable z represented by the symbol +, and the variable a represented by the symbol 60. The formula is written as f(x, y) = z + a.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{1}{x+8}=\\frac{10}{3}$$Therefore, the image represents the solution to the equation $x^2+8x+10=0$.",
        "gt_answers": "x = \\frac { 1 0 8 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_174.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{2x+3y}{x+y}=5$$where x and y are the variables.\n\nTo write this in LaTeX format, you can use the following code:$$\\frac{2x+3y}{x+y}=5$$This will give you the same formula written in LaTeX format.",
        "gt_answers": "x = 3 . 5\n",
        "image_path": "./data/HME100K/test_images/test_175.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Mass balance equation for the system: }$$\n\n$$\\text{Mass balance equation for the inlet: }$$\n\n$$\\text{Mass balance equation for the outlet: }$$\n\nIn these equations, the variables represent the mass of the substance in each section of the system. For example, M represents the mass of the substance in the middle section, and m represents the mass of the substance in the inlet and outlet sections. The subscripts i and o indicate the in",
        "gt_answers": "3 0 h = 2 7 \\Delta h - 8 \\Delta h\n",
        "image_path": "./data/HME100K/test_images/test_176.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX code for the given expression:\n\n$$\\begin{aligned} 3(a + 4) &= 10 \\\\ 3a + 12 &= 10 \\\n\\end{aligned}$$The above equation can be solved as follows:\n\n$$\\begin{aligned} 3a + 12 &= 10 \\\\ 3a &= 2 \\\n\\end{aligned}$$Substituting the value of $a$ in the second equation, we get:\n\n$$3(2) + 12 = 10 \\",
        "gt_answers": "3 a _ { 1 } + 9 d = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_177.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{1234+5678-91011}{2\\times 3\\times 4}$$\n\nwhere the numerator is the sum of the integers 1234 and 5678, and the denominator is the product of 2, 3, and 4.",
        "gt_answers": "1 \\sim 5 : B B D C B\n",
        "image_path": "./data/HME100K/test_images/test_178.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n`x^2 + 2x + 1`",
        "gt_answers": "\\angle B = \\angle C ^ { \\prime }\n",
        "image_path": "./data/HME100K/test_images/test_179.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a differential equation for a function y(x), which is a solution to the differential equation: dy/dx = x^2 - 2x. The image shows a graph of the solution to the equation, which is plotted for x values from 0 to 3 and has a horizontal asymptote at x = 2 and a vertical asymptote at y = 0. The equation is written in LaTeX format as follows:dy/dx = x^2 - 2x.",
        "gt_answers": "d = \\sqrt { a ^ { 2 } - 1 - \\frac { a ^ { 2 } - 1 } { 4 } } = \\frac { \\vert a ^ { 2 } - 1 \\vert } { \\sqrt { a - 1 } }\n",
        "image_path": "./data/HME100K/test_images/test_180.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ m\\_n = \\frac{m\\_{n-1}}{2}+\\frac{n+1}{2n}$$\n\nwhere $m\\_n$ is the sum of the first $n$ terms of the sequence defined by the recurrence relation, and $m\\_{n-1}$ is the sum of the first $n-1$ terms of the sequence.\n\nNote that the recurrence relation for this sequence is given by:\n\n$$ m\\_{n+1} = \\frac{3m\\_n +",
        "gt_answers": "B D = D M , D H \\bot B M\n",
        "image_path": "./data/HME100K/test_images/test_181.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can follow these steps:\n\n1. Select the formula in the image and copy it to the clipboard.\n2. Open a LaTeX editor, such as Overleaf or LaTeXiite, and paste the formula into a new document.\n3. Choose a font size and style that is appropriate for the formula.\n4. Format the formula using LaTeX commands, such as \\frac, \\sum, and \\cdot, to make it more readable and professional-looking.\n5. Save the document as a PDF file.\n\nHere",
        "gt_answers": "( y + 1 ) ^ { 2 } + ( y + 1 ) y + y ^ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_182.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This image does not show a formula. It is simply the name of the variable'Hilary Joyce' in a handwritten note. If you want to see the formula, please provide the formula and I will write it out using LaTeX format.",
        "gt_answers": "\\frac { 1 } { 3 } + 1 1 y = 1 0 y - 7\n",
        "image_path": "./data/HME100K/test_images/test_183.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is 16.66.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666",
        "gt_answers": "\\frac { 6 + a - 5 } { 5 } = \\frac { 1 0 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_185.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the given formula:\n\n\\begin{center} $ x = \\frac{3}{4} \\cdot \\frac{5}{6} \\cdot \\frac{4}{5} = \\frac{3}{20} $\\end{center}\n\nThis formula is the cross product of the fractions $\\frac{3}{4}$, $\\frac{5}{6}$, and $\\frac{4}{5}$. The cross product is defined as the product of two or more fractions, with the numerators and denominators being the factors of each fraction. The result is then simplified",
        "gt_answers": "x = \\frac { 6 4 0 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_186.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is 12+12+12+12+12=50.",
        "gt_answers": "\\frac { 1 7 } { 2 0 } > \\frac { 1 6 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_188.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX expression for the given formula:\n\n\\begin{align\\*}\nf(x) &= \\frac{1}{2x^2 + 3x - 2} \\ \\?\n\\end{align\\*}\nThis formula is a quadratic function with a leading coefficient of 1, a constant term of -2, and a quadratic term of 3x. To derive the formula, we can factor the expression as follows:\n\n\\begin{align\\*}\nf(x) &= \\frac{(2x + 3)(",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the expression of the formula in the image using LaTeX format:\n\n$$x=\\frac{4y^2+8y+c}{y^4+2y^3+6y^2+8y+c}$$",
        "gt_answers": "4 x ^ { 2 } - y ^ { 2 } = 4\n",
        "image_path": "./data/HME100K/test_images/test_190.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given as follows:\n\n![Image Content](https://i.imgur.com/rH8jJ7h.png)\n\nwhere $\\alpha$ is the angle between the light beam and the normal to the surface, $\\theta$ is the angle between the surface and the normal, and $\\lambda$ is the wavelength of the incident light. The refractive index of the medium is given by $n = \\sin(\\alpha)$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\nThe expression for the area of a rectangle with length $L$ and width $W$ is:\n\nA = L x W\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{center} $\\frac{4\\sqrt{x}}{x+5}$ \\end{center}\n\nThis formula represents the speed of an object falling under the influence of gravity, assuming that the acceleration of gravity is 9.8 meters per second squared. The variable x represents the height of the object from the ground, in meters.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is an equation written in LaTeX format. The equation is as follows:\n\n$$\\frac{2x}{1-x^2}$$",
        "gt_answers": "\\angle O B A = \\angle A B C = 6 0\n",
        "image_path": "./data/HME100K/test_images/test_195.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n\\begin{equation}\ny = \\frac{1}{2} x^2 + 3x + 1\n\\end{equation}\n\nThe equation represents a parabolic function with vertex at the origin, and has a minimum value of 1 at x = 0. The maximum value of the function is 7, which is attained at x = 3.",
        "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",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you have provided. Can you please provide a different image or a different format for me to work with?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by: f(x) = x^2 - 3x + 1.\n\nThis formula can be derived by substituting the given values for a, b, and c in the formula for a quadratic equation: ax^2 + bx + c = 0. Solving for x by dividing both sides by a, we get: x^2 - (b/a)x + (c/a) = 0. Squaring both sides, we get: x^4 - (2b/a)x^3 + (2b^",
        "gt_answers": "F _ { 1 } = 1 0 0 0 N\n",
        "image_path": "./data/HME100K/test_images/test_198.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n$$ 4x + 6 = 12 $$\n\nThis equation represents the equation in the image, where x is the variable representing the number of apples. The equation states that 4x (the number of apples) plus 6 (the number of oranges) is equal to 12.",
        "gt_answers": "\\frac { 3 . 6 } { 4 . 5 } = \\frac { 4 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_200.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot write out the expression for the formula in the image as I do not have the image provided. Could you please provide the image so that I can assist you with the LaTeX format?",
        "gt_answers": "\\angle 1 = 1 8 0 ^ { \\circ } - \\angle B A E = 1 8 0 ^ { \\circ } - 4 6 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_201.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is x^2 + 3x - 4.",
        "gt_answers": "x = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_202.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula is:$$\\frac{10 + 4i - 3i - 2i}{5 + 2i + 2i - 2i}$$This can be written as:$$\\frac{(10 + 4i) - (3i + 2i - 2i)}{(5 + 2i + 2i - 2i)}$$Simplifying the numerator:$$\\frac{14 - 5i - 5i - 2i}{10 + 2i + 2i - 2i}$$",
        "gt_answers": "a = \\frac { 9 5 } { 8 6 1 }\n",
        "image_path": "./data/HME100K/test_images/test_203.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the following LaTeX expression:\n\n$$\\frac{2^4\\*5^3\\*7^2}{3\\*4\\*6\\*5}$$\n\nwhere the variables are represented by the numbers on the right side of the expression.",
        "gt_answers": "2 4 0 \\times 3 = 7 2 0 2 4 0 \\times 4 = 9 6 0\n",
        "image_path": "./data/HME100K/test_images/test_204.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:$$x^2 + 2x + 1 = 0$$This is a quadratic equation in standard form, with a leading coefficient of 1, a constant term of 2, and a variable term of x squared.",
        "gt_answers": "( x - ) ( 3 x + 2 ) - 3 x ( x + 3 ) + 1 0 x\n",
        "image_path": "./data/HME100K/test_images/test_205.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not a mathematical expression, but rather a character in a foreign language. It is not possible to provide a LaTeX expression for it.",
        "gt_answers": "\\frac { 1 } { 6 } < \\frac { 4 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_206.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{1}{2}(a + b) - \\frac{1}{2}ab = \\frac{1}{2}(a - b) + \\frac{1}{2}ab$$\n\nThe image shows the formula for the sum of two numbers, a and b, with a common denominator of 2. The formula is a geometric series with a first term of a and a common ratio of -b/a. The sum of an infinite geometric series is given by the formula:\n\n$$S\\_n = a",
        "gt_answers": "y = \\pm \\frac { \\sqrt { b ^ { 2 } + 1 } } { b ^ { 2 } + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_207.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is: $\\frac{2x^2 - 4x + 3}{x + 1} = \\frac{1}{2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{z}\\_0 \\cdot \\frac{\\text{a}\\_0^2 + \\text{b}\\_0^2}{\\text{a}\\_0^2 + \\text{b}\\_0^2 - 4\\text{c}\\_0^2} = \\frac{\\text{a}\\_0^2 + \\text{b}\\_0^2 - \\sqrt{4\\text{c}\\_0^2 - (\\text{a}\\_0^2 + \\text{b}\\_",
        "gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_209.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{Im}\\_\\text{age}\\_1 = \\frac{1}{2}(\\text{Im}\\_\\text{age}\\_2 + \\text{Im}\\_\\text{age}\\_3) + \\text{Im}\\_\\text{age}\\_4$$Note: The formula has been written in LaTeX format, using the backslash `\\` to denote the logarithmic function of `ln`.",
        "gt_answers": "x = - \\frac { 5 } { 1 8 }\n",
        "image_path": "./data/HME100K/test_images/test_210.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not written in LaTeX format, but it can be written as follows:\n\n$$\\begin{aligned}a &= \\frac{1000\\text{km}}{300\\text{h}} \\\n\\frac{300\\text{h}}{60\\text{min}} \\\n\\frac{60\\text{min}}{60\\text{s}} \\\n\\frac{1000\\text{km}}{300\\text{h}} \\\n&= \\frac{16.67\\text{km}}{\\text",
        "gt_answers": ". a _ { 1 } = - \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_211.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n$$\\begin{align\\*} 1 + 3 &= 4 \\\n\\end{align\\*}$$",
        "gt_answers": "x _ { 2 } = \\frac { 3 \\sqrt { 6 } } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_212.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\frac{x^2 + 3x - 4}{x - 2}\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in LaTeX format, follow these steps:\n\n1. Select the text in the formula image and copy it to the clipboard.\n2. Open a LaTeX editor, such as TeXstudio, on your computer.\n3. Paste the copied formula into the LaTeX editor.\n4. Replace the variable names in the formula with their corresponding LaTeX commands. For example, replace x with \\ x, and replace y with \\ y.\n5. Use the LaTeX editor to format the formula as desired, such as changing the font or adding colors.\n6. Save the LaTeX code as",
        "gt_answers": "\\frac { 1 6 } { 3 } x = \\frac { 3 2 } { 3 5 }\n",
        "image_path": "./data/HME100K/test_images/test_214.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the formula in the image:\n\n\\begin{center}\n\\frac{463\\times10^8\\times0.0454\\times1.6}{0.254}\n\\end{center}\n\nThis formula calculates the number of atoms in a sample of an unknown substance, given the mass number, atomic number, and density of the substance. The variables used in the formula are:\n\n* 463 x 10^8: the number of atoms in the sample\n* 0.04",
        "gt_answers": "2 N O + O _ { 2 } \\rightarrow 2 N O _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_215.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the sum of two numbers: $\\frac{a+b}{2}$, where $a$ and $b$ are the two numbers being added. The formula can be written using LaTeX as follows: $\\frac{a+b}{2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\sqrt{x^2 + y^2}$.",
        "gt_answers": "\\rho _ { N A } : y = \\frac { 3 } { 2 } x - 1 2\n",
        "image_path": "./data/HME100K/test_images/test_219.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: $\\frac{x+y}{2}$. This is a simple arithmetic expression that calculates the average of two numbers, $x$ and $y$.\n\nTo write this formula in LaTeX format, you can use the following code: $\\frac{x+y}{2}$.",
        "gt_answers": "x + y - \\sqrt { x + y } = 2\n",
        "image_path": "./data/HME100K/test_images/test_221.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, you would use the following code:\n\n$$\\frac{x^2 + 3x - 4}{x - 2} = \\frac{a^2 + 3a - 4}{a - 2}$$\n\nThis equation is obtained by substituting the given values of x and y into the given formula:\n\n$$\\frac{x^2 + 3x - 4}{x - 2} = y$$\n\nand simplifying it using the distributive property of multiplication over addition and the fact",
        "gt_answers": "\\frac { 1 } { 2 } ( 3 0 \\% x - 4 ) = 2 0 \\%\n",
        "image_path": "./data/HME100K/test_images/test_222.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am unable to see the image you've provided. Could you please provide the image or describe it in more detail?",
        "gt_answers": "\\cos \\beta = \\frac { 3 } { 2 } \\cos \\alpha\n",
        "image_path": "./data/HME100K/test_images/test_223.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression given in the image is:\n\n$$c\\_1 + c\\_2 + c\\_3 = 0$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the image is given by:\n\nA = \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "5 0 0 \\approx 4 8 0\n",
        "image_path": "./data/HME100K/test_images/test_225.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a right triangle with legs of length 6 and 8 is: (a + b) / 2. To find the length of the hypotenuse of this triangle, we can substitute a = 6 and b = 8 into the formula: (6 + 8) / 2 = 14 / 2 = 7. Therefore, the length of the hypotenuse is 7 units.\n\nNote: This is just one way to find the length of the hypotenuse of a right triangle. There are other methods as well, such as using the Pythagorean",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula in the image is:\n\n$$\\text{E=mc^2}$$\n\nThis equation represents the theory of special relativity, which states that the speed of light is the same for all observers, regardless of their relative motion. The equation shows that energy (E) is equal to mass (m) multiplied by the speed of light (c) squared.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $\\sqrt{100x^2+50y^2+100z^2}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 2 - 1 + 5 \\* 10 = 16.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Extract the formula from the image.\n2. Write out the formula in LaTeX format, including all mathematical symbols and equations.\n\nThe formula in the image is given by:\n\nz = sqrt((x - 22)^2 + (y - 11)^2)\n\nIn LaTeX format, this can be written as:\n\n\\begin{align\\*}\nz &= \\sqrt{(x - 22)^2 + (y - 11)^",
        "gt_answers": "2 \\sin ( A - \\frac { \\pi } { 6 } ) = 1\n",
        "image_path": "./data/HME100K/test_images/test_233.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not a mathematical expression, but rather a graphical representation of the value of y in terms of x, where y is the dependent variable and x is the independent variable.\n\nThe image represents a function where the input is x and the output is y. The equation is not written in LaTeX format, but it can be written as:\n\ny = 2x",
        "gt_answers": "y _ { 1 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_234.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n\\begin{center}\n$\\frac{a + 3b}{c + 5d}$\n\\end{center}\n\nwhere `a`, `b`, `c`, and `d` are constants.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the given image:\n\n$$\\text{adc}\\_2 + \\text{adc}\\_1 \\geq 0.5$$\n\nIn this formula, the variables $\\text{adc}\\_1$ and $\\text{adc}\\_2$ represent the two points of the image, and the inequality symbol $\\geq$ indicates that the sum of the two points must be greater than or equal to 0.5.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To calculate the sum of the digits of the number 569348, we can write it in the following form:\n\n$$\\sum\\_{i=1}^{10} \\ i \\times (5+9+3+4+8) = \\sum\\_{i=1}^{10} i \\times 30 = 55$$\n\nHere, we have used the sum formula for the arithmetic series, which gives the sum of the first n terms of an arithmetic sequence. The first term is 5, the common difference is 4, and n is 10",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n$$ \\frac{1}{16} \\left( \\frac{13 \\times 5}{4} + \\frac{9 \\times 7}{4} \\right) = \\frac{25 \\times 7}{8} $$",
        "gt_answers": "\\angle B O S + \\angle S = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_240.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $x^4 + 3x^3 + 5x^2 - 7x + 2$.",
        "gt_answers": ". ( - 4 ) + 7 + ( - 9 ) + 8 + 6 + ( - 4 ) + ( - 3 ) = 1 k m\n",
        "image_path": "./data/HME100K/test_images/test_242.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:\n\n$$\\frac{\\frac{1}{3}+\\frac{4}{5}}{\\frac{2}{7}+\\frac{3}{8}}$$\n\nAlternatively, you can express it as:\n\n$$\\frac{(1+4)/(3+5)}{(2+3)/(7+8)}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given expression is:\n\n<Sup>x<Sup>6</Sup> + 2x<Sup>5</Sup> + 3x<Sup>4</Sup> + 5x<Sup>3</Sup> + 6x<Sup>2</Sup> + 8x<Sup>1</Sup> + 10</Sup>x<Sup>0</Sup> + 15</Sup>x<Sup>-1</Sup> =",
        "gt_answers": "2 8 0 \\div 5 0 = 6 \\cdots 3 0\n",
        "image_path": "./data/HME100K/test_images/test_244.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\sqrt{x^2 + 2x + 5}$.",
        "gt_answers": "x - a ^ { 5 } = - \\frac { 1 } { b \\sqrt { 1 0 } }\n",
        "image_path": "./data/HME100K/test_images/test_248.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for finding the derivative of f(x) = x^2 is: f'(x) = 2x.",
        "gt_answers": "\\frac { 1 } { a + b } = - \\frac { 1 } { 2 - 1 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_251.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is: $\\frac{1}{2}bh$. This formula can be used to find the area of any triangle, regardless of its shape or size. To find the area of a triangle, simply use the formula and plug in the values for the base (b) and height (h). For example, if the base of a triangle is 5 units and the height is 6 units, the area would be $\\frac{1}{2} \\* 5 \\* 6 = 6$. This formula is based on the concept of Heron's formula, which states",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as follows:\n\nx + y = 3\n\nx - y = 5\n\nx - 2y = 2\n\ny = (3 - x) / 2\n\ny = (5 - x) / 2\n\ny = 2(x - 3) / 2\n\ny = (x - 5) / 2\n\ny = 2(x - 3) / 2\n\ny = 2(x - 5) / 2\n\ny = (2x -",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a rectangle with a width of 4 cm and a height of 5 cm is given by the formula:\n\nA = l \\* w + h \\* h\n\nwhere l is the length of the rectangle, w is the width of the rectangle, and h is the height of the rectangle.\n\nSubstituting the given values into the formula, we get:\n\nA = 4 \\* 5 + 5 \\* 5\nA = 20 + 25\nA = 45 cm^2\n\nTherefore, the area",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX format for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\coordinate (1) at (0,0);\n\\coordinate (2) at (1,0);\n\\coordinate (3) at (1,1);\n\\coordinate (4) at (0,1);\n\\coordinate (5) at (0.5,0.5);\n\\draw (1) -- (2) -- (3) -- (4) -- (5) -- cycle;\n\\filldraw (5) circle (2pt) node[",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in LaTeX format is: $\\frac{2x}{3}+\\frac{4y}{5}+\\frac{5z}{6}=22$\n\nIn words, the equation is: The sum of two thirds of x plus four fifths of y plus five sixths of z is equal to 22.",
        "gt_answers": "y = \\frac { 1 } { 3 } x ^ { 2 } + b x + c\n",
        "image_path": "./data/HME100K/test_images/test_257.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n\\frac{4 \\times 6 + 7 \\times 8}{9 \\times 5} &= \\frac{24 + 56}{45} \\\n&= \\frac{70}{45} \\\n&= 1.5666666666666666666666666666666666666666666666666666",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is showing the equation of the derivative of x^4 with respect to x. The derivative of x^4 with respect to x is given by the formula:\n\nd/dx [x^4] = 4x^3\n\nThe image is showing this equation as:\n\nd/dx [x^4] = 4x^3",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Identify the variables in the formula: The variables in the formula are x and y.\n2. Write the formula using LaTeX format: The formula is given by: f(x,y) = (3x^2 + 4y^2 - 8x - 6y + 12) / (x + y - 4).\n3. Simplify the formula: We can simplify the formula using the distributive property of multiplication over addition and the identity 1 +",
        "gt_answers": "6 2 9 \\div 1 3 = 4 8 \\cdots 5\n",
        "image_path": "./data/HME100K/test_images/test_262.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is $\\pi$r^2$,$ where $r$ is the radius of the circle. For a circle with radius $r=8$, the area is $\\pi$8^2=32$pi$8=32\\*256\\*256pi\\*8=32\\*256\\*256\\*8pi$=32\\*256\\*256\\*8pi$=32\\*256\\*256\\*8\\*180",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \\frac{x+3}{x-5}.\n\nThis formula is a difference of two polynomials with a constant term of 3 and a variable x. The numerator is (x+3) and the denominator is (x-5). When x is equal to 5, the value of the formula is 8, which is the value of x+3 when x is equal to 5.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "1. The number of rows in a table is 4.\n\n2. The number of columns in a table is 2.\n3. The sum of the values in the first row is 24.\n4. The sum of the values in the second row is 18.\n5. The sum of the values in the third row is 24.\n6. The sum of the values in the fourth row is 24.\n7. The sum of the values in the table is 74.\n8. The average of the values in the table is 37",
        "gt_answers": "a \\geq - \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_265.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$E = \\frac{1}{2}mv^2 - \\frac{1}{2}mv^2$$\n\nwhere $E$ is the energy, $m$ is the mass, $v$ is the velocity.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as follows:\n\n\\begin{align\\*}\n\\text{ImageContent} = \\frac{1}{2}(3x^2 + 2xy + y^2) + \\frac{1}{2}(x - y)^2\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression:\n\n$$\\begin{aligned} x^2 + 2x - 3 &= 0 \\Rightarrow x = -\\frac{1}{2}\\ or x = \\frac{1}{2}\\end{aligned}$$\n\nThe formula is a quadratic equation in standard form, which means the coefficient of the squared term (x^2) is 2 and the coefficient of the linear term (x) is 1. The formula gives the solutions to the equation x^2 + 2x - 3 = 0, which are x = -1/2",
        "gt_answers": "x _ { 1 } = \\sqrt { 5 } + 1 , x _ { 2 } = 1 - \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_268.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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$$\\text{F} = \\frac{1}{4}(x^2+y^2+z^2)$$",
        "gt_answers": "D E + E C = D C = 3 . 5 c m\n",
        "image_path": "./data/HME100K/test_images/test_269.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To display the image, you can use the following LaTeX code:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=0.5]\n\\draw (0,0) -- (2,0) node[midway, right] {$x$};\n\\draw (0,1) -- (2,1) node[midway, right] {$y$};\n\\draw (0,2) -- (2,2) node[midway, right] {$z$};\n\\draw (0,0) -- (0,2) node[midway, above] {$w$};",
        "gt_answers": "1 = - 1 , x _ { 2 } = \\frac { 5 \\cdot } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_270.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nbe\\_{d\\_f}y f(x) = \\frac{1}{1 + e^{-x}}.\\\n\nNote that the subscript in the be\\_{d\\_f}y variable indicates that it represents the derivative of the function f(x) with respect to x. The expression is also written in the format of a mathematical equation with the function f(x) on the left side and the equation on the right side.",
        "gt_answers": "\\therefore B E = D F = y\n",
        "image_path": "./data/HME100K/test_images/test_271.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{250\\times \\frac{1}{2}}{36}$$The solution is:$$\\frac{250\\times \\frac{1}{2}}{36}= \\frac{50}{18}=\\boxed{\\frac{5}{9}}$$Therefore, the answer is $\\frac{5}{9}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "5x + 4y = 24",
        "gt_answers": "1 5 \\times 4 = 6 0 ( k g )\n",
        "image_path": "./data/HME100K/test_images/test_273.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a complex equation involving the trigonometric functions sin(x) and cos(x), as well as the exponential function e^x. The expression can be written out as follows:\n\ncos(x) = 4sin(x) + 3cos(x) - 5e^x + 2sin(x)cos(x) - 1\n\nThis equation can be solved for x by substituting the values of the trigonometric functions and exponential function into the equation. The solution is x = arcsin(4 + 3cos(x) - 5",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \u222bb2c2\u2212a2c2d2a2b2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: $\\frac{3}{4} \\cdot \\frac{2}{3} + \\frac{3}{4} \\cdot \\frac{1}{2} = \\frac{11}{12}$. This is obtained by substituting the given values into the formula for the sum of two fractions: $\\frac{a}{b} + \\frac{c}{d} = \\frac{a \\cdot d + b \\cdot c}{b \\cdot d}$. In this case, a = $\\frac{3}{4}$, b = $\\frac{2}{3}$, c",
        "gt_answers": "C D = 4 \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_279.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{347 + 117}{253 - 219}$\n\nIn LaTeX format, this would be: $\\frac{347 + 117}{253 - 219}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:5x3+3x5=30+5x3=35x5.",
        "gt_answers": "\\frac { 3 6 } { 4 } = \\frac { x } { 2 9 }\n",
        "image_path": "./data/HME100K/test_images/test_281.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by: A = l \\* w, where l is the length and w is the width of the rectangle. In LaTeX format, this formula can be written as: $\\text{A = l \\* w}$\n\nHere's how the formula would look like in LaTeX format:\n\nA = l \\* w",
        "gt_answers": "\\sin ( - \\frac { 8 7 } { 4 } \\pi ) = s i\n",
        "image_path": "./data/HME100K/test_images/test_282.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{3x + 2y + 1}{x + 2y - 3} = \\frac{3x + 2y + 1}{x + 2y - 3} = \\frac{3(x + 2y) + 1}{x + 2y - 3} = \\frac{3x + 2y + 1}{x + 2y - 3} = \\frac{3(x + 2y) + 1}{x +",
        "gt_answers": "1 6 \\times 6 = 9 6 c m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_283.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the given formula:\n\n\\begin{align}\ny &= \\frac{x^2}{4} + \\frac{9x}{2} - \\frac{15}{2}\\\n\\end{align}\n\nThis formula represents a parabolic function with a vertex at the origin and a maximum value of 15 at x=3.",
        "gt_answers": "y = \\frac { 9 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_285.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:\n\n$$x = 250\\sin{15}$$\n\n$$y = 150\\sin{30}$$\n\n$$z = 50\\sin{45}$$\n\nThe image is a three-dimensional representation of the function $f(x, y, z) = \\sin(x) \\sin(y) \\sin(z)$. The image shows the level sets of the function at the values of $x = 250$, $y = 150$, and $z = 50$.",
        "gt_answers": "7 5 0 + 1 5 0 ( x - 1 ) = \\frac { 3 0 0 x } { 2 } + \\frac { 1 0 0 x } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_287.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the sum of 4 and 3 is given by:$$4 + 3 = 7$$This is a simple arithmetic expression that can be expressed using LaTeX notation as follows:$$4 + 3 = 7$$Note that the sum of 4 and 3 is 7, which is the result of adding the two numbers together. The LaTeX notation shows this by combining the two numbers using the addition symbol ($ $) and the equal sign (=).",
        "gt_answers": "\\frac { 7 } { 8 } = \\frac { 4 2 } { 4 8 }\n",
        "image_path": "./data/HME100K/test_images/test_288.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: 3x + 4y = 18. This equation represents a line in the xy-plane that passes through the point (0, 2) and has a slope of 3. The equation can be written as y = (18 - 3x) / 4.",
        "gt_answers": "\\frac { 1 2 } { 1 6 } = \\frac { 9 } { 1 2 } \u3001 \\frac { 4 } { 1 2 } > \\frac { 5 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_289.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the binomial theorem for the power 3.\n\n$$ \\binom{n}{3} = \\frac{n!}{3! (n-3)!} = \\frac{6}{3} \\cdot \\frac{5}{3} \\cdot \\frac{4}{3} = 20 $$\n\nwhere $n=10$ and $n!$ is the factorial of $n$.",
        "gt_answers": "\\frac { B D } { C P } = 1\n",
        "image_path": "./data/HME100K/test_images/test_290.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{r}=\\frac{5}{3}$$This is a mathematical equation that states that the radius of a circle is equal to 5 divided by 3.",
        "gt_answers": "5 x = \\frac { 1 } { 2 } x + 3\n",
        "image_path": "./data/HME100K/test_images/test_291.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a formula for the force of gravity acting on a body in space. The formula is expressed as:</p>Fg=G&#x03B4;m&#x03B1;(r)&#x03BC;&#x03B4;(r)&#x03B2;&#x03B3;&#x03B3;&#x03B4;(r)&#x03BC;&#x03B4;(r)&#x03B2;&#x03B3;",
        "gt_answers": "C O _ { 2 } + C a ( O H ) _ { 2 } = C a C O _ { 3 } \\downarrow + H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_292.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$x = \\frac{b}{2}$$This formula is derived from the slope formula, which states that the slope of a line is equal to the ratio of the rise to the run. In this case, the rise is 4 and the run is 3, so the slope is 4/3. Dividing both sides of the equation by 2 gives the formula shown in the image.",
        "gt_answers": "x = \\frac { 1 6 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_293.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n$$\\begin{aligned} \\frac{1}{x}+\\frac{1}{y} &= \\frac{1}{xy}\\end{aligned}$$",
        "gt_answers": "x + 3 x = 2 + 1 - 1\n",
        "image_path": "./data/HME100K/test_images/test_294.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle can be expressed as:\n\nA = (b / 2) \\* h\n\nWhere:\n\n* A is the area of the triangle\n* b is the base of the triangle\n* h is the height of the triangle\n\nThe triangle in the image has a base of 6 cm and a height of 8 cm. Using the formula above, we can calculate the area of the triangle:\n\nA = (6 / 2) \\* 8\n= 36 cm\u00b2\n\nTherefore, the area of the triangle in the image",
        "gt_answers": "P = e g h = 1 \\times 1 0 ^ { 3 } k g / m ^ { 3 } \\times 0 . 1 m \\times 9 . 8 N / k g = 9 8 0 P a\n",
        "image_path": "./data/HME100K/test_images/test_295.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: 1 - 1 + 1 = 1.",
        "gt_answers": "\\frac { O E } { O B } = \\frac { O F } { O C }\n",
        "image_path": "./data/HME100K/test_images/test_296.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is given by:",
        "gt_answers": "x ^ { 2 } + x + 1 = ( x + \\frac { 1 } { 2 } ) ^ { 2 } + \\frac { 3 } { 4 } \\in [ - 1 , 1 ]\n",
        "image_path": "./data/HME100K/test_images/test_297.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$ \\begin{aligned} \\text{sin}\\ x &= \\frac{-y}{\\sqrt{1 - y^2}} \\ \\ \\ \\text{for}\\ 0 \\leq x \\leq \\pi \\\\ \\text{cos}\\ x &= \\frac{1}{\\sqrt{1 - y^2}} \\ \\ \\ \\text{for}\\ 0 \\leq x \\leq \\pi \\end{aligned} $$\n\nwhere $x$ is the angle whose sine and cosine are",
        "gt_answers": "\\sin ( \\frac { \\pi } { 6 } + x ) = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_298.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as: x^2 + 2x - 5 = 0. This is a quadratic equation with two variables, x and y, and one constant, 5.",
        "gt_answers": "\\frac { 6 } { x + 1 } = \\frac { x - 8 } { 3 } + 2\n",
        "image_path": "./data/HME100K/test_images/test_299.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```scss\n\n\\begin{center}\n\\frac{dV}{dt} = \\frac{Q}{t} - \\frac{V}{t^2} - \\frac{2m}{t^3}\n\\end{center}\n\nThis is the formula for the time derivative of a damped harmonic oscillator with mass `m` and damping coefficient `c`. The formula relates the rate of change of volume `V` with time `t` to the flow of energy `Q` into the system, taking into account the internal dissipation due to the d",
        "gt_answers": "\\angle A C D + \\angle B A C = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_300.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\text{k}=\\sqrt{\\frac{E}{m}}$$This is the formula for the velocity of an object in terms of its energy (E) and mass (m).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\frac{1}{2} \\* x^2 + \\frac{1}{2} \\* x + \\frac{1}{4} = 0\n\nThis equation is a quadratic equation, with the variable x. The solutions to this equation are the values of x that make the equation true. In this case, the solutions are:\n\nx = - \\frac{b}{2a} = - \\frac{1}{4}\nx = \\frac{b}{2a} = \\frac{1}{2}\n\nThere",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a trapezoid is:\n\nA = (b1 + b2) / 2 \\* h\n\nwhere b1 and b2 are the lengths of the parallel sides of the trapezoid, and h is the height of the trapezoid.\n\nThe area of this trapezoid is 80 cm^2.\n\nThe height of the trapezoid is 10 cm.\n\nThe length of the parallel sides of the trapezoid are 20 cm and 30 cm.\n\nTherefore,",
        "gt_answers": "x - 4 y + 5 = 0\n",
        "image_path": "./data/HME100K/test_images/test_303.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 2x + 3y = 11.",
        "gt_answers": "y = - \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_304.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{ImageContent} = \\text{a formula}$$\n\nwhere $\\text{a formula}$ is the image content.",
        "gt_answers": "\\frac { 4 } { 5 } S _ { A B C D } = 2 ( S _ { D B _ { 1 } C _ { 1 } } + S _ { B _ { 1 } C D _ { 2 } } + S _ { D _ { 2 } B A _ { 4 } } + S _ { C _ { 1 } A A _ { 4 } }\n",
        "image_path": "./data/HME100K/test_images/test_306.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format of the expression:\n\n\\begin{align\\*}\n\\text{The given equation represents a straight line with slope }k\\text{ and y-intercept }k. The equation can be written in slope-intercept form as: }\n\\end{align\\*}\n\ny = kx + b\n\nwhere b is the y-intercept, which can be calculated as the constant value in the equation when x = 0:\n\nb = - 3\n\nSo the equation can be written in slope-intercept form as:",
        "gt_answers": "N a O H + K N O _ { 3 } = N a N O _ { 3 } + K O H\n",
        "image_path": "./data/HME100K/test_images/test_307.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is:\n\n$$a + b = c$$\n\nwhere $a$, $b$, and $c$ are constants. The image shows the equation written in LaTeX format:\n\n$$a + b = c$$",
        "gt_answers": "B D = O D = \\frac { 1 } { 2 } B C\n",
        "image_path": "./data/HME100K/test_images/test_308.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is given by:\n\n$$A = \\frac{1}{2}bh$$\n\nwhere $A$ is the area, $b$ is the base, and $h$ is the height. The height is given by:\n\n$$h = \\sqrt{s(s-a)(s-b)}$$\n\nwhere $s$ is the semiperimeter, $a$ is the length of the base, and $b$ is the length of the other base. The semiperimeter is given by:\n\n$$s = \\frac{1",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n\\begin{center}\n\\begin{minipage}{0.45\\textwidth}\n\\begin{equation}\n\\text{The formula is: } \\frac{100}{x}\n\\end{equation}\n\\end{minipage}\n\\end{center}\n\nIn this LaTeX code, we use the center environment to center the text, the minipage environment to set the width of the text to 0.45\\textwidth, and the equation environment to write",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\nd(d)/dt = d(d^2)/dt = 2dd/dt\n\nThis is the derivative of d with respect to t, which is equal to the derivative of d^2 with respect to t. The second derivative of d with respect to t is 2d/dt.",
        "gt_answers": "\\frac { D E } { O D } = \\frac { B D } { D E }\n",
        "image_path": "./data/HME100K/test_images/test_312.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{6x^2+12x-8}{2x+4}$$\n\nNote: This answer assumes that the expression in the image is correct and has not been simplified.",
        "gt_answers": "\\pm \\sqrt { ( - 6 ) ^ { 2 } } = \\pm 6\n",
        "image_path": "./data/HME100K/test_images/test_313.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$ \\text{pe d} - \\text{b} $$\n\nwhere $\\text{pe}$ is the pressure of the gas in the cylinder, $\\text{d}$ is the diameter of the cylinder, and $\\text{b}$ is the pressure of the gas in the cylinder when it is fully expanded. The subtraction of these two pressures gives the difference in pressure between the fully expanded and fully compressed states of the gas.",
        "gt_answers": "D E ^ { 2 } = D O \\cdot D B\n",
        "image_path": "./data/HME100K/test_images/test_314.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\nx &= 2y + 3z \\\n&= (2y + 3z) \\\n&= 2y + 3z \\\n&= y + 3z \\\n&= y + (3z) \\\n&= y + 3z \\\n&= y + 3z \\\n&= y + 3z \\\n&= y + 3z \\\n&= y + 3z \\\n&= y + 3z \\\n&= y + 3z \\",
        "gt_answers": "2 x + y = 3 x + 6 y = 0\n",
        "image_path": "./data/HME100K/test_images/test_315.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\\begin{equation} x + y = 3 \\end{equation}\n\nThis is the equation of a line in the Cartesian plane with a slope of 1 and a y-intercept of 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is ln(90) - 2ln(0.5) + 2ln(1.5).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the equation of a line is given by:y = mx + bwhere m is the slope of the line and b is the y-intercept. In this case, the equation is given by y = 2x - 5. The equation is shown in the image.",
        "gt_answers": ". O A = \\sqrt { 1 ^ { 2 } + 4 ^ { 2 } } = \\sqrt { 1 7 }\n",
        "image_path": "./data/HME100K/test_images/test_318.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{center} $\\frac{2}{n} \\leq \\frac{1}{n-1} \\leq \\frac{n-2}{n}$ \\end{center}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the equation of a parabola with equation y = 2x^2+5x+3.",
        "gt_answers": "2 1 \\times 2 1 = 4 6 1\n",
        "image_path": "./data/HME100K/test_images/test_321.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle with sides measuring 3cm, 4cm and 5cm is: 3 + 4 + 5 = 12cm\u00b2.",
        "gt_answers": "k = \\frac { 1 9 } { 2 7 }\n",
        "image_path": "./data/HME100K/test_images/test_322.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "In LaTeX, the formula for the given expression would be:\n\n$$\\frac{5000 - 1175}{400} = \\frac{3825}{400}$$\n\nAlternatively, you can write the formula as:\n\n$$\\frac{a}{b} = \\frac{c}{d}$$\n\nwhere $a = 5000 - 1175$, $b = 400$, $c = 3825$, and $d = 400$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, the expression for the formula in the image is:\n\n\u222bt&#x007E;&#x007E;x&#x2212;ax2&#x2212;bx+C dx\" role=\"presentation\" style=\"position: relative;\">\u222bt\u20d7\u20d7x\u2212ax2\u2212bx+C dx\u222bt\u20d7\u20d7x\u2212ax2\u2212bx+C dx\\int\\_{t\\_0}^{t} \\frac{x-a}{x^2-bx+c}dx",
        "gt_answers": "V = \\frac { F + ( n + \\frac { 3 } { 4 } ) } { M } = W R\n",
        "image_path": "./data/HME100K/test_images/test_324.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{500+600+700+800+900+1000}{6} = \\frac{3000+4000+5000+6000+7000+8000}{6} = \\frac{30000+40000+50000+60000+70000+80000}{6} = \\frac{120",
        "gt_answers": "x = ( 5 0 + k _ { 1 } \\times 5 0 ) c m ( k _ { 1 } = 1 , 2 , 3 \\cdots )\n",
        "image_path": "./data/HME100K/test_images/test_325.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:12x3+5x44x3=x2+x42x3+x5x44x3=x2+x42x2x4x3=x42+x3x5x44x3=x42+x3x5x44x3=x42+x3x5x44x3=x42+x3x5x44x3=x42+x3x5x44x3=x42+x3",
        "gt_answers": "1 4 \u3001 - \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_326.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n\\frac{1}{\\left(\\frac{5\\left(\\frac{x\\left(2\\left(\\frac{2}{x}\\right)^2-1\\right)}{x-1}\\right)}{\\left(\\frac{1}{x}\\right)\\left(\\frac{2\\left(\\frac{2}{x}\\right)^2-1}{x-1}\\right)}\\right)}\n\\end{center}\n\nNote: The expression is a non-standard form and may not be solvable analyt",
        "gt_answers": "\\beta + \\alpha = 2 k \\pi + \\frac { \\pi } { 2 } ( k \\in z )\n",
        "image_path": "./data/HME100K/test_images/test_327.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\text{Image Content}$$",
        "gt_answers": "x _ { 1 } = - 5 x _ { 2 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_328.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{b}{a}+\\frac{c}{d}$$where b and c are the areas of the circles and a and d are their diameters.",
        "gt_answers": "x _ { 1 } = 0 x _ { 2 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_329.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The formula for the image is given by the following LaTeX expression:\n\n\\begin{center}\n$$\\frac{\\text{Area of circle}}{\\text{Area of square}}$$\n\\end{center}\n\nThis formula is derived from the image, where a circle is inscribed in a square, and the area of the circle is divided by the area of the square to find the ratio of the circle to the square.",
        "gt_answers": "( a + 1 ) ^ { 2 } + ( a - 1 ) ^ { 2 } = 3 4\n",
        "image_path": "./data/HME100K/test_images/test_330.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the formula in the image using LaTeX format is:\n\n$$\\frac{x + 3}{2x - 5}$$\n\nWhere x is the variable in the equation.",
        "gt_answers": "\\sqrt { 5 x - 4 } = - x + 2\n",
        "image_path": "./data/HME100K/test_images/test_331.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression of the formula in the image is:$$\\frac{x+y}{2}$$This is a simple arithmetic expression that adds the values of x and y and divides the sum by 2.\n\nNote that the expression is written in LaTeX format, which uses the `\\frac`command to produce a fraction. The expression is also enclosed in dollar signs, which indicate that it is a mathematical expression.",
        "gt_answers": "x _ { 2 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_332.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 3(x^2 + 2x + 1) - (2x^2 + 4x + 1) = x^2 - 4x + 1.\n\nNote that the expression has been written in LaTeX format, with the variable x written in uppercase letters, the exponent written in superscript, and the multiplication symbol written as \"\\*\".",
        "gt_answers": "1 \\div 2 = \\frac { 1 } { 2 } ( k g )\n",
        "image_path": "./data/HME100K/test_images/test_333.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: $ 2 \\times 4 \\times 2 = 8 $",
        "gt_answers": "- q _ { 1 } B V _ { 1 } = m \\frac { V _ { 1 } ^ { 2 } } { R }\n",
        "image_path": "./data/HME100K/test_images/test_334.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following equation:$$\\frac{x^2 - 4x + 2}{x - 2} = \\frac{x - 1}{x - 2}$$This formula can be read as \"the difference of x squared minus four times x plus two, divided by x minus two, is equal to the difference of x minus one divided by x minus two.\"The image shows a mathematical formula for solving a quadratic equation, which is a type of algebraic equation that involves the square of an variable. In this case,",
        "gt_answers": "x ^ { . } + \\frac { \\sqrt { 6 } } { 4 } = - \\frac { 3 } { 4 } \\sqrt { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_335.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a geometric series with initial value n = 1 and common ratio r = 2, which means the first term a1 = 1 and subsequent terms a2, a3, a4,... are obtained by multiplying the previous term by r.\n\nThe sum of the infinite geometric series is given by the formula: S = a1/(1 - r)\n\nIn this case, a1 = 1 and r = 2, so the sum is:\nS = 1/(1 - 2) = 1/(1 - 2) = 1/1 =",
        "gt_answers": "s x = 5\n",
        "image_path": "./data/HME100K/test_images/test_336.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n<LaTeX math mode> \n(1/2) \\* (1/2) \\* (2) = 1/4\n</LaTeX math mode>",
        "gt_answers": "\\angle A H C = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_337.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{center}\n\\frac{a^2+b^2}{2ab}\n\\end{center}\n\nwhere $a$ and $b$ are the lengths of the two chords shown in the image.",
        "gt_answers": "x = 2 \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_338.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{300+400+500-300-500-200}{300+400+500-200}$$\n\n$$\\frac{300+400+500-300-500-200}{300+400+500-200}$$\n\n$$\\frac{800-300-500}{300+4",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression of the formula in the image:\n\n\\begin{equation}\n\\frac{1}{2}(x + y) - \\frac{1}{4}(x - y) = \\frac{1}{2}x + \\frac{1}{2}y - \\frac{1}{4}x + \\frac{1}{4}y = \\frac{1}{2}x + \\frac{1}{2}y - \\frac{1}{4}x - \\frac{1}{4}y = \\frac{1}{2}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "In LaTeX format, the expression for the formula in the image would be:$$\\frac{1}{2} + \\frac{1}{4} - \\frac{1}{8} + \\frac{1}{16} - \\frac{1}{32} + \\frac{1}{64} - \\frac{1}{128} + \\frac{1}{256} - \\frac{1}{512} + \\frac{1}{1024} - \\frac{1}{2048} + \\frac{1}{4096",
        "gt_answers": "\\frac { 1 } { 3 } S _ { \\Delta } A B O = 2 4 \\times \\frac { 1 } { 3 } = 8 = S _ { \\Delta } A B P\n",
        "image_path": "./data/HME100K/test_images/test_341.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$\\frac { \\sqrt{225}}{7}$",
        "gt_answers": "a = \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_343.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$ \\text{Image Content}$$\n\nHere, the image content is represented by the variable `$\\text{Image Content}$`. The formula contains an algebraic expression that is evaluated using the values of the variables and constants involved in the formula. The expression is evaluated by replacing the variables and constants with their corresponding values and following the rules of algebra to simplify the expression.",
        "gt_answers": "9 x + G = 3 x + G\n",
        "image_path": "./data/HME100K/test_images/test_344.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$\\textstyle y = \\frac{x^2}{2} + \\frac{3x}{2} + 1$$\n```\nThis is the equation of a parabolic function with center at the origin and apex at $(1, 3)$.",
        "gt_answers": "( x - 2 b ) ( y - 2 a ) = x y - 2 a x - 2 b y + 4 a b\n",
        "image_path": "./data/HME100K/test_images/test_345.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:",
        "gt_answers": "( x _ { 0 } - m ) y = y _ { 0 } ( x - m )\n",
        "image_path": "./data/HME100K/test_images/test_346.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a system of nonlinear differential equations with parameter x and constant parameter k. The equations can be written as:",
        "gt_answers": "x > 2 x < - 2\n",
        "image_path": "./data/HME100K/test_images/test_348.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is shown below:\n\n![Image content](https://i.imgur.com/a/wUvBM8X.png)\n\n![Image content](https://i.imgur.com/a/wUvBM8X.png)\n\nIn LaTeX format, this equation would be written as:\n\n$$\\frac{1}{2} x^2 + \\frac{1}{4} x^4 = \\frac{1}{4} x^4 + \\frac{1}{8} x^6$$\n\nIn Japanese, the equation is written as",
        "gt_answers": "x = \\frac { 1 } { 6 } \\div \\frac { 3 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_349.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the given formula:\n\n\\begin{align\\*}\nm\\_1 + m\\_2 &= m\\_2 + m\\_1 \\\n&= m\\_2 + m\\_1 \\\n&= m\\_1 + m\\_2 \\\n&= m\\_2 + m\\_1 \\\n&= m\\_1 + m\\_2 \\\n&= m\\_2 + m\\_1 \\\n&= m\\_1 + m\\_2 \\\n&= m\\_2 + m\\_1 \\\n&= m\\_1 + m\\_2 \\\n&= m\\_2 + m\\_1 \\\n&= m",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n\\begin{equation}\n2x + 3y = 10\n\\end{equation}\n\nThis is a linear equation in two variables, with the constant term 10. The coefficient of x is 2 and the coefficient of y is 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is not specified. Please provide a formula to write out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is: 1/(1 + x) where x is the variable.\n\nThe given expression is equivalent to the formula: 1/(1 + x) where x is the variable.\n\nThe limit of this expression as x approaches 4 is: 1/5.",
        "gt_answers": "x _ { 2 } = \\frac { 1 } { - 4 }\n",
        "image_path": "./data/HME100K/test_images/test_354.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} \\frac{a+b}{c+d} \\ &= \\ \\frac{a}{c} + \\frac{b}{d} \\ \\ &= \\ \\frac{a}{c} + \\frac{b}{d} \\ &= \\ \\frac{a}{c}+\\frac{b}{d}\\ \\ &= \\ \\frac{a}{c}+\\frac{b}{d}\\ \\ &= \\ \\frac{a}{c}+\\frac{b}{d}\\ \\ &= \\ \\frac{a}{c}+\\frac",
        "gt_answers": "S _ { a } = S = 1 0 m\n",
        "image_path": "./data/HME100K/test_images/test_355.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: $\\frac{1}{2}\\left( \\frac{4}{3}\\right) + \\frac{1}{4}\\left( \\frac{2}{3}\\right) = \\frac{1}{2}\\left(\\frac{8}{9}\\right) = \\frac{8}{18} = \\frac{4}{9}$\n\nThis image represents a linear combination of two fractions with the variables x and y. The first fraction is $\\frac{4}{3}$, and the second fraction is $\\frac{2}{3}$. The linear combination is denoted by the",
        "gt_answers": "\\frac { 4 } { B D } = \\frac { 8 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_356.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the formula: A = l x w, where l is the length and w is the width of the rectangle. In this case, l = 10 inches and w = 1 inch. To find the area of the rectangle, we simply multiply l and w together: A = 10 x 1 = 10 inches squared. The answer is 10 inches squared.",
        "gt_answers": "y _ { 2 } = - \\frac { 2 \\sqrt { 7 } } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_357.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the formula A = l \u00d7 w, where l is the length and w is the width of the rectangle. To find the area of the rectangle in the image, we need to find the length and width of the rectangle.\n\nFrom the image, we can see that the width of the rectangle is 5 cm and the length is 7 cm. Therefore, the area of the rectangle is 5 cm \u00d7 7 cm = 35 cm\u00b2.\n\nTo evaluate the expression for the area of the rectangle, we can substitute the values of l and w into the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $ $\\frac{2}{x^2 + 6x + 8}$ $ $\\frac{4x - 3}{x^2 + 6x + 8}$ $ $ $ $\\frac{6x - 4}{x^2 + 6x + 8}$ $ $\\frac{8 - 3x}{x^2 + 6x + 8}$ $ $ $\\frac{1}{x + 4}$ $\\frac{2x - 3}{x^2 + 6x + 8}$ $\\",
        "gt_answers": "x _ { 1 } = 1 + \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_359.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=1.5]\n\\draw[thick,rounded corners] (0,0) rectangle (2,2);\n\\node at (1,1) {$$};\n\\end{tikzpicture}\n\\end{center}\n\nThis code generates a rectangle with a dollar sign in the middle. Let me know if you have any further questions!",
        "gt_answers": "1 \\div 9 = \\frac { 1 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_362.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\nx^2 + y^2 = r^2\n\nwhere x and y are the coordinates of any point on the circle and r is the radius of the circle.\n\nThe center of the circle is given by the point (0, 0). To find the equation of the circle, we can substitute (0, 0) for x and y in the formula:\n\n0^2 + 0^2 = r^2\n\n0 = r^2\n\nr = \u00b1sqrt(r^2)\n\nr = \u00b1",
        "gt_answers": "\\frac { 2 x - 1 } { 3 } = \\frac { 3 } { 4 } x - 5\n",
        "image_path": "./data/HME100K/test_images/test_364.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{f\\_i}{g\\_i}$\n\nWhere:\nf\\_i = x^2 + y^2\ng\\_i = (x + y)^2",
        "gt_answers": "\\frac { 1 } { 2 } ( x - t ) ( x - t + 4 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_365.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: f(x) = 2x + 3.\n\nHere is the LaTeX format for the equation:\n\n\\begin{align\\*}\nf(x) &= 2x + 3 \\\n\\end{align\\*}",
        "gt_answers": "4 x ^ { 4 } - 5 x ^ { 2 } - 4 = 0\n",
        "image_path": "./data/HME100K/test_images/test_368.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is not provided. Please provide the image so I can write out the LaTeX expression.",
        "gt_answers": "A B ^ { 2 } - A D ^ { 2 } = D B\n",
        "image_path": "./data/HME100K/test_images/test_369.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by: $\\frac{1}{2} \\cdot \\frac{5}{4} = \\frac{5}{8}$",
        "gt_answers": "1 5 - 5 = 1 0 ^ { \\circ } C\n",
        "image_path": "./data/HME100K/test_images/test_370.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize, but I cannot see the image as it is not provided. Please provide the image for me to assist you.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot provide the image as it is not available to me. Please provide the image so I can assist you with the question.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written as:\n\n$$\\text{ImageContent}\\times\\left(\\frac{a\\sin(x)}{b}\\right)^2$$\n\nwhere $a$ and $b$ are constants, and $x$ is a variable.",
        "gt_answers": "\\frac { 4 } { 5 } x = \\frac { 4 } { 5 } + \\frac { 2 5 } { 5 . }\n",
        "image_path": "./data/HME100K/test_images/test_376.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![Image Content](https://i.imgur.com/e5a4yx6.png)\n\nIn LaTeX format, this would be written as:\n\n\\begin{align\\*}\nf(x) &= \\frac{1}{x^2 + 4x - 2} \\\n&= \\frac{1}{(x + 2)(x - 2)} \\\n&= \\frac{1}{x - 2} + \\frac{1}{x + 2}\n\\end{align\\*}",
        "gt_answers": "\\angle D O H = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_378.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n<img src=\"https://www.khanacademy.org/math/geometry/cc-d/cc-d-congruent-cycles/cc-d-congruent-cycles.html\" alt=\"Congruent Circles\"/>\n\nIn LaTeX format, this would be written as:\n\n\\begin{center}\n\\includegraphics[width=3in]{https://www.khanacademy.org/math/geometry/cc-d/cc-d-congruent-cycles/cc-d",
        "gt_answers": "W _ { 1 } = V _ { 1 } I _ { 1 } t = V I _ { 1 } t = 6 v \\times 0 . 6 A \\times 1 0 s = 3 6 J\n",
        "image_path": "./data/HME100K/test_images/test_379.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:\n\n$$ 4x + 2y = 4 $$\n\nwhere $x$ and $y$ are variables.",
        "gt_answers": "4 x + 2 x - 2 = 4\n",
        "image_path": "./data/HME100K/test_images/test_380.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:$$m=g\\_{t}t$$where$m$is the mass of the object, $g$ is the acceleration due to gravity, $t$ is the time of fall. This formula is derived from the equation of motion for an object falling under the influence of gravity.",
        "gt_answers": "m g = G \\frac { M m } { R ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_382.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{Area} = \\frac{1}{2}ab$$\n\nwhere $a$ and $b$ are the lengths of the sides of the rectangle.",
        "gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
        "image_path": "./data/HME100K/test_images/test_383.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\text{P} = \\frac{360}{\\sqrt{2}}$$where P is the probability that the next card drawn from a standard deck of cards is a queen of spades.",
        "gt_answers": "\\tan \\angle O A B = \\frac { O B } { O A } = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_384.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by A = \u03c0r^2.\n\nIn LaTeX format, the formula can be written as:\n\n\\begin{align\\*}\nA &= \\pi r^2\n\\end{align\\*}\n\nThis formula states that the area of a circle is equal to the product of pi and the square of its radius.",
        "gt_answers": "6 0 m = 6 0 0 0 c m\n",
        "image_path": "./data/HME100K/test_images/test_385.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the given image:\n\n$$\\begin{aligned}\\text{Image Content} \\equiv \\frac{5+6\\times3}{7} \\times 2 \\cdot \\frac{5+7\\times 4}{8} + 5 \\cdot \\frac{5+8\\times 6}{9}\\end{aligned}$$",
        "gt_answers": "\\overrightarrow { E D } = ( 0 . 4 , - 3 )\n",
        "image_path": "./data/HME100K/test_images/test_386.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x^2+y^2}{x+y}=\\sqrt{x^2+y^2}$.",
        "gt_answers": "S = 2 4 . 5 \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_387.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: y = 2x + 3. The equation is a linear equation with a slope of 2 and an intercept of 3.",
        "gt_answers": "t _ { 1 } = \\frac { V _ { 1 } } { a _ { 1 } }\n",
        "image_path": "./data/HME100K/test_images/test_388.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: \u222bdV = Q / t.\n\nHere's the LaTeX format for the expression:\n\n\u222bdV = Q / t\n\nThe variable 'dV'represents the change in volume of a system, while 'Q' represents the amount of heat added to or removed from the system, and 't' represents the time interval over which the change in volume occurs. The equation expresses the relationship between the change in volume and the amount of heat added to or removed from the system, with the time interval taken into account.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear from the image provided. Can you please provide a clearer and legible image so that I can write out the expression of the formula in LaTeX format?",
        "gt_answers": "\\angle B D E = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_391.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is 2x^2 + 6x + 8.",
        "gt_answers": "( \\frac { 2 2 + 1 8 } { 4 0 } ) \\div 8 = 5\n",
        "image_path": "./data/HME100K/test_images/test_392.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not clear as it does not provide any information about the variables involved. To write out the expression of the formula using LaTeX format, we need to know the variables involved in the equation. Please provide the variables to write out the equation.",
        "gt_answers": "\\angle C = 1 2 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_395.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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 + (1/2)x = 3/4.\n\nThe image shows a diagram with a rectangle and two circles, one inside the other. The length of the rectangle is 2 cm, and the radius of the inner circle is 1 cm. The radius of the outer circle is 2 cm. The equation of the line passing through the centers of the two circles is given as y = x - 1.\n\nUsing this information, we can find the equation of the line passing through the midpoint of the rectangle and the center of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the following LaTeX expression: $\\text{A = l x w}$ where l is the length and w is the width of the rectangle.",
        "gt_answers": "C E ^ { 2 } = E A \\cdot E B = 2 k\n",
        "image_path": "./data/HME100K/test_images/test_399.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} \\text{Image Content} \\end{aligned}$$\n\nNote that this formula uses the double vertical parallel symbol `|` to denote the logical exclusive OR operator, and the double vertical pipe symbol `|` to denote the logical OR operator.",
        "gt_answers": "b \\neq - 1 \\therefore b + 1 \\neq 0\n",
        "image_path": "./data/HME100K/test_images/test_400.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n&#x2212;8&#x2212;6i&#x2212;4j + 6k\" role=\"presentation\" style=\"position: relative;\">\u22128\u22126i\u22124j+6k\u22128\u22126i\u22124j+6k \\frac{-8 - 6i - 4j + 6k}{-8 - 6i - 4j + 6k} \\frac{-\\frac{8}{6} - \\frac{i}{4} - \\frac{j}{",
        "gt_answers": "1 2 0 \\div 2 5 = 4 . 8 ( d m )\n",
        "image_path": "./data/HME100K/test_images/test_401.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$ f(x) = \\frac{1}{2}(5x^2 + 7x - 3) $",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{2}{3}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the derivative of y = x^2 at x = 4, we can use the power rule of differentiation, which states that the derivative of y = f(x) is y' = f'(x). Substituting x = 4 into the equation, we get y = 16.\n\nUsing the power rule, we can write the derivative as follows:\n\ny' = 2x\n\nSubstituting x = 4, we get y' = 8.\n\nTherefore, the derivative of y = x^2 at x = 4 is y",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$$\\frac{32}{56+14}-\\frac{56}{72-24}=0. 8933$$",
        "gt_answers": "b ^ { 2 } - 4 a c = 8 + 2 0 = 2 8 > 0\n",
        "image_path": "./data/HME100K/test_images/test_408.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "$\\frac{1}{m} \\cdot \\frac{600}{m} = \\frac{60}{m}$",
        "gt_answers": "\\angle M C F = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_409.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the derivative of y with respect to x. The derivative of y with respect to x is given by dy/dx.",
        "gt_answers": "\\frac { x + 1 } { x ^ { 2 } } = 1\n",
        "image_path": "./data/HME100K/test_images/test_410.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\text{x} + 4 = 5 $$\n\nThe variable $x$ represents the number 2, which is being added to 4 to get 5.",
        "gt_answers": "\\frac { 3 } { 1 4 } + \\frac { 5 } { 1 4 } - \\frac { 1 } { 1 4 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_411.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as:\n\n$$A = \\pi r^2$$\n\nwhere $A$ is the area of the circle, $r$ is the radius of the circle, and $\\pi$ is a mathematical constant that is approximately equal to 3.14159.\n\nTo calculate the area of the circle in the image, we can use the formula above and plug in the given values for $r$ and $\\pi$.\n\n$$A = \\pi r^2$$\n$$A = \\pi (1.3)^2$$\n$$",
        "gt_answers": "A E = \\frac { 1 } { n } A O\n",
        "image_path": "./data/HME100K/test_images/test_412.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = l \\* w\n\nwhere l is the length of the rectangle and w is the width of the rectangle.",
        "gt_answers": "\\frac { 1 } { x + y } = n \\frac { 1 } { x - y } = m\n",
        "image_path": "./data/HME100K/test_images/test_413.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: x3x3 - x2x2 + 3x2x + 2x - 4x + 1.",
        "gt_answers": "S ( x - 3 y ) ( x - y ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_414.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression shown in the image is given by:\n\n$$x^2 + 4x - 3 = 0$$",
        "gt_answers": "x = \\frac { 9 9 } { 1 9 } \u3002\n",
        "image_path": "./data/HME100K/test_images/test_415.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by the integral of pi \\* r^2 over the circle. The area of the circle is then given by the integral of pi \\* r^2 over the circle, which can be expressed as A = ( \u03c0 \\* r^2 ). To solve for the diameter of the circle, we can rearrange the formula to be r = sqrt(\u03c0 \\* A). The diameter of the circle is then given by r = sqrt(\u03c0 \\* A).",
        "gt_answers": "+ 3 x + 2 ( 3 - x ) + ( 3 + x ) ( - 2 ) = - x < 0\n",
        "image_path": "./data/HME100K/test_images/test_416.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is 16. This can be represented in LaTeX as $\\frac{48}{8}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression for the formula in the image:\n\n$$\\frac{3(2x + 1)}{x + 1} = \\frac{3(2x^2 + 3x + 1)}{x + 1}$$\n\nThis formula can be read as, 'the ratio of the sum of three times the product of 2x and 1, to the sum of x and 1 is equal to the ratio of the sum of 3 times the product of x and 1, to the sum of x and 1.'",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation:$$3^4\\times 2^6 + 3^5\\times 2^5 + 3^6\\times 2^4 = 3^5 \\times 2^8$$This equation can be simplified as:$$3^9 + 3^7 = 3^9$$Since the left and right sides of the equation are equal, the equation is satisfied, and the image shows the equation as true.\n\nNote: LaTeX format is a markup language for typesetting mathematics and is not needed to display the equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$\\frac{a\\_i^2 + b\\_i^2}{2a\\_i b\\_i}$",
        "gt_answers": "x _ { 1 } = \\sqrt { 2 } - 1 , x _ { 2 } = 1 - \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_422.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the derivative of y with respect to x is: dy / dx = 2x + 3y.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written on the wall in the image is: d/dt ( x2 + y2) = 0. This is a differential equation that describes a dynamic system where the rate of change of the sum of the squares of the x and y coordinates is equal to zero.",
        "gt_answers": "\\angle D B E = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_424.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the equation is given by:\n\ny = mx + b\n\nwhere m is the slope of the line and b is the y-intercept. The equation is a linear equation that represents a line.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given as:\n\n$$\\begin{align\\*} 2x + 5 &= 9 \\ 5x - 2 &= 9 \\ \\frac{2x + 5}{5x - 2} &= 9 \\ \\to x = 3\\end{align\\*}$$",
        "gt_answers": "y _ { 2 } = - \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_428.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the triangle with base b and height h can be written as:$$A = \\frac{b \\* h}{2}$$This expression is derived from the formula for the area of a triangle, which is given by$$A = \\frac{b \\* h}{2}$$The triangle in the image has base b and height h, so its area is given by$$A = \\frac{b \\* h}{2} = \\frac{5 \\* 7}{2} = 15$$Therefore, the area of the triangle in the image is 15 square units",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $\\frac{x^2}{x^4+1}$",
        "gt_answers": "\\rho = \\frac { m } { V }\n",
        "image_path": "./data/HME100K/test_images/test_430.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by\n\n$$ \\text{y} = \\frac{x^2}{2} - \\sqrt{x^4 + 4} $$\nThis can be written as\n$$ y = \\frac{x^2}{2} - \\sqrt{x^4 + 4} $$\nwhere x is the independent variable and y is the dependent variable.",
        "gt_answers": "y = \\frac { 1 7 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_431.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is:\n\n![Image content](https://i.imgur.com/oJKx6m3.png)\n\nIn LaTeX format, the formula would be:\n\n![Image content](https://i.imgur.com/oJKx6m3.png)",
        "gt_answers": "m = 6 0 \\times 0 . 1 = 6\n",
        "image_path": "./data/HME100K/test_images/test_432.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the derivative of a function f(x) with respect to x is given by:\n\ndy/dx = lim ( h-> 0 ) ( f(x+h) - f(x) )/h\n\nIn this case, the function is f(x) = x^4 - 5x^3 + 7x^2 + 6x + 1. Substituting this function into the derivative formula gives:\n\ndy/dx = lim ( h-> 0 ) ( (x+h)^4 - 5(x+h)^3 +",
        "gt_answers": "\\Delta = m ^ { 2 } - 1 6 = 0\n",
        "image_path": "./data/HME100K/test_images/test_433.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by the following LaTeX format:\n\n$$ 2\\times 4 + 6\\times 3 = 10 + 18 = 28 $$\n\nThe image shows the equation written on a blackboard.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in the image using LaTeX format, you can use the following LaTeX code:\n\n$$\\frac{1}{4\\sqrt{x^2 + 16}}$$\n\nThis formula can be used to solve for x, given that 4\u221ax^2 + 16 = 4. The result is x = 2.",
        "gt_answers": "5 0 + 5 x = 7 5 - 2 5 x\n",
        "image_path": "./data/HME100K/test_images/test_435.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is not clear as it is not provided. Please provide the image for me to be able to write out the expression of the formula in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of the circle is given by:\n\n$$A = \\pi r^2$$\n\nwhere $r$ is the radius of the circle. In the given image, the radius of the circle is given by the value of $r$ in the formula:\n\n$$r = \\sqrt{60000 - 20000\\sqrt{60000 + 20000}}$$\n\nThus, the area of the circle is given by:\n\n$$A = \\pi (\\sqrt{60000 - 2",
        "gt_answers": "S _ { \\Delta B D C } = \\frac { 1 } { 2 } B D \\cdot C D\n",
        "image_path": "./data/HME100K/test_images/test_437.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX format of the formula in the image:\n\n$$\\begin{aligned} E = \\frac{1}{2}mv^2 + \\frac{1}{2}mv^2 + \\frac{1}{2}I \\end{aligned}$$\n\nIn this formula, $E$ represents the energy of the system, $m$ represents the mass of the object, $v$ represents the velocity of the object, and $I$ represents the moment of inertia of the object.\n\nNote that this formula is the equation of motion for an object moving in one",
        "gt_answers": "f ( x ) \\leq \\vert 2 x - 6 \\vert\n",
        "image_path": "./data/HME100K/test_images/test_438.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n&#x2202;&#x2202;&#x2202;&#x2202;&#x2212;&#x2212;&#x2212;&#x2212;4 &#x2212; 2x2 + 3x + 1 = 0\" role=\"presentation\" style=\"position: relative;\">\u2212\u2212\u2212\u2212\u2212\u22124\u2212\u2212\u2212\u2212\u22122x2+3x+1=0\u2212",
        "gt_answers": "1 2 \\times 1 2 = 1 4 4 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_439.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ dp \\times dp \\times 100 $$",
        "gt_answers": "\\Delta B D P \\sqrt { 2 } + \\sqrt { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_440.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the equation can be written as:3x+2y2x+y3y3x+3ywhere x and y are the variables.\n\nNote that this equation represents a parabolic equation with a vertex at the origin and a focus at the point (2, 3). The equation has two real roots, which are approximately 1.73 and 0.50.",
        "gt_answers": "y _ { 1 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_441.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression in LaTeX format that represents the formula for a circle's circumference. Here is the LaTeX code for the image:\n\n\\begin{center}\n$\\pi$r$^2$\n\\end{center}\n\nHere is a breakdown of the expression:\n\n\\begin{itemize}\n\\item The symbol $\\pi$ represents the mathematical constant that is approximately equal to 3.14159.\n\\item The letter r represents the radius of the circle.\n\\item The symbol $^2$ represents the square of the radius.\n\\end",
        "gt_answers": "0 . 8 5 \\times 1 0 0 0 = 8 5 0 ( k g )\n",
        "image_path": "./data/HME100K/test_images/test_442.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\text{blind}\\_ 90$$\n\nwhere the underscore represents a subscript and the subscript is the number 90. The expression represents the concept of being blind to something, with the subscript 90 indicating a level of severity or degree of blindness.",
        "gt_answers": "\\angle N D E = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_443.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a circle with a radius of x and a center at the origin.\n\nThe x-coordinate of the center of the circle is (0,0).\n\nThe y-coordinate of the center of the circle is (0,0).\n\nThe equation of the circle is given by the formula:\n\nx^2 + y^2 = r^2\n\nwhere r is the radius of the circle. Substituting the given values, we have:\n\nx^2 + y^2 = (x)^2 + (y)^2\n\nExpanding the square, we",
        "gt_answers": "5 \\times \\frac { 9 } { 5 } = 9 ( t )\n",
        "image_path": "./data/HME100K/test_images/test_444.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you would use the following syntax:\n\n$$\\frac{x}{x+2}=\\frac{x}{2}$$\n\nThis equation states that the value of $\\frac{x}{x+2}$ is equal to $\\frac{x}{2}$. The $\\frac{}$ symbol is used to denote a fraction, and the $x$ symbol is used to represent the variable. The division sign ($/) is used to denote the division of two numbers.\n\nThe value of the fraction $\\frac{x}{x+2}$ can be calculated",
        "gt_answers": "\\frac { 1 } { x + 1 } + \\frac { 2 } { x - 2 } = - \\frac { 8 } { ( x + 2 ) ( x - 2 ) }\n",
        "image_path": "./data/HME100K/test_images/test_445.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{2}{x^2 + 5x - 6}$.",
        "gt_answers": "A M = \\sqrt { A B ^ { 2 } - B M ^ { 2 } } = 2 .\n",
        "image_path": "./data/HME100K/test_images/test_447.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format.\n\nHere is the LaTeX formula for the given expression:\n\n$$\\frac{\\text{Image Content}}{\\text{Image Content}}$$\n\nIn this formula, the expression inside the radical symbol represents the ratio of the area of the image to the area of the original image.\n\nPlease note that the image content may depend on the type of image and its properties. For example, if the image is a rectangle, then the area of the image would be equal to its width multiplied by its height. If the image is a",
        "gt_answers": "\\sqrt { 2 5 - x ^ { 2 } } = x - 1\n",
        "image_path": "./data/HME100K/test_images/test_448.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the number of 10 in the image is:\n\n$$\\begin{aligned}10 &= 10\\times 2\\div 3 \\times 4\\div 5\\div 6\\div 7\\div 8\\div 9\\div 10\\div 10\\div 10\\div 10\\div 10\\div 10\\div 10\\div 10\\div 10\\div 10\\div 10\\div 10\\div 10\\div",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{1}{1-x}$$",
        "gt_answers": "\\therefore O B \\bot A B\n",
        "image_path": "./data/HME100K/test_images/test_450.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as follows:\n\n\\begin{align}\nx^2 + 4x + 5 = 0 \\\n\\end{align}\n\nThe equation represents a quadratic equation in the form of ax^2 + bx + c = 0. The values of a, b, and c are 1, 4, and 5, respectively. The solution to the equation can be found using the quadratic formula:x = (-b +/- sqrt(b^2 - 4ac)) / 2a. In this case, x = (4 +/- sq",
        "gt_answers": "y _ { 1 } = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_451.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{Average speed} = \\frac{\\text{total distance}}{\\text{time taken}}$$where $\\text{Average speed}$ is the average speed of the car during the trip, $\\text{total distance}$ is the total distance traveled by the car during the trip, and $\\text{time taken}$ is the total time taken to travel that distance.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$x = \\frac{y+2}{2}$$",
        "gt_answers": "\\frac { 1 } { x - y } = b\n",
        "image_path": "./data/HME100K/test_images/test_453.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\frac{a+b}{2}\n```",
        "gt_answers": "a = \\frac { 7 x } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_454.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $ \\frac{a^2 - b^2}{2ab}$",
        "gt_answers": "A O = O C = O B = O D\n",
        "image_path": "./data/HME100K/test_images/test_455.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $\\frac{3x + 2}{x - 2} = \\frac{1}{x - 2}$. To evaluate this equation, we can substitute x = 4 into the equation: $\\frac{3(4) + 2}{4 - 2} = \\frac{1}{4 - 2}$. This simplifies to $\\frac{7}{3} = 2.3333$. Therefore, the equation evaluates to 2.3333 when x = 4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I am sorry, but I am not able to see any image as there is no image provided. Can you please provide the image?",
        "gt_answers": "\\frac { x } { a } + \\frac { x } { - a } = 1\n",
        "image_path": "./data/HME100K/test_images/test_458.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\begin{aligned}\n(1 + 2n) \\times 2 + 3 = 5n + 3\n\\end{aligned}$$",
        "gt_answers": "\\Delta = ( - 1 ) ^ { 2 } - 4 ( a - 1 ) \\leq 0\n",
        "image_path": "./data/HME100K/test_images/test_459.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{\\text{t}}{\\text{h}} = \\frac{\\text{v}}{\\text{a}}$$This formula represents the relationship between time, velocity, and acceleration, which can be used to calculate the time it takes for an object to reach a certain velocity or acceleration.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is:\n\n2x + 3y = 14\n\nThe equation represents a linear inequality in two variables. The solution to the equation is the set of values of x and y that satisfy the inequality.\n\nTo find the solution, we can substitute the equation into the inequality.\n\n2x + 3y = 14\n\n2x + 3y = 14\n\nNext, we can solve for each variable separately.\n\n2x = 14 - 3y\n\nSubstituting back into the equation, we get",
        "gt_answers": "\\frac { x } { 2 } + \\frac { 2 y } { 5 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_461.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{1}{2} \\times \\frac{1}{4} + \\frac{1}{3} \\times \\frac{1}{6} = \\frac{1}{12} + \\frac{1}{18} = \\frac{7}{18}$$\n\nTherefore, the sum of the fractions in the image is 7/18.",
        "gt_answers": "k _ { 2 } = \\frac { 9 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_462.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The chemical formula for water is H2O.\n\nIn LaTeX format, the chemical formula for water would be written as:\n\nH2O \\_ \\_ H2O\n\nThis is because water is composed of two hydrogen atoms and one oxygen atom, represented by the symbol H for hydrogen and O for oxygen. The subscript indicates the number of atoms or molecules in a compound.\n\nThe subscript can also be used to indicate the presence of ions or other charged particles in a compound. For example, the formula for sodium chloride, NaCl, can",
        "gt_answers": "\\frac { D H } { H C } = \\frac { A H } { D H }\n",
        "image_path": "./data/HME100K/test_images/test_463.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{sin}\\left(\\frac{x+45}{6}\\right) + 2 = \\frac{x+45}{6} - \\frac{x}{2}$$\n\nThis can be read as: the sine of the ratio of x plus 45 divided by 6, plus 2, is equal to the ratio of x plus 45 divided by 6, minus x divided by 2.",
        "gt_answers": "A > B > C B > A > C \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_464.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$2\\sqrt{3}+5\\sqrt{2}$$This is a sum of two squares of numbers. The expression is valid, and the result is a positive number.\n\nNote: This response is generated by a language model and may not be accurate for all cases.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901",
        "gt_answers": "\\frac { m + 1 8 } { 1 4 } > 1\n",
        "image_path": "./data/HME100K/test_images/test_467.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the given expression:\n\n$$\\frac{a+b}{c+d}$$",
        "gt_answers": "\\frac { 2 } { 3 } = \\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_468.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: $ \\frac{1}{3}\\frac{4}{5}\\frac{5}{6}\\frac{6}{7}\\frac{7}{8}\\frac{8}{9}\\frac{9}{10}x^{9} + \\frac{1}{2}\\frac{1}{3}\\frac{2}{3}\\frac{3}{4}\\frac{4}{5}\\frac{5}{6}\\frac{6}{7}\\frac{7}{8}\\frac{8}{9}\\frac{9}{10}x^{8} + \\frac{1",
        "gt_answers": "y = - \\frac { 1 5 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_470.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by the formula mg - a / r.\n\nIn LaTeX format, this can be written as:\n\n$$ mg - \\frac{a}{r} $$\n\nwhere $m$ is the mass of the object, $g$ is the acceleration due to gravity, $a$ is the radius of the circular path, and $r$ is the radius of the circular path.",
        "gt_answers": "M ( a , - a ^ { 2 } + 2 a + 3 )\n",
        "image_path": "./data/HME100K/test_images/test_472.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image using LaTeX format is:\n\n$$\\begin{aligned}\nx &= 2 \\times 3 \\\\\ny &= 4 \\times 5 \\\\\nz &= 6 \\times 7 \\\\\n\\end{aligned}$$\n\nor, written out in words:\n\nx is equal to 2 multiplied by 3\ny is equal to 4 multiplied by 5\nz is equal to 6 multiplied by 7",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:\n\n$$\\text{sin}\\left(\\frac{\\text{t}}{\\text{2}}\\right) = \\frac{\\text{t}}{\\text{2}}$$\n\nwhere $\\text{t}$ is the time in seconds.",
        "gt_answers": "a < \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_474.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: 1 - (2x^2 + 4x - 5).\n\nNote: This formula is based on the given image, but I cannot see the image as it is not provided.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n$$\\frac{1000 - 350}{400 + 200} = \\frac{650}{600} = 1.0875$$\n\nThis formula calculates the ratio of the length of the rectangle's base to its height, given the values of the base and height. The values 1000 and 350 represent the base of the rectangle, and the values 400 and 200 represent the height of the rectangle",
        "gt_answers": "P > \\frac { 1 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_476.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{r}{v\\_x}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "5 1 2 \\div 6 3 = 8 \\cdots 8\n",
        "image_path": "./data/HME100K/test_images/test_478.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the sum of the first $n$ positive integers is given by the following LaTeX code: $\\sum\\_{i=1}^{n} i$.\n\nThis formula can be read as the sum of the first $n$ positive integers, where $n$ is a positive integer. The subscript notation $\\sum\\_{i=1}^{n}$ indicates that the sum is taken over the range of integers from $1$ to $n$. The $i$ variable represents the current term in the sum.\n\nWhen $n=4$, the formula becomes $\\sum\\_{i=1}^{4}",
        "gt_answers": "\\frac { A H } { 2 } = \\frac { 4 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_479.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\text{Image}(x, y) = \\frac{1}{2}\\left(\\frac{x}{y} + \\frac{y}{x}\\right) - \\frac{1}{2}\\left(\\frac{x}{y} - \\frac{y}{x}\\right)$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n\\frac{2x^2+4x-5}{x^2-x+1}\n\nThis can be simplified to:\n\n\\frac{2x^2+4x}{x^2-x+1}\n\nTo find the domain and range of this function, we can use the definition of a function.\n\nThe domain of a function is the set of all possible inputs for which the function is defined. In this case, the domain is the set of all real numbers x that make the function defined.\n\nThe range of a function",
        "gt_answers": "\\frac { x } { x - 7 } + \\frac { 1 } { x - 7 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_481.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$$\\frac{x^2 - y^2}{x - y}$$\n\nThis is the standard formula for calculating the distance between two points in a two-dimensional coordinate system. The formula takes the difference of the squares of the x and y coordinates of the two points, and divides that difference by the difference of the x and y coordinates themselves. The result is the distance between the two points.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{2}{1}\\cdot\\frac{2}{5}+\\frac{1}{4}\\cdot\\frac{1}{3}=\\frac{1}{2}\\cdot\\frac{1}{5}+\\frac{1}{4}\\cdot\\frac{1}{3}=\\frac{2}{5}+\\frac{1}{4}\\cdot\\frac{1}{3}=\\frac{2}{5}+\\frac{1}{4}\\cdot\\frac{1}{3}=\\frac{2+1}{5+1}\\cdot\\frac{1}{3}=\\frac{3",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{1}{x+3} = \\frac{1}{x+5}$$\n\nThe left side of the equation is the derivative of the function $f(x) = \\frac{1}{x+3}$ with respect to $x$, while the right side is the derivative of the function $g(x) = \\frac{1}{x+5}$.\n\nThe two sides of the equation are equal because the derivative of $\\frac{1}{x+3}$ is $\\frac{1}{x+3}$",
        "gt_answers": "\\sqrt { 3 x } > \\sqrt { 5 } x - \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_484.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\n$$\\text{h}\\_{b}\\left(x\\right)=\\text{k}\\left(\\frac{x}{b}\\right)^{a}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{minipage}{0.4\\textwidth}\n\\begin{equation}\ny = mx + b\n\\end{equation}\n\\end{minipage}\n\\end{center}\n\nIn this formula, `y` is the dependent variable, `x` is the independent variable, `m` is the slope of the line, and `b` is the y-intercept. The equation represents a straight line with a constant slope `m`",
        "gt_answers": "4 x ^ { 2 } + ( 4 n - 4 ) x + n ^ { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_486.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the image is:\n\nA = \u222b\u03c0r^2 dr\n\nwhere A is the area of the circular sector, r is the radius of the circular sector, and \u03c0 is the constant ratio of a circle's circumference to its diameter.\n\nTo solve the problem, we can substitute the given values into the expression:\n\nA = \u222b\u03c0r^2 dr\nA = \u222b (3.14159 \u00d7 r^2) dr\nA = 3.14159r^2 + C\n\nwhere C is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{d}{dt} \\left(\\frac{1}{t}\\right) = \\frac{1}{t^2}$$\n\nwhere t is time and dtdt is the time derivative of t.",
        "gt_answers": "O B = B D = C D = O C\n",
        "image_path": "./data/HME100K/test_images/test_489.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:$$\\text{y} = 2x + 3$$This equation can be represented as follows:$$\\text{y} = 2x + 3$$This equation can be represented as follows:$$\\text{y} = 2x + 3$$This equation can be represented as follows:$$\\text{y} = 2x + 3$$This equation can be represented as follows:$$\\text{y} = 2x + 3$$This equation can be represented as follows:$$\\text{y} = 2x",
        "gt_answers": "2 [ \\frac { 4 } { 3 } x - ( \\frac { 2 } { 3 } x - \\frac { 1 } { 2 } ) ]\n",
        "image_path": "./data/HME100K/test_images/test_490.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we need to use the following syntax:\n\n$$\\text{expression}$$\n\nIn the image, the formula is given as:\n\n$$\\text{x}^{2}+\\frac{5}{2}\\text{x}+\\frac{15}{4}$$\n\nTo write this formula in LaTeX format, we can use the following syntax:\n\n$$\\text{x}^{2}+\\frac{5}{2}\\text{x}+\\frac{15}{4}$$\n\nThis will render the formula as:\n\nx2+5",
        "gt_answers": "( 1 2 + 3 y ) ^ { 2 } - 5 y ( 1 2 + 3 y ) + 6 y ^ { 2 } = a\n",
        "image_path": "./data/HME100K/test_images/test_491.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\frac{2x}{x + 3} - \\frac{x - 1}{x^2 - 6}$$\n\nThis formula is derived from the given image, where the red and blue lines represent the numerator and denominator of the fraction respectively. The variable x is used in both the numerator and denominator.\n\nI hope this helps! Let me know if you have any other questions.",
        "gt_answers": "a = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_492.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n( 5 )( 1 ) = 5( 1 ) = 5.\n\nThis is a multiplication of two binomials. The first binomial is ( 5 )( 1 ), which means 5 multiplied by 1. The second binomial is ( 1 ), which means 1 multiplied by 1. The result of the multiplication is 5 multiplied by 1, which equals 5.",
        "gt_answers": "V = \\frac { m } { \\rho } = \\frac { 9 k g } { 0 . 9 \\times 1 0 ^ { 3 } k g / m ^ { 3 } } = 1 0 ^ { - 2 } m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_493.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ab}\\_2 + \\text{ab}\\_4 + \\text{bc}\\_2 + \\text{bc}\\_4 = \\frac{9}{2}$$",
        "gt_answers": "A B = 2 a = \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_494.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is not available as the given image is not available.",
        "gt_answers": "W > 0\n",
        "image_path": "./data/HME100K/test_images/test_495.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is not provided.\n\nHowever, assuming that the expression is represented by the image, we can write it as follows:\n\n$$\\frac{1}{2}\\left(x^2 + y^2\\right) + \\frac{1}{2}\\left(a^2 + b^2\\right) + c$$\nwhere $x$ and $y$ are the coordinates of the point $(x, y)$ and $a, b, $ and $ c$ are constants.",
        "gt_answers": "\\sim \\Delta E A C \\sim \\Delta E C B\n",
        "image_path": "./data/HME100K/test_images/test_496.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, you would use the following code:$$\\begin{align}f(x) = \\frac{1}{x^2}\\end{align}$$This formula is derived from the quadratic formula, which is given by$$\\begin{align}x = \\frac{-b\\pm\\sqrt{b^2 - 4ac}}{2a}\\end{align}$$Plugging in the values for the given image, we get$$\\begin{align}f(x) = \\frac{1}{x^2}\\end{align}$$Sub",
        "gt_answers": "x _ { 2 } = - 2 - \\sqrt { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_497.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not a mathematical equation but a text equation. To write it in LaTeX format, you can use the following code:\n\n\\begin{center}\nText Equation\n\\end{center}\n\nThis will produce the text equation in the center of the page.",
        "gt_answers": "y = 3 x - 5 .\n",
        "image_path": "./data/HME100K/test_images/test_498.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \\frac{x+y}{2}.\n\nThe numerator is the sum of x and y.\nThe denominator is 2.\nThe formula simplifies to: x+y222222222222222222222222222222222222222222222222222222222222222222222222222222",
        "gt_answers": "x _ { 2 } = \\frac { - b + 6 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_499.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the formula for the area of a circle:$$A = \\pi r^2$$where $A$ is the area, $r$ is the radius, and $\\pi$ is a constant that represents the circumference of a circle.",
        "gt_answers": "\\frac { 4 ( a - 2 ) } { a ( a - 2 ) } > 0\n",
        "image_path": "./data/HME100K/test_images/test_501.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\nf(x) &= \\frac{1}{x^2+4x+4} \\\n&= \\frac{1}{(x+2)^2} \\\n&= \\frac{2}{(x+2)^3} \\\n&= \\frac{3}{(x+2)^4} \\\n&= \\frac{4}{(x+2)^5} \\\n&= \\frac{5}{(x+2)^6} \\\n&= \\frac{6}{(x+2)^7} \\\n&=",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is: $\\frac{x}{x+3}$\n\nThis is the formula for the given image: $\\frac{x}{x+3}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given expression is: $\\frac{3xy^2 - x^3}{y}$.",
        "gt_answers": "( 3 ) ( ( 3 k - 7 ) = 7\n",
        "image_path": "./data/HME100K/test_images/test_506.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image. Please provide a clear and legible image so that I can assist you.\n\nOnce I have the image, I can write out the expression of the formula in LaTeX format as follows:\n\n\\begin{align\\*}\n\\frac{d^2x}{dt^2} + \\frac{dx}{dt}\\frac{d^2t}{dt^2} - \\frac{d^2t}{dt^2}\\frac{dx}{dt} = \\frac{d}{dt}(\\frac{dx}{dt}\\frac{dt}{dt",
        "gt_answers": "1 \\geq - \\frac { 1 } { 2 } x \\geq - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_508.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\u200b\n\nThe expression for the area of the image can be written as:\n\n$$A = \\frac{1}{2}bh$$\n\nwhere $A$ is the area of the image, $b$ is the width of the image, and $h$ is the height of the image.\n\nThe expression for the volume of the image can be written as:\n\n$$V = \\frac{1}{3}b^2h$$\n\nwhere $V$ is the volume of the image, $b$ is the width of the image, and $h$ is the height",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression in the image:\n\n\\begin{align\\*}\nx &= \\frac{1}{2} \\left( \\frac{3y - 4z}{y + z} \\right) \\\n&= \\frac{1}{2} \\left( \\frac{3(2) - 4(1)}{2 + 1} \\right) \\\n&= \\frac{1}{2} \\left( \\frac{3 - 4}{2 + 1} \\right) \\\n&= \\frac{3 - 4}{7",
        "gt_answers": "y _ { 1 } = - 1 y _ { 2 } = - 2 1\n",
        "image_path": "./data/HME100K/test_images/test_511.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{aligned}\n4x^2 + 3x + 2 &= 9 \\\n\\end{aligned}\n\nThis is a quadratic equation in standard form, where the coefficients of the variable x are 4, 3, and 2, and the constant term is 9. The solutions to this equation can be found by factoring the equation and solving for the variable x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is $\\frac{a}{b}=\\frac{c}{d}$.",
        "gt_answers": "1 \\div 2 0 = \\frac { 2 0 } { 1 }\n",
        "image_path": "./data/HME100K/test_images/test_514.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 2x + 3y = 6, where x and y are variables. The solution to this equation is x = 2 and y = 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write the expression of the formula in the image using LaTeX format.\n\nThe image shows a mathematical expression with the variables x and y, and the expression is as follows:\n\n$$\\begin{aligned} x^2 + 3x + 2y^2 - 5y = 2x + 4y \\end{aligned}$$\n\nIn LaTeX format, this expression would be written as:\n\n$$\\begin{aligned} x^2 + 3x + 2y^2 - 5y = 2x + 4y \\end{aligned}$$",
        "gt_answers": "S : \\pi \\times ( \\frac { 3 a } { 2 } ) ^ { 2 } = \\frac { 9 \\pi a ^ { 2 } } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_517.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$g = \\frac{1}{2} \\left(x^2 - \\frac{1}{4}x^4\\right) + \\frac{1}{4}x^4$$\n\nThis formula is derived from the quadratic equation $x^2+bx+c=0$, where $b=\\frac{1}{4}$ and $c=-\\frac{1}{2}$. The term $\\frac{1}{2}x^2$ represents the horizontal asymptote of the parabola, and the term $\\frac{",
        "gt_answers": "\\vert g \\vert a _ { n + 1 } \\vert - \\vert g \\vert a _ { n } \\vert = \\vert g \\frac { \\vert a _ { n + 1 } \\vert } { \\vert a _ { n } \\vert . }\n",
        "image_path": "./data/HME100K/test_images/test_519.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\text{Treatment} \\left(\\frac{\\text{age}}{\\text{45}}\\right) + \\text{control} \\left(\\frac{\\text{age}}{\\text{45}}\\right) \\leq \\text{Treatment} + \\text{control} $$",
        "gt_answers": "3 0 \\div 3 6 = \\frac { 3 6 } { 3 0 } = \\frac { 6 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_520.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ \\begin{aligned} x + 2y &= 16 \\ \\ x - y &= - 8 \\end{aligned} $$\n\nThis is a system of linear equations in two variables x and y, which can be solved using the method of substitution. To solve the system, we substitute x = 4 for y in the first equation, which gives us the equation:\n\n$$ 2y + 2y = 16 $$\n\nSimplifying the equation gives us:\n\n$$ 4y = 1",
        "gt_answers": "x _ { 2 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_521.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} f(x) &= \\frac{2(x+1)}{x-2} \\quad (1) \\end{aligned}$$\n\nwhere x is an arbitrary real number.\n\nTo verify the formula using the given image, we can substitute x = 1 into the formula and evaluate the expression:\n\n$$\\begin{aligned} f(1) &= \\frac{2(1+1)}{1-2} \\quad (2) \\end{aligned}$$\n\nComparing the results",
        "gt_answers": "3 6 \\div 1 2 = 3 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_523.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{2x^2+3x-5}{x^2-x+1}=\\frac{2(x+\\frac{5}{2})(x-\\frac{1}{2})}{(x-\\frac{1}{2})^2-\\frac{9}{4}}$$",
        "gt_answers": "0 < \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_524.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is written as follows:\n\n$$ \\frac{P}{T} = \\frac{1}{2}\\frac{T}{P} $$\n\nThis equation represents the efficiency of a heat engine, where P is the pressure of the working fluid and T is the temperature of the working fluid.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n\\begin{center}\n\\begin{equation}\n\\begin{aligned}\ny &= 2x^2 \\\\\n&= 4x^2 - 4x \\\\\n&= 4x^2 - 4x + 2x^2 \\\\\n&= 6x^2 - 8x\n\\end{aligned}\n\\end{equation}\n\\end{center}\n\nThis formula represents a quadratic function with a minimum value of $2$ at $x = 0$ and a maximum value of $",
        "gt_answers": "\\frac { 1 } { 3 0 } = \\frac { 1 } { 3 0 }\n",
        "image_path": "./data/HME100K/test_images/test_527.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write out the expression of the formula in the image using LaTeX format.\n\nHere is the formula in LaTeX format:\n\n\\begin{align\\*}\nx^3 - 2x^2 + 3x - 1 = 0\n\\end{align\\*}\n\nThis formula is a cubic equation with one variable, x. It has three roots, which are the values of x that make the equation true. The formula has a degree of three, which means that the highest power of x is raised to the third power.\n\nThe coefficients of the formula are",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $ f(x) = 4x^2 - 3x + 1 $.\n\nIn LaTeX format, this can be written as:\n\n$ f(x) = 4x^2 - 3x + 1 $",
        "gt_answers": "( 3 ) S = 1 4 \\times 0 . 3 m ^ { 2 } = 4 . 2 m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_530.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows in LaTeX format:\n\n\\begin{center}\n$y = mx + b$\n\\end{center}\n\nwhere $m$ is the slope of the line of best fit, $b$ is the y-intercept of the line of best fit, and $x$ and $y$ are the coordinates of the data points on the line.",
        "gt_answers": "\\Delta B D C \\sim \\Delta A E C\n",
        "image_path": "./data/HME100K/test_images/test_531.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$ \\frac{3x + 2y}{x + 5y} = \\frac{2x + 5y}{3x + 2y} $\n\nThis can be read as, 'the ratio of x to y in the numerator is equal to the ratio of x to y in the denominator.'",
        "gt_answers": "- \\sqrt { 3 } x + 4 \\sqrt { 3 } = ( \\sqrt { 3 } x\n",
        "image_path": "./data/HME100K/test_images/test_532.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that! Here's the LaTeX formula for the given expression: $\\text{ImageContent}$\n\nNote that the formula uses a double vertical line character to denote the limit of integration, which is often used in calculus to represent the upper or lower limit of a function.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$ E = mc^2 $$\n\nThis is the formula for the equation of energy, where E represents the energy, m represents the mass, and c represents the speed of light in a vacuum.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:x2 + 3x - 4 = 0.\n\nTo solve for x, we can use the quadratic formula:x = (-b +/- sqrt(b^2 - 4ac))/(2a).\n\nPlugging in the values from the image, we get:x = (-(-3 +/- sqrt((-3)^2 - 4(1)(0)))/(2(1))) = (-3 +/- sqrt((9 - 4)(1)(0)))/(2(1)) = (-3 +/- sqrt",
        "gt_answers": "( x ^ { 2 } + \\frac { 1 } { 3 } ) ^ { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_535.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: $\\frac{2}{3}x^2 + \\frac{2}{5}x^5 - \\frac{1}{4}x^4$",
        "gt_answers": "5 : 4 = 2 5 : 2\n",
        "image_path": "./data/HME100K/test_images/test_537.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$$\\frac{3\\times 6+5\\times 9}{4\\times 36+5\\times 65}$$This can be written as:$$\\frac{18+45}{189+300}$$Simplifying this expression gives:$$\\frac{45}{189}$$This simplifies to:$$\\frac{7}{11}$$which is the same as the result obtained using the method of adding like terms.\n\nThe result is $\\frac{7}{11}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle can be expressed as follows:\n\nA = lw, where l is the length and w is the width of the rectangle.",
        "gt_answers": "A P = \\sqrt { ( 0 + 1 ) ^ { 2 } + ( 1 + 1 ) ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_540.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image in LaTeX format is:\n\n$$\\begin{aligned}\n\\frac{a}{b} &= \\frac{c}{d} \\\\\n&= \\frac{e}{f} \\\\\n&= \\frac{g}{h}\n\\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is \\frac{a}{b} - \\frac{c}{d}.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is A = l \u00d7 w, where l is the length and w is the width. The area of the image is given by:\n\nA = 10 \u00d7 3 = 30\n\nTherefore, the area of the rectangle is 30 square units.",
        "gt_answers": "b = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_543.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX formula for the image:\n\n$$\\frac{a+b}{c+d}=\\frac{a+d}{b+c}$$\n\nIn this formula, $a, b, c, and d$ are all variables. The left side of the equation is the ratio of the sum of $a$ and $b$ to the sum of $c$ and $d$. The right side of the equation is the ratio of the sum of $a$ and $d$ to the sum of $b$ and $c$.\n\nThe",
        "gt_answers": "\\frac { x } { a + 2 } + \\frac { y } { b - 1 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_544.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n\\begin{center}\n\\begin{equation}\nS = \\frac{1}{2} \\cdot (\\frac{4}{3} + \\frac{1}{2})\n\\end{equation}\n\\end{center}\n\nThe expression is the sum of $\\frac{4}{3}$ and $\\frac{1}{2}$, evaluated as the sum of their reciprocals.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is \\frac{x^2+3x+1}{x^2+5x+1}.\n\nHere is the LaTeX code for the formula:\n\n\\frac{x^2+3x+1}{x^2+5x+1}",
        "gt_answers": "D A = \\frac { 8 } { 3 } k\n",
        "image_path": "./data/HME100K/test_images/test_546.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle with base b and height h is given by:\n\nA = bh/2\n\nwhere b is the base of the triangle and h is the height of the triangle.",
        "gt_answers": "6 4 x - 8 0 x < - 2 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_547.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length l and width w is given by A = l \\* w.\n\nHere, l is the length of the rectangle and w is the width of the rectangle.",
        "gt_answers": "y _ { 1 } = 7 , y _ { 2 } = 5\n",
        "image_path": "./data/HME100K/test_images/test_548.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the formula in the image is not visible, as it is written in a handwriting script. However, if the equation is written in LaTeX format, it would look like this: $\\frac{a}{b}$.\n\nNote that this is just an example, and the actual equation in the image may be different.",
        "gt_answers": "A M g ( O H ) _ { 2 } + 2 H C\n",
        "image_path": "./data/HME100K/test_images/test_550.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\n$$ 2x + 4y = 6 $$\nwhere x and y are the coordinates of the point where the line intersects the y-axis.",
        "gt_answers": "\\sin \\angle B A C = \\frac { B C } { A B }\n",
        "image_path": "./data/HME100K/test_images/test_552.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \u222b\u222b \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the equation: x = 4y - 3z.",
        "gt_answers": "B ( - \\frac { 1 } { 2 } , - 4 )\n",
        "image_path": "./data/HME100K/test_images/test_554.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 7^3 + 3^7 + 1^4 = 1939 $$\n\nwhere $7^3$ represents $7^3 = 343$, $3^7$ represents $3^7 = 333$, and $1^4$ represents $1^4 = 1$.",
        "gt_answers": "\\frac { 3 } { 7 } \\times 2 = \\frac { 6 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_556.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{equation}\n\\begin{aligned}\n5x^2 + 3x - 2 &= 0 \\\\\n2x^2 + 5x - 7 &= 0 \\\\\n\\end{aligned}\n\\end{equation}\n\\end{center}\n\nThe image shows two equations, both of which are quadratic equations of the form $ax^2 + bx + c = 0$. The first equation is $5x^2 + 3x - 2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the formula in the image can be expressed as:\n\nx = (4 + 5i) / (3 - 2i)\n\nThis can be simplified using algebra as:\n\nx = (4 + 5i) / (3 - 2i)\nx = (4 + 5i) / (3 + 2i)\nx = (4 + 5i) / (3 + 2i)\nx = 4 / 3 + i / (3 + 2i)\nx = 4 / 3 + i / 5",
        "gt_answers": "\\frac { 2 } { x + y } + \\frac { 1 } { x - y } = 1\n",
        "image_path": "./data/HME100K/test_images/test_560.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize, but I cannot see the image you provided. Please provide a description of the image or another means to see the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{1}{a}=\\frac{1}{b}+\\frac{1}{c}$$\n\nwhere a, b, and c are the lengths of the sides of the triangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is not specified in the image. It is likely a mathematical expression or equation.",
        "gt_answers": "r _ { c } = C H = 6\n",
        "image_path": "./data/HME100K/test_images/test_563.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\frac{a^2+b^2}{c^2+d^2}\n```\nThis is a fraction that represents the ratio of the sum of the squares of two numbers (a and b) to the sum of the squares of two other numbers (c and d).",
        "gt_answers": "y = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_564.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle can be expressed as: A = l \\* w, where l is the length of the rectangle and w is the width of the rectangle. The formula can be written in LaTeX format as:\n\n$$ A = l \\times w $$\n\nwhere l and w are variables representing the length and width of the rectangle, respectively.",
        "gt_answers": "a - k ^ { 2 } - 1 .\n",
        "image_path": "./data/HME100K/test_images/test_565.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image using LaTeX format is:\n\n$$\\text{Image Content}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the derivative of a polynomial function of degree n with leading coefficient a is given by:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:<br>CuSO4 + 4HCl \u2192 CuCl4 + SO42\u2212<br>This reaction is a redox reaction, as the number of electrons in the reactants and products is different. The copper sulfate (CuSO4) and hydrogen chloride (HCl) react to form copper chloride (CuCl4) and sulfur dioxide (SO42\u2212).</br>The sulfur dioxide produced in the reaction is a byproduct and can be removed by washing",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Image content}=\\frac{b+m}{2}$$\n\nwhere $b$ is the blue pixel value and $m$ is the green pixel value. The denominator $2$ is used to ensure that the sum of the numerator and denominator is equal to the image content.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "3x + 2y = 12 and 4x + 3y = 20 can be solved using the substitution method as follows:x = (12 - 4y) / 3y = 4y - 12 / 3y = 2y - 8x = (20 - 4y) / 3y = 4y - 20 / 3y = 2y - 62x + y = (12 - 2y) / y = 2y - 12 / y = 2y",
        "gt_answers": "\\vert m \\vert - 2 = 1\n",
        "image_path": "./data/HME100K/test_images/test_573.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is $\\frac{400\\text{ mm}^2}{35\\text{ cm}^2}$. This can be written in LaTeX format as $\\frac{400mm^2}{35cm^2}$.",
        "gt_answers": "B M ^ { 2 } + M O ^ { 2 } = B D ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_576.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I cannot see the image as it is not provided. Please provide the image for me to help you.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows an expression involving the variables x, y, and z, and the function f(x) = 2x + 3y - 4z. The expression is written as follows:$$\\begin{aligned} f(x) &= 2x + 3y - 4z \\ \\\\ &= 2(2x + 3y) - 4(4z) \\ \\\\ &= 2(x + 3y) - 8z \\ \\\\ &= (x + 3y) - 8z \\ \\\\ \\end{aligned}$$This expression can be used to find",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is \\frac{7}{3} x 2 = 14.\n\nTo write this in LaTeX format, you can use the following code:\n\n$$\\frac{7}{3} \\times 2 = 14$$\n\nThis will render the formula in the same way as it appears in the image.",
        "gt_answers": "0 . 7 \\approx 1 . 0\n",
        "image_path": "./data/HME100K/test_images/test_581.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f \u222f",
        "gt_answers": "y = \\frac { 1 } { 2 } x ^ { 2 } + 4 x - 5\n",
        "image_path": "./data/HME100K/test_images/test_582.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->] (0,0) -- (4,0) node[right] {$ x$};\n\\draw[->] (0,0) -- (0,4) node[above] {$ y$};\n\\filldraw (2,2) circle (2pt) node[above right] {$(2,2)$};\n\\filldraw (1,3) circle (2pt) node[above right] {$(1,3)$};",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{a+b}{2}$. This is because the formula is asking for the sum of the numbers 3 and 5 divided by 2. The answer would be $\\frac{3+5}{2}=6$.\n\nPlease note that this is just an example and the actual answer will depend on the numbers used in the formula.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in LaTeX format is: x + 2y - 4 = 10.\n\nThe equation can be read as: the sum of x and 2y is equal to 10.",
        "gt_answers": "y = \\frac { 1 } { 4 x - 8 }\n",
        "image_path": "./data/HME100K/test_images/test_585.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image given is:\n\n$$\\text{Image Content} = \\frac{1}{8}+\\frac{1}{4}+\\frac{1}{2}+\\frac{1}{8}+\\frac{1}{4}+\\frac{1}{2}+\\frac{1}{8}+\\frac{1}{4}+\\frac{1}{2}+\\frac{1}{8}+\\frac{1}{4}+\\frac{1}{2}+\\frac{1}{8}+\\frac{1}{4}+\\frac{1}{2}+\\frac{1}{8}+\\frac{1}{4}+\\frac{1}{2}+\\frac",
        "gt_answers": "\\frac { 8 1 } { 8 1 + 1 7 5 } = ( \\frac { 3 } { 4 } ) ^ { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_586.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is x + 10y - 8z = 4.",
        "gt_answers": "( x + \\frac { b } { 2 a } ) ^ { 2 } = \\frac { b ^ { 2 } - 4 a c } { 4 a }\n",
        "image_path": "./data/HME100K/test_images/test_590.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is given by: $\\frac{a}{b}$ where $a$ and $b$ are positive integers.",
        "gt_answers": "y = \\frac { 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_592.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\sqrt{1000+2500}$$\\sqrt{1000+2500}=\\sqrt{3500}$$\\sqrt{1000+2500}=\\sqrt{3500}$The formula in the image is: $3500=\\sqrt{1000+2500}$3500=\\sqrt{1000+2500}$3500=$\\sqrt{1000+2500}$This formula",
        "gt_answers": "1 3 g = 1 3 \\div 1 0 0 0 0 = \\frac { 1 3 } { 1 0 0 0 } k g\n",
        "image_path": "./data/HME100K/test_images/test_593.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression written in LaTeX format:\n\n$$\\frac{500+300\\sqrt{5}+400\\sqrt{3}}{3\\sqrt{2}+2\\sqrt{5}}=\\frac{1200+75\\sqrt{5}+300\\sqrt{3}}{6\\sqrt{2}+4\\sqrt{5}}=160.3535\\sqrt{2}+72.5535\\sqrt{3}$$\n\nThis expression can be simplified using the Pythagorean theorem to:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n\\begin{center}\n$A=mx+b$\n\\end{center}\n\nwhere:\n\n\\begin{center}\n$A$ is the y-intercept of the line\n\\end{center}\n\n$m$ is the slope of the line\n\n$b$ is the y-intercept of the line intercepted by the x-axis\n\nThis formula represents the standard form of a linear equation in two variables.",
        "gt_answers": "x + \\frac { n ( n + 1 ) } { x } = 2 n + 1\n",
        "image_path": "./data/HME100K/test_images/test_595.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:5x^2+2x+12x^3+5x+12x^4+5x^5.",
        "gt_answers": "8 0 x = 2 . 5\n",
        "image_path": "./data/HME100K/test_images/test_596.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: 2x + 4y = 6, where x and y are variables.\n\nNote: This answer is based on the assumption that the image is of a linear equation in two variables.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: 1 + x = x\u00b2 + 2x\u00b2 + 3x\u00b2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the formula in the image:\n\n\\begin{center}\n\\begin{equation}\nf(x) = \\frac{1}{2}\\left(\\frac{1}{x} + \\frac{1}{3}\\right)\n\\end{equation}\n\\end{center}\n\nThis formula calculates the average rate of change of a function f(x) over the interval [1, 3]. It is the antiderivative of the function with respect to x, denoted by the symbol $\\frac{d}{dx}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not provided.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ \\frac{a}{b}$$",
        "gt_answers": "f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 1 2 x\n",
        "image_path": "./data/HME100K/test_images/test_601.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{dV}/dt = \\frac{c\\_1V\\_1 - c\\_2V\\_2}{V\\_1 + V\\_2}$$This is the general formula for the rate of change of the voltage of a capacitor with two capacitors in series, given the capacitances of the two capacitors and their respective charging currents.",
        "gt_answers": "c ^ { 4 } - a ^ { 2 } c ^ { 2 } = a ^ { 2 } c ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_603.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 108.5 cm / 12 cm = 9.04 meters.",
        "gt_answers": "x + 2 y = 1\n",
        "image_path": "./data/HME100K/test_images/test_605.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n<latex code>5x^2 + 10x + 6</latex code>\n\nwhere x is the variable.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is given by:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is 2x^2 + 4x - 8.\n\nThe image shows a person with their arms outstretched, as if they are trying to catch something. The formula for the expression in the image represents the person's movement. The x^2 term represents the person's arms being stretched out, and the x term represents the person's movement towards the center of the image. The - 8 term represents the person's arms being stretched out as far as they can go.",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_608.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n\u222b(\u222b(2y)dy)dx = \u222b(\u222b(xdy)dx)y)dx = \u222b(\u222b(x2)dx)y dy)dx = (\u222b(x2)dx)y + \u222b(\u222b(y2)dx)y dx)y = \u222b(x2 + y2)dx dy)dx = \u222b((\u222b(x2)dx)y + \u222b(\u222b(y2)dx)y dx)y dy)dx = \u222b(\u222b(2y)",
        "gt_answers": "- \\frac { b } { 2 a } = + \\frac { b } { + 2 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_609.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the given image:\n\n\\begin{center}\n\\frac{2}{x} + \\frac{1}{x^2} = \\frac{10}{x}\n\\end{center}\n\nThis formula represents a quadratic equation with two terms in the numerator and one term in the denominator. The left side of the equation represents the sum of the coefficients of the terms, which is 2 + 1 = 3. The right side of the equation represents the constant term 10. The equation can be solved for the value of x using the",
        "gt_answers": "\\frac { 1 } { 2 } : \\frac { 2 } { 3 } = \\frac { 3 } { 4 } : x\n",
        "image_path": "./data/HME100K/test_images/test_610.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$ r = \\sqrt{ (x^2 + y^2) - (a^2 + b^2) } $$\nwhere $a$ and $b$ are the lengths of the hypotenuse and legs of the right triangle, respectively, and $x$ and $y$ are the coordinates of the point on the hypotenuse that is closest to the origin.",
        "gt_answers": "\\sqrt { 3 a } \\div \\sqrt { 6 a b }\n",
        "image_path": "./data/HME100K/test_images/test_611.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$\\frac{480\\sin{x}}{3\\cos{x}}-\\frac{640\\cos{x}}{3\\cos{x}}+\\frac{1280}{3}$This formula represents the position of an object relative to the horizontal plane at a given angle of elevation $x$ from the horizon. The numerator represents the vertical component of the object's position, while the denominator represents the horizontal component.",
        "gt_answers": "\\frac { 1 } { 3 } \\times 3 . 1 4 \\times ( 2 \\div 2 ) ^ { 2 } \\times 0 . 6 = 0 . 6 2 8 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_613.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{sin}(x) = \\frac{\\text{opposite}}{\\text{hypotenuse}} $$\n\nThe formula in the image represents the sine function. The function maps each point in the interval [0, pi] to its sine value. The opposite and hypotenuse are given in the formula. The opposite is the side opposite to the angle, while the hypotenuse is the side opposite to the right angle.\n\nNote: In LaTeX format, the sine function is represented by the command \\sin",
        "gt_answers": "( x - y = 0\n",
        "image_path": "./data/HME100K/test_images/test_614.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center} $\\frac{1}{3} x^2 - \\frac{1}{2} x - \\frac{1}{6}$ \\end{center}\n\nThis formula can be derived by setting the derivative of the given equation with respect to x to zero and solving for x.\n\nThe image shows a graph of the formula with the x-axis representing x and the y-axis representing the value of the formula. The graph has a local minimum at x = -2.25, with a value of -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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$x = \\frac{y - 3}{2}$\n\nwhere $x$ and $y$ are variables.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that!\n\nHere's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\frac{1}{2} \\* m\\_1 + \\frac{1}{3} \\* m\\_2 + \\frac{1}{4} \\* m\\_3\n\\end{center}\n\nwhere $m\\_1$, $m\\_2$, and $m\\_3$ are the masses of the three blocks, and the subscripts represent their respective masses. The fraction bars are used to indicate the ratio of each mass to the total mass",
        "gt_answers": "D E = \\sqrt { C E ^ { 2 } - A D ^ { 2 } } = 6\n",
        "image_path": "./data/HME100K/test_images/test_617.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given as: $\\sqrt { 1 + \\frac{1}{4} }$.",
        "gt_answers": "y ^ { 2 } = \\frac { 4 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_618.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the image:\n\n\\begin{center}\n\\begin{minipage}{0.3\\textwidth}\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[step,thin, gray!50] (0,0) grid (3,3);\n\\draw[thick] (0,0) -- (3,3);\n\\node[right] at (3,3) {$x$};\n\\node[above] at (0,0) {$y$};\n\\end{tikzpicture}\n\\end{center}",
        "gt_answers": "2 ^ { 2 } x \\in ( \\frac { 3 \\pi } { 2 } , 2 \\pi )\n",
        "image_path": "./data/HME100K/test_images/test_619.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the sum of 5 and 3 can be written as follows:\n\n5 + 3 = 8\n\nIn LaTeX format, the equation can be written as:\n\n5 + 3 = 8\n\nThis equation can be used to calculate the sum of two numbers.",
        "gt_answers": "\\frac { 3 } { 4 } : \\frac { 2 } { 3 } = 9 : 6\n",
        "image_path": "./data/HME100K/test_images/test_621.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "\\textcircled { 2 } x = 2 y = 3\n",
        "image_path": "./data/HME100K/test_images/test_623.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$\\sqrt {-2}+1$",
        "gt_answers": "\\frac { 1 } { 2 } x = 1 + 1\n",
        "image_path": "./data/HME100K/test_images/test_625.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent}$$\n\nThe variable $x$ represents the amount of water and $y$ represents the amount of flour. The constant $c$ represents the amount of butter.",
        "gt_answers": "C _ { 1 } O + H _ { 2 } = C u + H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_626.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$x^2 + 2x - 3 = 0$$\n\nThis equation represents a quadratic equation with two variables, x and y. The solutions to the equation can be found by completing the square method or using the quadratic formula.\n\nThe solutions to the equation are given by:\n\nx = \u00b1\\sqrt{2}\n\nThe graph of the equation is a parabola that opens upwards and passes through the point (0,3).",
        "gt_answers": "x = \\frac { 4 0 } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_627.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image you provided is not available. Could you please provide another image for me to work with?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is 4x^2 + 4x - 5x^3.\n\nLaTeX code:\n\n\\begin{center}\n\\begin{align}\n4x^2 + 4x - 5x^3\n\\end{align}\n\\end{center}\n\nImage:\n\n[Img]4x^2 + 4x - 5x^3[/Img]",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for finding the value of a quadratic equation with two variables. The equation is: x^2 + y^2 = r^2.\n\nThe formula for finding the value of x when y = 3 is: x = sqrt(r^2 - 9).\n\nThe formula for finding the value of y when x = 2 is: y = sqrt(r^2 - 4).\n\nThe image shows the values of x and y when r = 5. The value of x is 2, and the value of y is 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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} a &= \\frac{x^2+y^2}{r^2} \\, \\\\ b &= \\frac{2xy}{r^2} \\, \\ c &= \\frac{x^2-y^2}{r^2} \\, \\ d &= \\frac{2x}{r} \\. \\end{aligned}$$\n\nHere, $x$ and $y$ are the coordinates of the point on the circle and $r$ is the radius of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw (0,0) rectangle (2,2);\n\\draw[thick,rounded corners] (1,1) -- (1,0) -- (2,0);\n\\draw[thick,rounded corners] (1,2) -- (1,1) -- (2,1);\n\\node at (1,1) {4};\n\\node at (1,2) {3};\n\\node at (2,1) {2};",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is the formula for the dot product of two vectors.\n\nTo find the dot product of two vectors, a and b, we use the following formula:\n\n&#x2222;a&#x2222;b&#x22C5;b&#x2222;a&#x22C5;1\" role=\"presentation\" style=\"position: relative;\">a\u22c5b\u22c5c\u22c5b\u22c5a\u22c5c\u22c51a\u22c5b\u22c5c\u22c5b\u22c5a\u22c5c\u22c51\\cdot a \\cdot b \\cdot c \\cdot b",
        "gt_answers": "- 3 k + 2 - k + 1 = 0 , k = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_633.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a right triangle with legs of length a and b and hypotenuse c can be written as:c2 = a2 + b2.\\begin{align}c^2 &= a^2 + b^2\\end{align}This formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.\n\nThe Pythagorean theorem can be derived using the following steps:\n\n1. Draw a right triangle with legs of length a",
        "gt_answers": "\\therefore \\frac { b } { a } = \\tan \\frac { \\pi } { 3 } = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_634.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the triangle is A = 0.5(0.5a + 1.5b) = 0.5(0.5 + 1.5) = 0.5(0.5 + 0.75) = 0.5(0.75) = 0.375 square units.\n\nThe expression for the perimeter is P = 2(0.5a + 1.5b) = 2(0.5 + 1.5) = 2(1.5) = 3",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![ImageContent](https://www.adobe.com/content/dam/help/en/photoshop/how-to/using/layers/workflow/overlays/blend-if/blend-if-overlay.png)\n\n![ImageContent](https://www.adobe.com/content/dam/help/en/photoshop/how-to/using/layers/workflow/overlays/blend-if/blend-if-overlay.png)",
        "gt_answers": "A E = E D , C E\n",
        "image_path": "./data/HME100K/test_images/test_636.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\frac{x+3}{x-2}\n```",
        "gt_answers": "f ( x ) = x ^ { 2 } - 4 x + 1\n",
        "image_path": "./data/HME100K/test_images/test_637.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$x^2 + 4x + 12 = 0$\n\\end{center}\n\nThis is the standard quadratic formula for solving a quadratic equation of the form ax^2 + bx + c = 0, where a = 1, b = 4, and c = 12.",
        "gt_answers": "1 2 \\div 4 = 3\n",
        "image_path": "./data/HME100K/test_images/test_638.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\frac{2\\sqrt{2} - 3}{5 + \\frac{7}{3}}$$\n\nIn the denominator, we have $5 + \\frac{7}{3} = 5 + 2.333 = 7.333$. In the numerator, we have $2\\sqrt{2} - 3 = 2.414 - 3 = -0.686$.\n\nWhen we simplify the expression, we get:\n\n$$\\",
        "gt_answers": ", x = \\frac { 2 9 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_639.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as follows:\n\ny = x\u00b2 + 2x + 10\n\nwhere x is a variable and y is the dependent variable.",
        "gt_answers": "y = \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_640.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given as follows:\n\n$ \\frac{m}{t} = \\frac{P}{t} + \\frac{W}{t} $\n\nwhere m is the mass of the body, P is the force applied to the body, and W is the work done on the body by the force.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not provided, so I cannot write it out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image using LaTeX format is: $\\text{y} = \\frac{x^{2}}{2}$.\n\nThis formula can be read as, `y is equal to the square of x divided by 2`.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{y} = 10\\text{x} + 5$$\n\nwhere $\\text{x}$ is the input variable and $\\text{y}$ is the output variable.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the given image:\n\n\\begin{aligned}\n\\frac{\\sqrt{a^2 + b^2}}{2ab} &= \\frac{a + b}{2ab} - \\frac{a - b}{2ab} \\\\\n&= \\frac{2ab - (a - b)^2}{2ab} \\\\\n&= \\frac{a^2 + b^2 - 2ab}{2ab} \\\\\n&= \\frac{a^2 + b^2}{2a^2 + 2b^2} - \\frac{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The expression for the formula in the image using LaTeX format would be:\n\n\\begin{center}\n\\begin{equation}\n75 - 37 = 38\n\\end{equation}\n\\end{center}\n\nThis is because the image shows a number line with the numbers 37, 38, and 75, and the expression is simply the difference between 75 and 37, which equals 38.",
        "gt_answers": "7 0 - 7 0 = 0\n",
        "image_path": "./data/HME100K/test_images/test_646.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$\\frac{a^2+b^2}{2ab}=\\frac{25^2+26^2}{2\\times 25\\times 26}=525$\n\\end{center}\n\nI hope this helps!",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: \\frac{1}{2}x^2 + \\frac{1}{3}x^3 + \\frac{1}{4}x^4.\n\nNote: The formula is written using LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $\\text{V} = \\frac{\\text{P}}{\\text{t}} = \\frac{1}{2} \\times \\frac{\\text{h}}{\\text{t}} = \\frac{1}{4} \\times \\frac{\\text{l}}{\\text{t}} = \\frac{1}{4} \\times \\frac{\\text{d}}{\\text{t}} = \\frac{1}{4} \\times \\frac{\\text{s}}{\\text{t}} = \\frac{1}{4} \\times \\frac{\\text{",
        "gt_answers": "y = x ^ { 2 } - 6 x + 9 = ( x - 3 ) ^ { 2 . }\n",
        "image_path": "./data/HME100K/test_images/test_649.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$ \\text{magnitude of the vector} = \\sqrt{\\left(\\frac{y\\_2-y\\_1}{d}\\right)^2 + \\left(\\frac{x\\_2-x\\_1}{d}\\right)^2} $$\nwhere $\\text{magnitude of the vector} = $ the magnitude of the vector connecting the points $(x\\_1, y\\_1)$ and $(x\\_2, y\\_2)$, $d = $ the distance between the two points, and $\\left(\\frac{y\\_2-y\\_1",
        "gt_answers": "x _ { 3 } = \\frac { - 5 + \\sqrt { x - 1 } } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_650.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is \\frac{x^2 - 2x}{x^2 + 4x - 4}.",
        "gt_answers": "\\frac { 3 } { 2 x + y } = 1\n",
        "image_path": "./data/HME100K/test_images/test_652.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\begin{aligned}x = \\frac{1}{2}(3y - 2z)\\end{aligned}$$This formula represents the equation of a line that passes through the points (3, 4) and (2, 2).",
        "gt_answers": "5 \\times \\frac { 1 } { 3 0 } = \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_653.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$a = \\frac{1}{2} (2x + 3y)$$\n\nThis formula can be read as: a is equal to half of the sum of 2x and 3y.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$c\\_d^2 = a\\_1^2 + b\\_1^2 + a\\_2^2 + b\\_2^2$$\n\nwhere $c\\_d$ is the conjugate of $d$, $a\\_1$ and $b\\_1$ are the components of $a\\_1$ and $b\\_1$ are the components of $b\\_1$.",
        "gt_answers": "C D \\bot M B\n",
        "image_path": "./data/HME100K/test_images/test_656.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$\\begin{aligned} e = \\frac{1}{2}mv^2 \\\n```\n\nwhere e is the energy of the system, m is the mass of the system, and v is the velocity of the system.\n\n$$\\begin{aligned} e = \\frac{1}{2}mv^2 \\\n```\n\nThis formula expresses the relationship between the energy of a system and its mass and velocity. The energy of a system is directly proportional to the square of its velocity, and inversely proportional to its mass.\n##",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a mathematical expression that describes the relationship between two variables. It can be written using LaTeX format as follows:\n\nLet x and y be the variables such that x is the independent variable and y is the dependent variable. Then the equation is:\n\ny = mx + b\n\nwhere m is the slope of the line and b is the y-intercept. The slope is the rate of change of y with respect to x, while the y-intercept is the point where the line intercepts the y-axis.",
        "gt_answers": "4 0 - 5 y + 3 y\n",
        "image_path": "./data/HME100K/test_images/test_660.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\text{P} = \\frac{1}{2}\\text{V}^2 + \\text{mgh}$$\n\nIn the image, the formula is written as $P = \\frac{1}{2}V^2 + mgh$, which means that the pressure at a given point in a fluid is equal to half the square of the velocity of that fluid at that point, plus the sum of the pressure at the surface of the fluid and the force exerted by the gravitational field on the fluid.\n##",
        "gt_answers": "\\varphi x _ { 2 } = \\frac { 2 _ { n } } { m + m }\n",
        "image_path": "./data/HME100K/test_images/test_661.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by: x^2 - 2x - 3. This can be written as: x^2 - 2x - 3, where x is the variable and -2 and -3 are constants.\n\nThe equation is a quadratic equation in one variable x. The solutions to the equation can be found by completing the square method.",
        "gt_answers": "x + y = 1\n",
        "image_path": "./data/HME100K/test_images/test_662.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ 5 \\times 5 + 7 \\times 3 = 35 + 21 = 56 $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n$$w = \\frac{1000 - 400}{400 - 300} \\times 0.4$$\n\nThe image shows the equation for the weighted average of two values, 1000 and 400, where the weight of the second value is 0.4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 2x3+x2. To write it out in LaTeX format, you would use the following code: 2x3 + x2.\n\nThe variable x represents the independent variable in this equation, and the variable y represents the dependent variable. The equation is a linear equation in standard form with the slope of 2 and the y-intercept of 3.",
        "gt_answers": "( 2 a - 3 ) x = 2\n",
        "image_path": "./data/HME100K/test_images/test_665.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}\\times\\frac{1}{3}+\\frac{1}{4}\\times\\frac{1}{4}+\\frac{1}{4}\\times\\frac{1}{4}=\\frac{1}{4}$.\n\nThe formula is the sum of the fractions $\\frac{1}{2}\\times\\frac{1}{3}$, $\\frac{1}{4}\\times\\frac{1}{4}$, and $\\frac{1}{4}\\times\\frac{1}{4}$. The fractions can be simplified using the rule",
        "gt_answers": "x _ { 2 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_666.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format would be:\n\n$$648 \\times 10^6 + 648 \\times 10^5 + 648 \\times 10^4 + 648 \\times 10^3 + 648 \\times 10^2 + 648 \\times 10^1 + 648 \\times 10^0 = 648 \\times 10^6$$\n\nThis expression represents the sum of the products of the powers of 6",
        "gt_answers": "6 1 4 \\approx 6 0 0\n",
        "image_path": "./data/HME100K/test_images/test_667.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear as it is written in a handwritten style and the letters are not clearly visible. However, assuming the formula is a mathematical expression, it is not possible to write it out in LaTeX format without the clear image.\n\nIf you have the clear image, I can try to write out the formula in LaTeX format for you. Please provide the clear image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression that can be written in LaTeX format as follows:\n\n$$\\begin{aligned} s &= \\frac{a^2 + b^2}{2ab} \\\\\n&= \\frac{(6)^2 + (10)^2}{2 \\cdot 6 \\cdot 10} \\\\\n&= \\frac{36 + 100}{12 \\cdot 6 \\cdot 10} \\\\\n&= \\frac{46}{60 \\cdot 6 \\cdot 10} \\\\\n&= \\frac{46}{3600}",
        "gt_answers": "S _ { \\Delta B O C } = O B \\cdot C E \\cdot \\frac { 1 } { 2 } = 4 \\times 3 \\times \\frac { 1 } { 2 } = 6\n",
        "image_path": "./data/HME100K/test_images/test_669.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n$$ 2x^2 + 2x - 5 = 0 $$\n\nThis is a quadratic equation in the form of a quadratic formula, where x is the variable. The solution of the equation is the value of x that makes the equation true. In this case, the solution is x = - 3, which can be verified by substituting this value into the equation and checking whether it is true.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n\\frac{1}{2}x^2 + \\frac{1}{2}x - \\frac{1}{4}x^4 - \\frac{1}{8}x^6 + C\n\nwhere C is the constant of integration.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear. Can you please provide the image so that I can assist you with the LaTeX formula?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: d 3 + 2d 2 - 2d 3 + 2 = d 5 - 2d 3 + 2.",
        "gt_answers": "\\frac { D E } { B C } = \\frac { 1 } { 3 } .\n",
        "image_path": "./data/HME100K/test_images/test_674.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows:\n\n$$\\begin{aligned} E & = \\frac{1}{2}mv^2 + \\frac{1}{2}mgh \\\\ &= \\frac{1}{2}m(v + h)^2 - \\frac{1}{2}mgh \\end{aligned}$$",
        "gt_answers": "\\therefore - 3 < x \\leq 4\n",
        "image_path": "./data/HME100K/test_images/test_675.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x^4 - x^3 + 2x^2 - 3x + 4.\n\nThis formula can be derived by adding or subtracting the exponents of each term in the expression. For example, the expression (x^4 - x^3) can be simplified by adding the exponents to get x^4 - x^3 + 0x^2. Then, we can add the exponents of the remaining terms to get x^4 - x^3 + 2x^2 - 3x + 4.",
        "gt_answers": "\\frac { 1 } { 3 } + \\frac { 1 } { 5 } = \\frac { 8 } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_676.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}a &= 4x + 3y \\\\b &= 2x - 5y \\end{aligned}$$\n\nIn this formula, a is the first equation and b is the second equation.",
        "gt_answers": "2 \\cdot ( - \\frac { 1 } { 3 } ) \\cdot 3 6 + 9 6\n",
        "image_path": "./data/HME100K/test_images/test_678.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{n+3}{n-2}$$",
        "gt_answers": "= \\frac { - B H } { A H } = \\tan \\angle D A G\n",
        "image_path": "./data/HME100K/test_images/test_679.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:$$ x = 2 \\cdot x $$This is a recursive equation that defines x as a function of itself. The left side of the equation represents the current value of x, while the right side represents the previous value of x. The equation shows that the current value of x is equal to twice the previous value of x, which means that the value of x will double each time it is used in the equation.\n\nIn general, this equation represents a situation where the current value of x is determined by the previous value of x, with the previous value being multiplied by a constant",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick, fill=white] (0,0) rectangle (2,2);\n\\node[text width=1cm,align=center] at (1,1) {$\\mathbf{ImageContent}$};\n\\end{tikzpicture}\n\\end{center}\n\nHere, the thick white rectangle represents the image, and the text node with the label $\\mathbf{ImageContent}$ is positioned in the center of the rectangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[line width=1pt, black] (0,0) -- (0.5,1) -- (1,0) -- (0.5,-1) -- cycle;\n\\filldraw[black] (0.25,0.5) circle (2pt) node[below left] {$ $};\n\\filldraw[black] (0.5,1) circle (2pt) node[above right] {$ $};\n\\filldraw",
        "gt_answers": "x = \\frac { 1 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_682.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: $\\frac{a + b}{c + d}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is: $\\frac{1}{2} \\times \\frac{1}{4} + \\frac{1}{4} = \\frac{1}{2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not provided, so I cannot write it out using LaTeX format.\n\nHowever, assuming the equation is in the format of y = mx + b, we can write it out as follows:\n\ny = 3x - 2",
        "gt_answers": "x - \\frac { 1 } { 3 } x = \\frac { 2 } { 3 } x\n",
        "image_path": "./data/HME100K/test_images/test_685.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{2x}{x+4}$$The formula in the image is $\\frac{2x}{x+4}$ and the value of the expression is $\\frac{2x}{x+4}$ when x=3.",
        "gt_answers": "3 \u3001 2 4 \\div 7 = 3 \\cdots 3\n",
        "image_path": "./data/HME100K/test_images/test_686.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the image is given by the equation b = (a / (a + 1)) \\* 1. This formula is derived from the formula for the derivative of a polynomial with one variable, which is given by b = (a / (a + 1)) \\* x. By substituting x with 1, we obtain the formula for the derivative of a constant function, which is b = (1 / 1) \\* 1 = 1.\n\nThe expression for the image is a constant function, given by the equation y = 1. This means that the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula for the area of a circle is:\n\nA = \u03c0r^2\n\nWhere A is the area, r is the radius, and \u03c0 is the constant 3.14159.\n\nSo, if we know the radius of the circle, we can calculate its area using this formula. For example, if the radius of the circle is 5cm, the area is:\n\nA = \u03c0(5)^2 = 78.5398\n\nI hope that helps! Let me know if you have any other questions.",
        "gt_answers": "\\frac { 1 } { x + y } = m\n",
        "image_path": "./data/HME100K/test_images/test_688.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written in the image is not clear, as the text is partially obscured by the image itself. However, assuming that the formula in the image is written in LaTeX format, it would be written as follows:\n\n$$\\text{csc}^2 x + \\text{sec}^2 x = 1$$\n\nThis formula is a quadratic equation in the variable x, with the left-hand side being the sum of the squares of the cosecant and secant of x, and the right-hand side being 1. The equation can be solved for the value of x using various methods,",
        "gt_answers": "2 N a O H + B a C O _ { 3 } \\downarrow\n",
        "image_path": "./data/HME100K/test_images/test_689.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{1}{x^2+3x+5}$$",
        "gt_answers": "\\angle 2 = \\frac { 1 } { 2 } \\angle A O D = 6 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_690.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\frac{d^2x}{dt^2} = \\frac{k}{m} \\frac{dx}{dt}\n```",
        "gt_answers": "x = 6\n",
        "image_path": "./data/HME100K/test_images/test_691.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\frac{4y+5}{2x-3}$$\n\nThis is a linear equation with a slope of $\\frac{4y+5}{2x-3}$ and a y-intercept of 5.",
        "gt_answers": "x = 1 8 , y = - 9\n",
        "image_path": "./data/HME100K/test_images/test_693.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a width of 6 inches and a height of 8 inches is:\n\nA = l x w\n\nwhere l is the length and w is the width.\n\nSubstituting the given values, we get:\n\nA = 6 x 8\n\nTherefore, the area of the rectangle is 48 square inches.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is A = l \u00d7 w, where l is the length and w is the width.\n\nGiven l = 1 and w = 3, the area of the rectangle is A = 1 \u00d7 3 = 3.",
        "gt_answers": "1 2 3 \\div 3 = 4 1\n",
        "image_path": "./data/HME100K/test_images/test_695.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n\\begin{align\\*}\nx^2 + y^2 &= r^2 \\\n\\end{align\\*}\n\nwhere x, y, and r are constants.",
        "gt_answers": "x = 0 . 6\n",
        "image_path": "./data/HME100K/test_images/test_696.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression written in LaTeX format. The expression is as follows:\n\n\\frac{1}{3} \\* 2 + \\frac{1}{4} \\* 3 = \\frac{11}{12}\n\nThis expression represents a problem in algebra, where the goal is to find the sum of the fractions 1/3 \\* 2 and 1/4 \\* 3. The solution is to simplify the fractions by finding common denominators, which in this case is 12. The final result is then 11/12.##",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression for the sum of two squares. The expression is written as follows:\n\n\\begin{equation} 2x^2 + 4y^2 = 16 \\end{equation}\n\nThis equation represents the area of a square with sides of length x and a second square with sides of length y. The sum of the areas of the two squares is equal to 16, which is the value written on the image.",
        "gt_answers": "\\frac { 5 0 } { 3 } + b = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_698.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\begin{aligned} x^2 + 2x - 5 &= 0\\end{aligned}$$This formula is a quadratic equation with one variable, x. It represents a parabolic shape, which has the shape of a U with the vertex at the origin. The equation has two solutions, which can be found by solving for x. The solutions are x = - 2 and x = 2. These solutions can be verified by substituting them into the equation and verifying that they satisfy the equation.",
        "gt_answers": "- \\frac { 9 } { 5 } x - \\frac { 2 } { 3 } x \\leq 2 - 3 \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_699.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{2x + 5}{x - 3} $$",
        "gt_answers": "3 0 \\% + 2 0 \\% y = 1 3 0\n",
        "image_path": "./data/HME100K/test_images/test_700.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX format for the expression of the formula in the image:\n\n\\begin{align\\*}\ny & = \\frac{10}{x^2 + 8x + 5}\n\\end{align\\*}\n\nThis formula gives the output value of the given function for any input value of x.",
        "gt_answers": "2 8 + 9 3 = 3 0 x - 5 x\n",
        "image_path": "./data/HME100K/test_images/test_701.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is given as:\n\n\\begin{equation}\\text{ImageContent}\\end{equation}\n\nwhere $\\text{ImageContent}$ is the image content.",
        "gt_answers": "( b - c ) - ( a + d ) = b - c - a - d\n",
        "image_path": "./data/HME100K/test_images/test_702.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{x - y}{\\sqrt{x^2 + y^2}}$$",
        "gt_answers": "y = \\frac { 6 } { k + 4 }\n",
        "image_path": "./data/HME100K/test_images/test_704.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is given by: $\\frac{100\\times 0.5\\times 0.25}{1000\\times 0.25}=0.125$\n\nThe image represents a box with a label on it that says \" ImageContent\".",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is:\n\n$x = 2y + 5z$\n\nwhere x, y, and z are variables.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{4} + \\frac{1}{4} = \\frac{1}{2}$.",
        "gt_answers": "r = d \\div 2 = 1 0 \\div 2 = 5\n",
        "image_path": "./data/HME100K/test_images/test_709.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{x^2}{x+6}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{x+4y}{3}$$\n\nwhere x and y are the coordinates of the points in the plane.",
        "gt_answers": "x = - \\frac { 2 } { 7 + 4 \\sqrt { 3 } }\n",
        "image_path": "./data/HME100K/test_images/test_711.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:\n\n$$5+2i$$",
        "gt_answers": "\\frac { 1 } { 2 } x = \\frac { 2 } { 3 } \\times \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_712.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\frac{1}{3} - \\frac{1}{4} - \\frac{1}{6} + \\frac{1}{8} + \\frac{1}{12} - \\frac{1}{16} - \\frac{1}{24} + \\frac{1}{32} - \\frac{1}{48} + \\frac{1}{64} - \\frac{1}{96} + \\frac{1}{128} - \\frac{",
        "gt_answers": "\\frac { 2 } { x - 1 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_713.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by the following LaTeX code:\n\n$$\\frac{x^2+y^2}{x^2-y^2}=1$$\n\nThe equation represents a circle in the Cartesian plane with center at the origin and radius 2. The equation is the unit circle.",
        "gt_answers": "x = - \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_714.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n$$ 2x^2 + 4x - 6 = 0 $$\n\nThis formula can be used to solve for the solutions of the equation. The solutions can be found by setting the equation equal to zero and solving for x:\n\n$$ 2x^2 + 4x - 6 = 0 $$\n$$ 2x(x + 2) - 6 = 0 $$\n$$ 2x(x + 2) = 6 $$\n$$ x(x + 2) =",
        "gt_answers": "O G / / B C\n",
        "image_path": "./data/HME100K/test_images/test_715.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} 5x + 6y &= 19 \\\nx + y &= 4 \\\nx - y &= 3 \\\nx + 3y &= 13 \\\nx - 3y &= 13 \\\n\\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: $\\frac{r}{2}$ for the red dot on the left side of the image, and $\\frac{r}{2}$ for the red dot on the right side of the image. The expression is $\\frac{r}{2}+\\frac{r}{2}=r$.\n\nNote: The expression is in terms of the variable 'r' which is the radius of the circle shown in the image.",
        "gt_answers": "\\angle B O D = 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_717.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ 3x + 5 = 18 $$\n\nThis is a linear equation in one variable with a constant term of 5 and a coefficient of 3 for the variable x. The solution to this equation is given by:\n\n$$ x = 6 $$\n\nThis is the value of x that satisfies the equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\text{The formula is: } 3x + 4y = 10$$\n\nThe solution to the equation is:\n\n$$\\text{The solution is: } x = 2, y = 3$$\n\nAlternatively, the formula can be written as:\n\n$$\\text{The formula is: } 3x + 4y = 10$$\n\n$$\\text{The solution is: } x = 2, y = 3$$\n\nOr, the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is $\\frac{2x^2+2x-5}{x+3}$, which simplifies to $\\frac{x^2+x-5}{x+3}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{30+12}{4}=\\frac{33}{4}$.",
        "gt_answers": "3 6 \\div 4 = \\boxed { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_722.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{a+b}{c-d}$",
        "gt_answers": "a + 3 b\n",
        "image_path": "./data/HME100K/test_images/test_723.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 0.068 + 0.225 = 0.293. This can be represented in LaTeX format as: $\\frac{0.068 + 0.225}{1000}$.\n\nIn LaTeX format, the formula can be written as: $y = \\frac{0.068 + 0.225}{1000}$. This formula calculates the value of $y$ when $x = 1000$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{a^2+b^2}{2a}$$",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_725.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the equation:$$\\frac{x+y}{2}\\geq \\frac{x-y}{2}$$This is the equation for the distance between two points in a two-dimensional space, where x and y are the coordinates of the two points.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format of the expression for the formula in the image:\n\n\\begin{align}\nA &= \\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}",
        "gt_answers": "x = k \\pi + \\frac { \\pi } { 2 } , k \\in z ]\n",
        "image_path": "./data/HME100K/test_images/test_727.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a width of 100 and a height of 50 is:\n\nArea = width x height\nArea = 100 x 50\nArea = 5000\n\nSo the area of the rectangle is 5000 square units.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is not provided. However, assuming the image represents a rectangle, the formula for the area of the rectangle can be calculated as follows:\n\nArea of the rectangle = length x width\n\n= 10 x 4\n\n= 40 square units.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the formula:\n\n$$\\frac{100\\times(20+30)}{25\\times40}=130\\_{x\\_{20}}$$\n\nThe above formula represents the equation that has been written in LaTeX format.",
        "gt_answers": "x = - \\frac { \\sqrt { 1 0 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_731.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: 1 - (1 + x)^2\n\nThe formula is written in LaTeX format as follows:\n\n$$ 1 - \\left(1 + x\\right)^2 $$",
        "gt_answers": "x + 5 ( m - 8 ) = m + 2 0\n",
        "image_path": "./data/HME100K/test_images/test_732.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the rectangle in the image is given by the formula:\n\narea = length \u00d7 width\n\nwhere the length and width of the rectangle are given by the two red lines in the image. To calculate the area, we can substitute the given values into the formula:\n\narea = (2 \u00d7 3) \u00d7 (4 \u00d7 5) = 40 \u00d7 20 = 800 \u33a1\n\nTherefore, the area of the rectangle in the image is 800 \u33a1.",
        "gt_answers": "f ( 5 ) = \\cos \\frac { 5 \\pi } { 3 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_733.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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$$\\begin{aligned}x^2 + y^2 &= r^2\\end{aligned}$$\n\nThis is the formula for the distance between two points in a two-dimensional space. The x and y coordinates of the two points are known, and r is the radius of the circle that passes through both points.",
        "gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_734.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}\nf(x) &= \\sqrt{2(3x - 5)} \\\n\\end{aligned}$$\n\nNote that this formula is in terms of the variable $x$, and the radical symbol $\\sqrt{\\text{}}$ is used to denote the square root of the expression inside the parentheses.",
        "gt_answers": "\\{ x 1 - b \\leq x \\leq 3 \\}\n",
        "image_path": "./data/HME100K/test_images/test_735.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->] (0,0) -- (2,0) node[right] {$x$};\n\\draw[->] (0,0) -- (0,2) node[above] {$y$};\n\\draw (1,1) circle (1cm);\n\\node at (1,1) {$f(x,y)$};\n\\end{tikzpicture}\n\\end{center}\n\nIn this image, the function $f(x,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is A = \u03c0r^2, where r is the radius of the circle. Using the formula, the area of the circle is \u03c0 (3.14) \\* (1.25)^2 = 3.89 square inches.",
        "gt_answers": "\\angle 1 = \\angle 2 = \\angle 3 = \\angle D E C\n",
        "image_path": "./data/HME100K/test_images/test_737.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in LaTeX format for the given image is:$$x = \\frac{3\\cdot5+2}{6}\\cdot\\frac{100}{40}\\cdot\\frac{8}{5} = \\frac{9\\cdot8+16}{25}\\cdot\\frac{100}{40}\\cdot\\frac{8}{5} = \\frac{9\\cdot16+16}{25}\\cdot\\frac{100}{40}\\cdot\\frac{8}{5} = \\frac{9\\cdot48+32}{",
        "gt_answers": "a = \\frac { 2 \\ln x } { x ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_738.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: $\\frac{b}{a} \\times \\frac{d}{c}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle with length (a) and width (b) can be written as:\n\nA = ab\n\nwhere A is the area of the rectangle and a and b are the length and width, respectively.",
        "gt_answers": "A O = \\frac { 1 } { 2 } B C\n",
        "image_path": "./data/HME100K/test_images/test_740.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 0.5m is A = \u03c0r^2, where r is the radius of the circle. Using LaTeX format, we can write the formula as:A = \\pi r^2. Here, r is the radius of the circle, which is given as 0.5m. Using the given radius, we can calculate the area of the circle as:A = \\pi (0.5 m)^2A = \\pi (0.5 m)^2= \u03c0r^2= \u03c0 (0.5 m)^2=",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a polynomial equation of degree 5, given by the following expression:x^5 + 4x^4 + 5x^3 + 4x^2 + 5x + 1.",
        "gt_answers": "x = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_742.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ C\\_s = \\frac{T}{T + 2}$$\n\nwhere $C\\_s$ is the speed of sound in the solid and $T$ is the absolute temperature in Kelvin.",
        "gt_answers": "\\cos c = \\frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { 2 a b }\n",
        "image_path": "./data/HME100K/test_images/test_743.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, follow these steps:\n\n1. Select the text in the image, which is 6x + 3y = 18.\n2. Copy the selected text and paste it into a new LaTeX document.\n3. Format the LaTeX document according to the provided guidelines, including the use of double dollar signs for variables, double parentheses for function notation, and double vertical bars for absolute value.\n4. Compile the LaTeX document to obtain the final expression:\n$$6x + 3y = 18$$",
        "gt_answers": "6 ( \\frac { x } { 6 } - \\frac { 6 a - 1 } { 3 } ) = 6 ( x - \\frac { 5 a - 1 } { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_744.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{F}=\\frac{mg}{d} \\times \\sqrt{12}$$\n\nHere, `F` is the force acting on the object, `m` is the mass of the object, `g` is the acceleration due to gravity, `d` is the distance between the point of contact of the object and the surface on which it is resting, and `12` is a constant that represents the normal force acting on the object perpendicular to the surface.",
        "gt_answers": "Z n + 2 H C l = H _ { 2 } \\uparrow +\n",
        "image_path": "./data/HME100K/test_images/test_746.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nf(x) = (x^2 - x) / (x - 1)\n\nThis formula is derived from the given expression: (x - 1) / (x - 1). To find f(x), we can substitute x = 1 into the denominator, resulting in 1 / (1 - 1) = 1. Then, we can substitute x = 2 into the numerator, resulting in (2^2 - 2) = 4 - 2 = 2. Thus, the",
        "gt_answers": "\\frac { 1 } { ( n + 1 ) ^ { 2 } } < \\frac { 1 } { n ( n + 1 ) } = \\frac { 1 } { n } - \\frac { 1 } { n + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_749.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\text{a} = \\frac{\\text{b} \\times \\text{c}}{\\text{d}}$$",
        "gt_answers": "\u3001 A D \u3001 B C = A B \u3001 D C\n",
        "image_path": "./data/HME100K/test_images/test_751.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format. Here is the LaTeX code for the formula:\n\n\\begin{align\\*}\n&\\text{F} = \\frac{1}{2}mv^2 \\\\\n&= \\frac{1}{2}m(2kg)(2m/s)^2 \\\\\n&= 2 kg \\frac{m^2}{s^2}\n\\end{align\\*}\n\nIn this formula, F represents the force acting on an object with mass m and acceleration a, and v is the velocity of the object. The",
        "gt_answers": "x - 2 y = 0\n",
        "image_path": "./data/HME100K/test_images/test_752.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\text{2/5 + 3/5 = 5/10}$$\n\nThe image shows a formula for adding two fractions. The fractions are 2/5 and 3/5. When you add these fractions, you get 5/10.",
        "gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_754.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the provided image does not contain any mathematical expression. It's just a blank whiteboard with some writing on it. Please provide an image with a mathematical expression or formula to solve.",
        "gt_answers": "( 6 + 1 5 ) x = 5 4\n",
        "image_path": "./data/HME100K/test_images/test_755.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Please provide the image so that I can write the LaTeX formula.",
        "gt_answers": "D O E = \\angle D B E + \\angle A E B = 7 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_756.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not provided. Please provide the image for me to write out the equation.",
        "gt_answers": "\\cdot \\angle B C D = \\frac { 1 } { 2 } \\times 5 0 ^ { \\circ } = 2 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_758.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression for the formula in the image using LaTeX format. Here it is:\n\n$$\\frac{\\frac{n}{2} - 1}{n - 1} = \\frac{n - 1}{2}$$\n\nThe expression is simply the result of dividing the numerator by the denominator, which gives us the fractional value of the expression.",
        "gt_answers": "A N = \\frac { 1 } { 2 } A _ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_759.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{sin}(x) = \\frac{\\text{cos}(x)}{\\sqrt{1 - \\text{cos}^2(x)}}$$",
        "gt_answers": "D E = \\frac { 1 } { 2 } A C > E F = \\frac { 1 } { 2 } A B ,\n",
        "image_path": "./data/HME100K/test_images/test_760.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{ImageContent} $$\n\nwhere $\\text{ImageContent}$ is the image content.",
        "gt_answers": "1 2 \\times 4 = 4 8 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_761.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2} x^2 - 2x$.\n\nThe variable x is used twice in the formula, so the exponent of x is 2. The first term in the formula is $\\frac{1}{2}x^2$, which is the coefficient of x^2. The second term is -2x, which is the constant term in the formula.\n\nTherefore, the formula is: $\\frac{1}{2}x^2 - 2x$.",
        "gt_answers": "u _ { e } = \\alpha - \\alpha V\n",
        "image_path": "./data/HME100K/test_images/test_763.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = l x w\n\nwhere l is the length and w is the width. The formula for the area of a circle is:\n\nA = \u03c0r^2\n\nwhere r is the radius. The formula for the volume of a rectangular prism is:\n\nV = l x w x h\n\nwhere l is the length, w is the width, and h is the height. The formula for the volume of a cylinder is:\n\nV = \u03c0r^2h\n\nwhere r is the radius and h",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am unable to see the image as it appears to be a black box with no visible text or numbers. Can you please provide more information or context about the image so that I can better understand what you're asking?",
        "gt_answers": "b _ { n + 1 } - b _ { n } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_765.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: x + 5y = 10.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n\\begin{align\\*}\nn = \\left\\lfloor\\frac{100}{x}\\right\\rfloor\n\\end{align\\*}\n\nwhere,\n\n* n is the number obtained by dividing 100 by x and taking the floor function of the result.\n* x is the number that divides 100 without any remainders.\n* $\\lfloor \\cdot \\rfloor$ is the floor function, which rounds down a number to the nearest integer.\n*",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![](https://i.imgur.com/img.jpg)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is s/6+3-4\\*5.",
        "gt_answers": "S = 6 0 - 1 5 = 4 5 ( d m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_769.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:",
        "gt_answers": "y = 2 x - 3\n",
        "image_path": "./data/HME100K/test_images/test_770.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n\\begin{center} $\\frac{1}{4}(x + 3) = \\frac{1}{2}x + \\frac{1}{4}$ \\end{center}\n\nThis can be derived by adding 3 to both sides of the equation, and then dividing both sides by 4:\n\n\\begin{center} $\\frac{1}{4}(x + 3) + \\frac{3}{4} = \\frac{1}{2}x + \\frac{3}{4}$ \\end{center}\n\nSimpl",
        "gt_answers": "\\frac { 1 } { 1 2 } x = 7 + \\frac { 1 } { 6 } - 1\n",
        "image_path": "./data/HME100K/test_images/test_771.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not visible in the provided image. Can you please provide the image so I can help you with your question?",
        "gt_answers": "x \\div 1 . 2 = 4\n",
        "image_path": "./data/HME100K/test_images/test_772.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is:\n\nx = 2y + 1",
        "gt_answers": "7 0 3 \\approx 7 0 0\n",
        "image_path": "./data/HME100K/test_images/test_773.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the expression in the image:\n\n\\begin{equation}\nf(x) = \\frac{1}{2} x^2 - \\frac{3}{2} x + 1\n\\end{equation}",
        "gt_answers": "A B = 2 \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_774.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n$$\\begin{aligned}\nf(x) &= \\frac{1}{2}x^2 + 4 \\\\\n&= \\frac{1}{2} \\left( 2x + 1 \\right)^2 + 4 \\\\\n&= \\frac{1}{2} (2x + 1)^2 + 4 \\\\\n&= \\frac{1}{2} (2x + 1)^2 + 4\n\\end{aligned}$$\n\nThe formula is a quadratic function of x,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Copy the image and paste it into a LaTeX editor.\n2. Use the `\\draw` command to draw the graph of the function.\n3. Use the `\\node` command to label the coordinates of the graph.\n4. Use the `\\label` command to label the graph.\n\nHere is the LaTeX code for the given image:\n\n\\draw[->] (0,0) -- (2,0) node[right] {$x$};\n\\draw[->] (",
        "gt_answers": "x = - \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_777.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a circle can be represented using the formula:\n\nA = \u03c0r^2\n\nWhere A is the area of the circle, \u03c0 is the mathematical constant pi, and r is the radius of the circle.\n\nGiven the radius of the circle, r = 5, we can calculate the area as:\n\nA = \u03c0(5)^2\n= 25\u03c0\n\nTherefore, the area of the circle is 25\u03c0.",
        "gt_answers": "x _ { 2 } = 1 - \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_778.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression for the formula in the image using LaTeX format:\n\n\\begin{align\\*}\nr &= \\frac{h}{t} \\\n&= \\frac{1}{4}\\\n&= \\frac{1}{4} \\\n&= 0.25 \\\n&= 0.25 \\\n&= 0.25 \\\n&= 0.25 \\\n&= 0.25 \\\n&= 0.25 \\\n&= 0.25 \\\n&= 0.25 \\\n&= 0.25 \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = l \u00d7 w\n\nwhere l is the length and w is the width.\n\nIn this case, the length is 3 and the width is 4. So the area is:\n\nA = 3 \u00d7 4 = 12",
        "gt_answers": "x = \\sqrt [ 3 ] { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_781.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:$$\\frac{2x+5}{x+3}=2\\frac{2x+5}{x+3}=\\frac{2x+5}{x+3}=\\frac{2x+5}{x+3}=2$$This is a fraction with a numerator of $2x + 5$ and a denominator of $x + 3$. The expression evaluates to $2$.",
        "gt_answers": "( x - a ) ^ { 2 } + ( y - 1 ) ^ { 2 } = a ^ { 2 } - 1\n",
        "image_path": "./data/HME100K/test_images/test_782.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$\\text{Treatment group vs Control group}$$\n\n$$\\text{Estimator of the treatment effect}$$\n\n$$\\text{Estimator of the control effect}$$\n\n$$\\text{Total effect}$$\n\n$$\\text{Overall effect}$$\n\n$$\\text{Net effect}$$\n\n$$\\text{Clinical effect}$$\n\n$$\\text{Population effect}$$\n\n$$\\text{All-cause mortality rate}$$\n\n$$\\text{Cardiovascular mortality rate}$$\n\n$$\\text{",
        "gt_answers": "a ^ { 2 } + a = - 1\n",
        "image_path": "./data/HME100K/test_images/test_783.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:$\\frac{\\frac{1}{2} + \\frac{5}{6}}{\\frac{3}{4} - \\frac{2}{3}} = \\frac{3}{8}$",
        "gt_answers": "6 . m = \\pm 2 . 5\n",
        "image_path": "./data/HME100K/test_images/test_785.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\frac{d}{dt}\\left(\\frac{dx}{dt}\\right)^2 + \\frac{d}{dt}\\left(\\frac{dy}{dt}\\right)^2 = \\frac{d}{dt}\\left(\\frac{x}{dt}\\right)\\frac{d}{dt}\\left(\\frac{y}{dt}\\right) - \\frac{d^2}{dt^2}\\left(\\frac{x}{dt}\\right) - \\frac{d^2}{dt^2}\\left(\\frac{y}{dt}\\",
        "gt_answers": "f ^ { \\prime } ( x ) - 9 x = 3 x ^ { 2 } + ( 2 b - 9 ) x + c = 0\n",
        "image_path": "./data/HME100K/test_images/test_786.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:$$P = \\frac{r}{d}\\text{, where }P \\ is the pressure of the fluid at a depth of d below the surface and r is the density of the fluid. This equation is derived from the principle of buoyancy, which states that the pressure of a fluid at any point below the surface is equal to the weight of the fluid that is displaced by that point. In this case, the pressure at a depth of d below the surface is equal to the weight of the fluid that is displaced by that point, which is equal to the density of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the power of a light bulb in a room with a volume of 1000 cubic feet is given by: P = 1000 \\* 0.5 = 500 W. The time taken for the light bulb to reach half of its initial brightness is given by t = 500 / 2 = 250 seconds. Therefore, the energy required to power the light bulb for 2 hours is given by: E = P \\* t = 500 \\* 2 = 1000 W \\*",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n\u222b\\_0^af(x)dx=(a2+2ax)\u222b\\_0^af(x)dx=\u222b\\_0^af(x)dx=\u222b\\_0^af(x)dx=\u222b\\_0^af(x)dx=\u222b\\_0^af(x)dx=\u222b\\_0^af(x)dx=\u222b\\_0^af(x)dx=\u222b\\_0^af(x)dx=\u222b\\_0^af(x)dx=\u222b\\_0^af(x)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the image is: $ 2a^2 + 2b^2 = 20$\n\nwhere a and b are the lengths of the sides of the image.\n\nUsing LaTeX format, the expression is:\n\n\\begin{align\\*}\n2a^2 + 2b^2 &= 20 \\\n\\end{align\\*}\n\nTo solve for the area of the image, we need to find the values of a and b that satisfy the equation. We can do this by using the method of substitution:\n\n\\begin{align\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\nThe expression is a mathematical formula that represents the relationship between two variables, x and y. The formula can be used to solve problems in calculus and other mathematical fields.\n\nThe formula is written in LaTeX format using the following syntax:\n\nwhere a, b, and c are constants and x and y are variables.\n\nThe formula can be used to calculate the derivative of a function with respect to x. To do this, we simply substitute the variable x with the derivative of the function with respect to x.\n\nThe derivative of a",
        "gt_answers": "y _ { 2 } = \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_793.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is:$$\\frac{a+b}{c+d}$$ where $a,b,c,d$ are integers.",
        "gt_answers": "+ \\frac { 1 } { 3 } = \\frac { 4 } { 1 0 } = \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_794.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{3\\times 5}{3+5}$$ which simplifies to$$\\frac{3\\times 5}{8}$$",
        "gt_answers": "3 x = \\frac { 3 } { 5 } \\times \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_796.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r can be written as:\n\nA = (\u03c0r^2) / 4\n\nwhere A is the area of the circle and r is the radius of the circle.",
        "gt_answers": "\\angle C A B = 1 3 4 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_797.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: 1 + 2i.\n\nIn LaTeX format, this can be written as:\n\n$$ 1 + 2i $$",
        "gt_answers": "O B = O A + O B\n",
        "image_path": "./data/HME100K/test_images/test_799.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear as it is not written in LaTeX format. Can you please provide the image?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as:x+y=10. This is a linear equation with a slope of 1 and a y-intercept of 10. To solve for x, we can substitute y with 10 and solve for x. For example, if y=10, we can write the equation as 10+x=10, which simplifies to 10=10, so x=0. If y is any other value, we can substitute that value for y and solve for x accordingly.\n\nTo solve for y, we can substitute x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the equation:\n\nA = lw, where l is the length and w is the width.\n\nThe area of the rectangle in the image is 24 square meters. To find the length and width of the rectangle, we can use the formula above.\n\nFirst, we need to find the width of the rectangle. To do this, we can divide the area by the width:\n\nw = A / l\nw = 24 / 5\nw = 4.8 meters\n\nNext, we can find the length of the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n\\begin{align}\n(3x + 2y)^2 + (x - y)^2 &= 9 \\\n\\begin{aligned}\n3x^2 + 2xy + 2y^2 + x^2 - 2xy + y^2 &= 9 \\\n\\end{aligned}\n\\end{align}\n\nIn this equation, the left side is the sum of the squares of the terms on the right side. The right side is the given value.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression for the formula in the image using LaTeX format:\n\n$$\\frac{4x^3+6x^2-8x+4}{2x^2+5x-6}=\\frac{2x^2+5x-6}{4x^3+6x^2-8x+4}=4$$\n\nThis is the equation that represents the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format:\n\n$$\\text{Gravitational acceleration of an object at the surface of the Earth}$$\n\n$$g = \\frac{G\\_{earth}M\\_earth}{r^2}$$\n\nwhere $G\\_{earth}$ is the gravitational constant for the Earth, $M\\_earth$ is the mass of the Earth, and $r$ is the radius of the Earth.\n\nPlease let me know if you have any other questions.",
        "gt_answers": "x = 2 0 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_805.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the image:\n\n\\begin{center}\n\\frac{1}{2} + \\frac{1}{4} = \\frac{3}{4}\n\\end{center}\n\nThis formula is derived from the image, which shows two overlapping squares with one square cut out of the other. The left square has an area of $\\frac{1}{2}$, the right square has an area of $\\frac{1}{4}$, and the cut-out square has an area of $\\frac{1}{4}$. The formula expresses the sum of the areas of the",
        "gt_answers": "x = - \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_807.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:$$\\sqrt x^2 + \\sqrt x^2 = \\sqrt 2x^2$$This can be derived by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is x^2 and the other two sides are also x^2, so the formula simplifies to the given expression.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{x^2 + 3x - 4}{x - 2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is not visible in the provided image. It is a black and white image with a message in Japanese.",
        "gt_answers": "3 x + 1 > 5 x - 5\n",
        "image_path": "./data/HME100K/test_images/test_810.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$ \\frac{1}{4}(x\\_1^2 + x\\_2^2 + x\\_3^2 + x\\_4^2) + \\frac{1}{2}(x\\_1^2 + x\\_2^2 + x\\_3^2 + x\\_4^2) + \\frac{1}{4}(x\\_1^2 + x\\_2^2 + x\\_3^2 + x\\_4^2) $\n\nwhere $x\\_1, x\\_2, x\\_3,$ and $x\\_",
        "gt_answers": "P _ { 4 } ( - 1 + \\sqrt { 3 } , 2\n",
        "image_path": "./data/HME100K/test_images/test_811.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n$$\\begin{aligned}\nG &= \\frac{F}{m} \\quad \\text{or} \\quad G = \\frac{F}{m} \\\n\\end{aligned}$$\n\nIn this formula, G represents the gravitational force between two objects, F represents the force applied to the object, and m represents the mass of the object.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a diameter of 6 inches is A = \u03c0r^2, where r is the radius of the circle. In this case, the diameter is 6 inches, so the radius is half of that, or 3 inches. The area of the circle is therefore A = \u03c0(3^2) = 3\u03c0.\n\nThe volume of a sphere with a diameter of 4 inches is V = (4/3)\u03c0r^3, where r is the radius of the sphere. In this case, the radius is 2 inches, so the volume",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\nThe expression for the area of a rectangle with a perimeter of 24 units is:\n\nA = lw + ht\n\nwhere l is the length of the rectangle, w is the width of the rectangle, and h is the height of the rectangle.\n\nPlugging in the values given in the image:\n\nl = 4\nw = 6\nh = 5\n\nA = 4(4) + 5(6)\n\nA = 16 + 30\n\nA = 46\n\nTherefore, the",
        "gt_answers": "\\angle B O F = \\frac { 1 } { 2 } a\n",
        "image_path": "./data/HME100K/test_images/test_815.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 3x^2 - 11x + 5. This formula represents the equation of a parabolic shape with its vertex at the origin and its axis of symmetry passing through the center of the circle.",
        "gt_answers": "k = - \\frac { 1 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_817.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$P\\_t=\\frac{1}{1+e^{-rT}}$$\n\nwhere P\\_t is the price of the asset at time t, r is the interest rate, and T is the time to maturity.",
        "gt_answers": "y =\n",
        "image_path": "./data/HME100K/test_images/test_818.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is not visible in the given image. Can you please provide a clearer image or the LaTeX format for the expression?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:\n\n$$x = \\frac{1}{3}\\left(\\frac{3y}{2}+\\frac{5z}{2}\\right)$$\n\nwhere x, y, and z are variables.",
        "gt_answers": "y = \\frac { 1 } { 2 } x ^ { 2 } - x - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_821.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$$\\frac{2}{3}$$x + $\\frac{8}{9}$y = $\\frac{10}{3}$x + $\\frac{16}{9}$y$$\\frac{2}{3}$$x + $\\frac{8}{9}$y = $\\frac{10}{3}$x + $\\frac{16}{9}$yThis expression can be used to calculate the result of the image.",
        "gt_answers": "x ^ { 2 } - x - 6 + 4 = 2 x ^ { 2 } - 8\n",
        "image_path": "./data/HME100K/test_images/test_822.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following code:\n\n\\begin{align\\*}\nx = \\frac{500}{4}\\sqrt{\\frac{200}{2}\\left(\\frac{100}{5}\\right)^2}\n\\end{align\\*}\n\nThis formula represents the x-coordinate of the point where the line passing through the point (0, 0) and (200, 500) intersects the line passing through the point (100, 200) and",
        "gt_answers": "1 5 0 x = 8 0 \\times 1 5\n",
        "image_path": "./data/HME100K/test_images/test_823.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\sqrt{x^2 + y^2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image: $\\frac{1}{2} x^2 + \\frac{1}{3} x - \\frac{1}{4}$",
        "gt_answers": "V _ { c } = \\frac { 1 } { 2 } m / s\n",
        "image_path": "./data/HME100K/test_images/test_825.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ 10x^2 + 10y^2 = 200$$This equation represents a quadratic equation with x and y as variables and 200 as the constant value.\n\nThe equation is in standard form, with the coefficients of the variables positive and the constant term non-negative. The equation has two solutions, one positive and one negative, which can be found by solving for the roots of the quadratic expression. The solutions are given by the quadratic formula:$$x = \\frac{-b \\pm \\sqrt{b^2 -",
        "gt_answers": "y _ { \\min } = 2 , y _ { m } G x = 4\n",
        "image_path": "./data/HME100K/test_images/test_826.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{equation}\nx = \\frac{a}{b}\n\\end{equation}\n```\nIn this equation, 'a' and 'b' are constants, and 'x' is the solution.",
        "gt_answers": ") = \\frac { 3 } { 6 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_827.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nlatex format:\n\n\\begin{equation}\n 5x^2 + 6x - 7 = 0\n\\end{equation}\n\nimage format:\n\n5x^2 + 6x - 7 = 0\n```",
        "gt_answers": "x = - \\sqrt { 4 3 }\n",
        "image_path": "./data/HME100K/test_images/test_828.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$ \\frac{1}{2} x^2 + \\frac{1}{4} x^4 + \\frac{1}{6} x^6 + \\frac{1}{8} x^8 + \\frac{1}{10} x^{10} = \\frac{1}{2} x^2 + \\frac{1}{4} x^4 + \\frac{1}{6} x^6 + \\frac{1}{8} x^8 + \\frac{1",
        "gt_answers": "x 1 = 1 + \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_829.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression:$\\frac{1}{1+x^2}=\\frac{1}{1+\\left(\\frac{1}{2}\\right)^2}=\\frac{1}{1+\\left(\\frac{1}{4}\\right)^2}=\\frac{1}{1+\\left(\\frac{1}{8}\\right)^2}=\\frac{1}{1+\\left(\\frac{1}{16}\\right)^2}=\\frac{1}{1+\\left(\\frac{1}{32}\\right)^2}=\\frac{1}{1+\\left(\\frac{1}{6",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula can be written as follows:$$\\begin{aligned} \\frac{3+5\\*6}{8-3} \\times \\frac{12\\*7}{11-4} \\times \\frac{16\\*8}{15-7}\\end{aligned}$$In LaTeX format, this can be written as follows:$$\\begin{aligned}\\frac{3 + 5\\*6}{8 - 3} \\times \\frac{12 + 7}{11 - 4} \\times \\frac{16 + 8}{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\left( \\frac{2^2 + 3^2}{5^2} \\right) \\left( \\frac{4^2 + 6^2}{7^2} \\right) = \\frac{16 + 22}{25} = \\frac{38}{25} = \\boxed{1.56} $$\n\nThe calculation involves dividing the sum of squares of the numbers in the numerator by the sum of squares of the numbers in the denominator.",
        "gt_answers": "O A \\cdot M P = 1 2\n",
        "image_path": "./data/HME100K/test_images/test_832.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we first need to identify the variables and their corresponding values.\n\nThe formula is given as:\n\ny = x\u00b2 + 2x + 1\n\nwhere x is the independent variable and y is the dependent variable.\n\nWe can substitute the given values of x and y into the formula to get:\n\ny = 3\u00b2 + 2(3) + 1\n\ny = 9 + 6 + 1\n\ny = 16\n\nTherefore, the value of y when x =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\filldraw (0,0) circle (2pt);\n\\filldraw (0,2) circle (2pt);\n\\filldraw (2,0) circle (2pt);\n\\filldraw (2,2) circle (2pt);\n\\draw[thick] (0,0) -- (2,0) -- (2,2) -- (0,2) -- cycle;\n\\draw[thick, dashed] (0,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$\\frac{1}{2} x^2 + 4x - \\frac{1}{3} x^3 = 1$\n\\end{center}\n\nHere, $x$ is a variable representing the distance from the origin to the point of intersection of the circle with the x-axis. The left-hand side of the equation represents the area of the circle with radius $x$, and the right-hand side represents the equation of the line tangent to the circle at that point. The constant",
        "gt_answers": ". B D \\bot B C\n",
        "image_path": "./data/HME100K/test_images/test_835.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$P = \\frac{t}{2} - \\frac{1}{4}$$\n\nwhere t is the time at which the ball is launched from the ground.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the expression shown in the image:\n\n$$\\frac{2+4i-3+2i}{5-3+i}$$",
        "gt_answers": "\\frac { 1 } { 3 } < k < 1\n",
        "image_path": "./data/HME100K/test_images/test_837.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the equation given in the image is: x + 2y = 6. This can be derived by adding 2y to both sides of the equation x + y = 3.\n\nThe solution of the equation is x = 3 - y, which can be verified by substituting this value into the equation x + 2y = 6 and obtaining 3 + 2(3 - y) = 6.",
        "gt_answers": "x ^ { 2 } + \\frac { 1 } { x ^ { 2 } } = 2\n",
        "image_path": "./data/HME100K/test_images/test_838.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}(x+2)^2+(x-1)^2=x^2+4x-3$.",
        "gt_answers": "x = - 2\n",
        "image_path": "./data/HME100K/test_images/test_839.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for this image is y = 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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{25}{x} = \\frac{x+5}{25} $$\n\nwhere $x$ is an integer variable.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a formula for the derivative of a function. It is written in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{d}{dx} \\left( \\frac{1}{x^2+4x+4} \\right) = \\frac{-2x-4}{x^2+4x+4}\n\\end{equation}",
        "gt_answers": "x _ { 1 } = \\frac { 3 } { 2 } , x _ { 2 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_842.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{x^2} + \\frac{5}{x^3} - \\frac{3}{x^4} - \\frac{4}{x^5} + \\frac{2}{x^6}$",
        "gt_answers": "O D = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_843.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not provided, so I cannot write it out in LaTeX format. However, if you provide the equation, I can help you write it out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:$\\frac{4x^2 + 4x - 12}{x - 3}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Determine the variables and coefficients in the formula. The variables in the formula are x and y, and the coefficient for x is 3 and the coefficient for y is 5.\n2. Write out the formula using LaTeX format. The formula is given by:\n\ny = 3x + 5\n\n3. Use the LaTeX format to write out the formula. The LaTeX code for the formula is:\n\n$ y = 3x + 5 $\n\nNote",
        "gt_answers": "1 \\div 3 = \\frac { 1 } { 3 } ( k g )\n",
        "image_path": "./data/HME100K/test_images/test_846.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image contains a formula written in LaTeX format. The formula is:\n\n![label] $\\mathrm{E} = \\frac{1}{2}m\\_0c^2 + \\frac{1}{2}mv^2$[/label]\n\nThis formula represents the equation of energy in the form of mass-energy equivalence, E = mc^2/2 + (1/2)mv^2. The formula uses the symbols for mass (m), velocity (v), and the speed of light (c).",
        "gt_answers": "\\angle A B C = 3 0 ^ { \\circ } . O B =\n",
        "image_path": "./data/HME100K/test_images/test_847.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image. Can you provide the image?",
        "gt_answers": "C _ { 1 0 } ^ { 4 } x ^ { 6 } ( \\sqrt { 2 } y ) ^ { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_848.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format. However, since I do not have access to the image, I will assume that the formula is `y = 2x + 3`.\n\nThe expression for `y` can be written as:\n\ny = 2x + 3$",
        "gt_answers": "O A = O C = O B , O\n",
        "image_path": "./data/HME100K/test_images/test_849.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "y _ { 4 } = - \\frac { V } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_850.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n    \\frac{a^2 - b^2}{2ab} = \\frac{1}{2}\n```",
        "gt_answers": "P = \\frac { F } { S }\n",
        "image_path": "./data/HME100K/test_images/test_851.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is pi \\* r^2, where r is the radius of the circle. The radius of the circle is 5 cm. Therefore, the area of the circle is 3.14 \\* 5^2 = 31.41 cm^2.",
        "gt_answers": "e ^ { 2 } > 2\n",
        "image_path": "./data/HME100K/test_images/test_852.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{100 - 30}{20 + 10}$. This formula is a proportion and calculates the percentage of a number that is being divided by another number. In this case, the number being divided is 100 and the number being used for the division is 30. The sum of the two numbers being used for the division is 20 + 10 = 30, which is then subtracted from 100 to give the result of 70. The result is then divided by the",
        "gt_answers": "x < \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_853.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent}\\_\\_\\_\\_\\_ \\times \\frac{2}{9} = \\frac{11}{3}$$\n\nwhere $\\text{ImageContent}$ is the image content and $\\frac{2}{9}$ is the proportion of the image that is black. The fraction $\\frac{11}{3}$ represents the proportion of the image that is not black.",
        "gt_answers": "x = - \\frac { - 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_854.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n$$\\text{Image content}$$",
        "gt_answers": "\\angle D E A = 1 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_855.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{2x + 3y}{x + 2y}$. This is a fraction expression that can be written in LaTeX as $\\frac{2x + 3y}{x + 2y}$.",
        "gt_answers": "k = - \\frac { 1 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_856.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image appears to be a mathematical expression. However, it is difficult to determine the exact expression without the actual equation. Please provide the equation to help me write out the expression.",
        "gt_answers": "\\frac { 1 } { x - y } : \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_857.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be expressed as follows:\n\n\\begin{align\\*}\nf(x) = \\frac{x^2 - 4x + 3}{x - 1}\n\\end{align\\*}\n\nThis is a quadratic function with a vertical asymptote at x = 1, where the function has a pole.",
        "gt_answers": "\\sqrt { 2 5 } x ^ { 2 } = x - 1\n",
        "image_path": "./data/HME100K/test_images/test_860.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize, but I cannot see the image you have provided. Can you please provide a different image or a text representation of the formula?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you can use the following code:\n\n$$\\begin{aligned}y&=-2x^2+5x-1\\end{aligned}$$\n\nThis formula represents the quadratic function shown in the image. The x-coordinate of the vertex of the parabola is -1, and the y-coordinate of the vertex is -2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:$$\\frac{x+y}{2}=\\sqrt{x^2+y^2}$$This formula is a quadratic equation in two variables, $x$ and $y$, and represents the distance between the midpoint of the line segment connecting the two points, $(0,0)$ and $(x,y)$ on the $xy$ plane.\n\nThe expression can be read as: the sum of $x$ and $y$ divided by $2$ is equal to the square root of the sum",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression in LaTeX format, which can be written as:$$\\text{r = 4cos}$$This expression represents a right triangle with hypotenuse $4$ and side length $cos$. The angle between the hypotenuse and each side is denoted by the trigonometric function cosine.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{m}{n}$$\n\nwhere,\n\n$m$ is the number of males\n\n$n$ is the number of females",
        "gt_answers": "\\rho = \\frac { M } { V }\n",
        "image_path": "./data/HME100K/test_images/test_866.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed using LaTeX as follows:\n\n$$A = \\pi r^2$$\n\nwhere $A$ is the area of the circle, $r$ is its radius, and $\\pi$ is the mathematical constant approximately equal to 3.14159.\n\nSo, for a circle with a radius of $r=5$, its area is:\n\n$$A = \\pi (5)^2 = \\pi \\cdot 25 = 785.3981633974483$$",
        "gt_answers": "3 = - \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_867.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ (x + 2y)^2 = 4x^2 + 4y^2 $$\n\nThe formula represents the area of a square with side length x + 2y.",
        "gt_answers": "a ^ { - 1 } = \\frac { 1 } { a }\n",
        "image_path": "./data/HME100K/test_images/test_870.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The given image shows a right triangle with hypotenuse length of 5 and heights of 3 and 4. The area of the triangle can be calculated as follows:\n\narea = (1/2) \\* base \\* height\n= (1/2) \\* 5 \\* (3 + 4)\n= (1/2) \\* 5 \\* 7\n= 35/2\n= 17.5\n\nTherefore, the area of the triangle is 17.5 square units.",
        "gt_answers": "\\frac { b } { \\sin B } = \\frac { C } { \\sin C }\n",
        "image_path": "./data/HME100K/test_images/test_872.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:$$\\text{r} = \\frac{5}{3} - \\frac{2}{x}.$$",
        "gt_answers": "- 0 . 5 = 1 8\n",
        "image_path": "./data/HME100K/test_images/test_873.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ \\frac{1}{2}x^2 + \\frac{1}{2}x + C$$where $x$ is the independent variable, $C$ is the constant of integration, and $\"=\"$ represents equality.",
        "gt_answers": "= 6 \\times \\sqrt { x }\n",
        "image_path": "./data/HME100K/test_images/test_875.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{1}{x} = \\frac{1}{2} + \\frac{3}{4} $$\n\nwhere $x$ is the variable in the formula.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:$\\frac{x^2 + 4x - 4}{x + 2}$",
        "gt_answers": "\\square A B C D\n",
        "image_path": "./data/HME100K/test_images/test_877.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 4 cm can be written as:\n\nA = (\u03c0r^2)\n\nwhere r is the radius of the circle. Substituting 4 for r, we have:\n\nA = (\u03c0 \\* 4^2)\nA = (\u03c0 \\* 16)\nA = 64\u03c0\n\nTherefore, the area of the circle with a radius of 4 cm is 64\u03c0 square centimeters.",
        "gt_answers": "r = 8 \\div 2 = 4 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_878.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by the formula: $\\frac{2x+3}{x^2-x+1}$.",
        "gt_answers": "3 \\times ( - 8 ) + 8 = \\frac { 3 \\times ( - 8 ) } { 4 } + m\n",
        "image_path": "./data/HME100K/test_images/test_879.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not provided, so it is not possible to write it in LaTeX format. Please provide the equation in the image for me to write it in LaTeX format.",
        "gt_answers": ". a _ { n } = 2 ^ { n } ( n \\in N ^ { \\ast } )\n",
        "image_path": "./data/HME100K/test_images/test_880.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{1}{2}\\sqrt{x^2 + y^2} = \\frac{1}{2}\\sqrt{49^2 + 16^2} = \\frac{1}{2}\\sqrt{2001} = 100'00\"'00\"'00\"'00\"'00\"'00\"'00\"'00\"'00\"'00\"'00\"'00\"'00\"'00\"'00\"'00",
        "gt_answers": "S _ { n } = \\beta n ^ { 2 } + q n\n",
        "image_path": "./data/HME100K/test_images/test_881.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by\n\n$$\\text{Area} = \\frac{1}{2}ab$$\nwhere $a$ and $b$ are the length of the rectangle's sides.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation for finding the product of 3 and 6.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is: 3x + 5y = 9.",
        "gt_answers": "1 5 \\div 5 \\times 1 = 3\n",
        "image_path": "./data/HME100K/test_images/test_887.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the given expression:\n\n$$\\frac{2 \\cdot 4 + 3 \\cdot 5 - 7 \\cdot 6}{15}$$\n\nThe numerator is:\n\n$$2 \\cdot 4 + 3 \\cdot 5 - 7 \\cdot 6 = 2 \\cdot 4 + 3 \\cdot 5 - 7 \\cdot 4 = 14 - 21 = -7$$\n\nAnd the denominator is:\n\n$$15 = 3 \\cdot 5$$\n\nSo",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a quadratic equation in the form of y = ax^2 + bx + c, where a, b, and c are constants. The solution to the equation is given by x = - b / (2a).",
        "gt_answers": "\\frac { 1 } { 4 } + \\frac { 1 } { 5 } = \\frac { 9 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_889.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot write out the expression of the formula in the image as LaTeX code since the image is not available. Please provide the image for me to write out the formula.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is y = x2 + x - 10.\n\nHere's how you can write it out using LaTeX format:\n\ny = x^2 + x - 10\n\nThe above formula represents a parabolic equation with an x-intercept at x = -10 and a y-intercept at y = 0. It can be used to graph the equation and determine its maximum and minimum points, inflection points, and other properties.",
        "gt_answers": "y - \\frac { 1 } { 6 } z = + 1\n",
        "image_path": "./data/HME100K/test_images/test_892.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by: x = 12 + 5y, where y is the number 5.",
        "gt_answers": "x = \\frac { 3 2 0 } { 4 1 }\n",
        "image_path": "./data/HME100K/test_images/test_893.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the equation of a right triangle. The legs of the triangle are x = 3 and y = 5. To find the length of the hypotenuse, use the Pythagorean theorem: c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the legs. The length of the hypotenuse is c = sqrt(a^2 + b^2) = sqrt(9 + 16) = sqrt(25) = 5.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write the expression of the formula in the image using LaTeX format.\n\nThe image shows the formula for the cross product of two vectors. The cross product is denoted by the symbol \"\u00d7\" and is a binary operation that takes two vectors as inputs and returns a third vector as output.\n\nThe formula in the image is:\n\n&#x2220;x&#x2212;&#x2211;&#x2220;y&#x2212;&#x2220;z&#x2212;&#",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for an algebraic expression can be written as: x + y = 4a + 2b.",
        "gt_answers": "( a + 2 b ) ( 2 a - 4 b )\n",
        "image_path": "./data/HME100K/test_images/test_899.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The formula in the image is:$$$2x^2+x-3=0$$$This is a quadratic equation in the form of ax^2+bx+c=0, where a=2, b=x, and c=-3. The solutions to this equation are the values of x that make the equation true, which are x= -1 and x= 1.",
        "gt_answers": "x = 2 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_900.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{sin}(x) = \\frac{e^ {-x}}{1 + e^ {-x}} $$\n\nThis formula is the sine function with the argument x.",
        "gt_answers": "x _ { 1 } = \\frac { 5 } { 3 } \\times 2 = - 1\n",
        "image_path": "./data/HME100K/test_images/test_901.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is not clear, as it does not contain any information about the formula. Please provide more information or context for the image to be able to write out the expression in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given formula:$$\\frac{5x + 6y}{x + 2y}$$This is the same expression as the one given in the image, just written in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\nC + 2c = 4c\n\nThis is an equation that states that the sum of two quantities, C and 2c, is equal to four times the quantity C. The symbols used in this equation are the addition symbol +, the constant symbol c, and the multiplication symbol x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\nP &= \\frac{1}{2} \\times \\frac{1}{3} \\times \\frac{1}{4} \\times \\frac{1}{5} \\times \\frac{1}{6} \\times \\frac{1}{8} \\times \\frac{1}{10} \\times \\frac{1}{12} \\times \\frac{1}{16} \\times \\frac{1}{20} \\times \\frac{1}{24}",
        "gt_answers": "\\frac { 4 } { 5 } : \\frac { 3 } { 4 } = 1 6 : 1 5\n",
        "image_path": "./data/HME100K/test_images/test_905.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the equation 3x + 2y = 11. The equation represents a line in the x-y plane with a slope of 3 and a y-intercept of 2. The equation can be graphed on a coordinate plane with the x-axis as the horizontal axis and the y-axis as the vertical axis. The graph of the equation is a straight line passing through the point (0, 9) and having a slope of 3.\n\nNote that the slope of the line is 3, and the y-intercept is 2.",
        "gt_answers": "y ^ { 2 } = \\frac { 1 } { b ^ { 2 } + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_906.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is as follows:\n\n\\begin{center}\n$2x^2 + 4x - 6 = 0$\n\\end{center}\n\nThis equation represents a parabolic equation with two variables, x and y, and four coefficients, 2, 4, and -6. The solutions to this equation are the values of x that make the equation true, which are:\n\n\\begin{center}\n$x = \\frac{1}{2} \\sqrt{16 + 8} \\approx 3.",
        "gt_answers": "\\frac { x ^ { 2 } } { 4 } + \\frac { y ^ { 2 } } { 3 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_908.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is not provided. Please provide the formula for the image.",
        "gt_answers": "k ^ { 2 } - 1 2 < 0\n",
        "image_path": "./data/HME100K/test_images/test_909.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b\u222b[a, b] f(x) dx = (b^n - a^n)/n\n\u222b\u222b[a, b] x^n dx = (b^n - a^n)/n\n\n\u222b\u222b[a, b] (x-a)^n dx = (b^n - a^n)/n\n\n\u222b\u222b[a, b] x^(n+1) dx = (b^(n+1) - a^(n+1))/(n+1)\n\n\u222b\u222b",
        "gt_answers": "x _ { 1 } = \\frac { \\sqrt { 3 a + 3 } } { a + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_910.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format.\n\nThe expression in the image is given by the formula:\n\na = 5cos\u00b2\u03b8 + 1cos\u03b8 \u2212 2sin\u00b2\u03b8",
        "gt_answers": "\\frac { A E } { A C } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_911.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$t = 2 \\cdot \\sqrt{x^2 + y^2}$$\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\text{m(n) = \\frac{n}{m}}$$\n\nwhere $m$ and $n$ are integers.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\nP(x) &= \\frac{1}{n}\\sum\\_{i=1}^{n} x\\_i\\\n&= \\frac{1}{n}\\sum\\_{i=1}^{n} \\frac{x\\_i - \\bar{x}}{s} \\\n&= \\frac{1}{n}\\sum\\_{i=1}^{n} \\frac{x\\_i - \\frac{1}{n}\\sum\\_{j=1}^{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 3\\sin^2x + 2cos^2x = 3sin^2x + cos^2x + 2cos^2x $$\n\nExpanding the left side of the equation:\n\n$$ 3\\sin^2x + 2(cos^2x) = 3\\sin^2x + cos^2x + 2cos^2x $$\n\nSimplifying the right side of the equation:\n\n$$ 3\\sin^2x + 2cos^",
        "gt_answers": "x + y - 3 = 0\n",
        "image_path": "./data/HME100K/test_images/test_915.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression in LaTeX format:$$\\frac{1}{2}x^2 + 4x - 8$$This formula calculates the equation of a parabolic function with a vertex at the origin and a minimum value of -4 at x = 2.",
        "gt_answers": "W = 4 0 0 ( x + 3 y )\n",
        "image_path": "./data/HME100K/test_images/test_916.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is:\n\n$$\\text{Area of the circle} = \\frac{pi}{4}$$r^2$$\\text{Volume of the cylinder} = pi r^2 h$$\\text{Pressure} = \\frac{F}{A}$$p$$\\text{Acceleration due to gravity} = \\frac{g}{m}$$a\\_g$$\\text{Kinetic energy of the ball} = \\frac{1}{2}mv^2$$K$$\\text{Potential energy of the ball} = mgh$$V$$\\text",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is $\\frac{k \\cdot \\text{mass}}{t}$, where $k$ is the proportional constant, $\\text{mass}$ is the mass of the object dropped from rest, and $t$ is the time it takes for the object to reach the ground.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{a^2 - 4ab + b^2}{2a}$.",
        "gt_answers": "a = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_919.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n&#x2212;&#x2211;&#x2212;(&#x222A;&#x2212;&#x2211;&#x2212;&#x222A;&#x2212;&#x2211;&#x2212;&#x222A;&#x2212;&#x2211;&#x2212;&#x222A;&#x2212",
        "gt_answers": "3 0 m = 3 0 0 0 c m\n",
        "image_path": "./data/HME100K/test_images/test_920.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula for the area of a right triangle is:\n\nA = (1/2) \\* b \\* h\n\nwhere A is the area, b is the base, and h is the height of the triangle.\n\nFor the image you provided, we can calculate the area of the triangle as follows:\n\nb = 8\nh = 6\n\nA = (1/2) \\* 8 \\* 6\nA = (1/2) \\* 48\nA = 24\n\nTherefore, the area of the right triangle in",
        "gt_answers": "1 3 + x = \\frac { 1 } { 2 } ( 4 7 + x )\n",
        "image_path": "./data/HME100K/test_images/test_921.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression of the formula in the image:\n\n\\begin{align\\*}\n& \\frac{1}{2}(6^2 + 5^2) - \\frac{1}{2}(2^2 + 4^2) + \\frac{1}{4}(5^2 - 2^2) \\\n&= \\frac{1}{2}(22 + 25) - \\frac{1}{2}(14 + 16) + \\frac{1}{4}(15 - 8) \\\n&= \\",
        "gt_answers": "m ^ { 2 } - 5 m - 6 = 0\n",
        "image_path": "./data/HME100K/test_images/test_925.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is written in LaTeX format as:\n\n$$\\begin{aligned} \\frac{a + b}{2c} \\leq \\sqrt{\\frac{ab}{2c}} \\leq \\frac{a + b}{c}\\end{aligned}$$\n\nThis is a mathematical inequality that states that the sum of a and b divided by 2c is less than or equal to the square root of ab divided by 2c, which is less than or equal to the sum of a and b divided by c.",
        "gt_answers": "\\frac { 9 } { 4 } + \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_926.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned}x^2 + 2x + 1 &= x^2 + 2x + 1\\end{aligned}$$\n\nThe right-hand side of the equation is equal to the left-hand side, so the equation is satisfied for any value of x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\frac{1000 - 500}{500 + 300}\n```\nThis is the formula written in LaTeX format.",
        "gt_answers": "x = \\sqrt { 2 } + 1\n",
        "image_path": "./data/HME100K/test_images/test_928.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is $\\frac{x^2}{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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n\\begin{center}\n\\begin{align\\*}\nf(x) & = \\frac{1}{2}\\left(\\frac{2x}{1}\\right)^{2} + 4x - 8x^{2} + 8x^{3} - \\frac{9}{2}x^{4} \\\\\n&= \\frac{1}{2}\\left(\\frac{2x}{1}\\right)^{2} + 4x - \\frac{7}{2}x^{2} + \\frac{",
        "gt_answers": "\\frac { x } { 3 } = \\frac { y } { 4 } = x : y = ( 3 ) : ( 4 )\n",
        "image_path": "./data/HME100K/test_images/test_933.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n\\begin{aligned}\nx + 2y &= 10 \\\\\nx - 3y &= -5\n\\end{aligned}\n\nThis system of equations can be solved using the substitution method or the elimination method.",
        "gt_answers": "\\frac { 1 } { 2 } x + 3 = 1\n",
        "image_path": "./data/HME100K/test_images/test_934.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\theta = \\frac{h}{\\sin \\theta}$$\n\nThis formula is a trigonometric identity that relates the height of an object to the angle of inclination of the object with respect to the horizon. It is derived from the law of sines and the law of cosines.\n\nIn the image, the formula is written in blue ink on a white background. The handwriting is clear and easy to read.",
        "gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_935.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, you can use the following code:\n\n$$\\frac{2x+3}{x+5}=5$$\n\nThe formula can be read as \"two times x plus three, divided by x plus five, equals five.\"",
        "gt_answers": "\\frac { 3 } { 4 } \\times \\frac { 3 \\times 5 } { 5 4 \\times 5 } = \\frac { 1 5 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_936.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:$$\\frac{x+2y-3z}{x+y-3z}$$where x, y, and z are variables. This formula represents the point on the line segment between the points (2, 1) and (2, 5).",
        "gt_answers": "\\frac { 1 } { 3 } ( \\frac { 3 } { 2 } x - 1 ) = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_937.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{aligned}\nx &= \\frac{48-24}{48-32} \\\n&= \\frac{24}{48} \\\n&= \\frac{1}{2} \\\n&= 0.5\n\\end{aligned}\n\nTherefore, the sum of the two numbers in the image is 24.",
        "gt_answers": "\\frac { 2 4 } { 6 } = 4\n",
        "image_path": "./data/HME100K/test_images/test_938.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n![Img](https://i.imgur.com/gGJwGJj.png)\n\nwhere x is the input variable and y is the output variable.",
        "gt_answers": "\\frac { 1 } { 7 } [ \\frac { 1 } { 5 } ( \\frac { x + 2 } { 3 } + 4 ) + 6 ] + 8 = 9\n",
        "image_path": "./data/HME100K/test_images/test_939.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{1}{4}x^2 + \\frac{1}{2}x + \\frac{1}{8} = \\frac{1}{2}x + \\frac{3}{8} $$",
        "gt_answers": "a d = b c = 8\n",
        "image_path": "./data/HME100K/test_images/test_940.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{2x+3}{x+5}=\\frac{x+3}{x+5}$. This is a proportion equation that can be solved using cross-multiplication. To solve, we have: $\\frac{2x+3}{x+5}=\\frac{x+3}{x+5}$ $\\frac{2x+3}{x+5}=\\frac{x+3}{x+5}$ $\\frac{2x+3}{x+5} = \\frac{x+3}{x+5}$ $\\frac{2x+3}{x+",
        "gt_answers": "x = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_941.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n\\begin{center}\n$x = \\frac{3y + 4}{y - 2}$\n\\end{center}\n\nThis formula can be derived by using the point-slope form of a line, where the slope is given by $\\frac{dy}{dx}$ and the y-intercept is given by $b$. In this case, the slope is $\\frac{4}{1}$ and the y-intercept is $-\\frac{6}{1}$.\n\nTo find the equation of the line, we can substitute the values of",
        "gt_answers": "\\frac { 1 } { 2 } + \\frac { 3 - a } { 3 } = \\frac { a } { b } - 3 \\times \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_942.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$c = \\frac{a+b}{2}$$where c is the average of a and b.\n\nNote: The image is not available to me. Please provide the image for me to answer your question.",
        "gt_answers": "c = 4\n",
        "image_path": "./data/HME100K/test_images/test_943.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula using LaTeX format is:\n\n$$\\frac{t}{t+4}$$\n\nIn this formula, $t$ represents the time taken to reach a certain position, and the expression $\\frac{t}{t+4}$ represents the average speed. The numerator $t$ represents the time taken to reach a certain position, while the denominator $t+4$ represents the total time taken to reach that position at an average speed of 4 units per second. Therefore, the formula gives the average speed at which the object traveled to reach the position.",
        "gt_answers": "x = - 2 \\pm \\sqrt { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_945.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a representation of the formula 1 + 1 = 2 in the LaTex format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the formula in the image is given by: \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{V} = \\frac{\\text{P}\\times\\text{t}}{\\text{2}\\times\\sqrt{\\text{t}^{2}+\\text{h}^{2}}}$$\n\nwhere V is the velocity of the object, P is the pressure of the fluid, t is the time, and h is the height of the object above the fluid.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I'd be happy to help. Here is the LaTeX code for the expression in the image:\n\n\\begin{align\\*}\nP &= \\frac{1}{2}mgh - \\frac{1}{2}mv^2 \\\\\n&= \\frac{1}{2}mgh - \\frac{1}{2}mv^2\n\\end{align\\*}\nThis equation represents the work done on an object as it moves from point A to point B in a gravitational field, where P is the work done, m is the mass of the object, g is the acceleration due",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula using LaTeX format is:\n\n\\begin{align\\*}\nx &= 2t - 4 \\\\\ny &= 4t - 8 \\\\\nz &= 8t - 16\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{5}{x} - \\frac{4}{x+3}$.",
        "gt_answers": "x = \\frac { 1 5 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_952.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned}3 - 2i &= 3 - 2i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot i \\cdot",
        "gt_answers": "\\sqrt { 3 } + \\sqrt { 3 } = \\sqrt { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_953.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{3\\sqrt{2} + 4\\sqrt{3}}{5\\sqrt{2} - 2\\sqrt{3}} = \\frac{3+4\\sqrt{3}}{5-2\\sqrt{3}} = \\frac{8+8\\sqrt{3}}{10} = \\frac{16}{10} = \\frac{1}{10} = 0.1$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$\\begin{aligned} \\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6 = \\frac{1}{2}x^2 + \\frac{9}{8}x^4 + \\frac{27}{16}x^6 \\end{aligned}$$\nThis is the formula for the sum of an arithmetic series, where the first term is $a=1$, the common",
        "gt_answers": "\\frac { a b } { 2 } = S _ { \\Delta } a b c = 7\n",
        "image_path": "./data/HME100K/test_images/test_955.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{align\\*}\n    & (a + 2b) \\times (c + 3d) \\\n    = (a + 2b) \\times (c + 3d) \\\n    = ac + 2ad + 2bc + 4bd \\\n    = ac + 2ad + 2bc + 4bd \\\n    = (ac + 2ad) + (2bc + 4bd) \\\n    = ac + 2ad + 2bc + 4bd",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given image:\n\n$$\\begin{aligned} \\frac{b}{a} \\cdot \\frac{c}{b} \\cdot \\frac{d}{c} &= \\frac{bd}{ab}\\\\ &= \\frac{b \\cdot d}{a \\cdot b} \\cdot \\frac{c}{d} \\cdot \\frac{c}{b} \\cdot \\frac{b}{a} \\cdot \\frac{c}{b} \\cdot \\frac{d}{c}\\\\ &= \\frac{b \\cdot d \\cdot c}{a \\cdot b",
        "gt_answers": "\\frac { B G } { A G } = \\frac { B H } { A F }\n",
        "image_path": "./data/HME100K/test_images/test_957.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{3(b - a)}{(b + a)(b - 3a)}$$",
        "gt_answers": "k - 3 > 0 \\Rightarrow k > 3\n",
        "image_path": "./data/HME100K/test_images/test_958.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$2\\cdot3+6\\cdot2-10$$This equation represents the equation in the image, which shows a system of linear equations. The variables x and y are used to represent the coefficients of the equation, while the coefficients themselves are represented by the numbers in the equation.",
        "gt_answers": "- x . - 8 = \\frac { 1 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_959.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a formula for the derivative of the inverse tangent function with respect to x. It is used to find the rate of change of the inverse tangent function with respect to x. The formula can be written as: d/dx [arctan (x)] = 1/x2",
        "gt_answers": "x = \\frac { \\pi } { 6 } o r \\frac { 2 \\pi } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_960.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{align}\nL &= \\frac{1}{2}m\\_1v\\_1^2 + \\frac{1}{2}m\\_2v\\_2^2 - \\frac{1}{4}(m\\_1+m\\_2)v\\_1v\\_2 \\tag{1}\\label{eq1}\n\\end{align}\n\\end{center}\n\nwhere $L$ is the mechanical energy of the system, $m\\_1$ and $m\\_2",
        "gt_answers": "f ^ { \\prime } ( x ) = 3 x ^ { 2 } + 2 b x + 6\n",
        "image_path": "./data/HME100K/test_images/test_961.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a fraction line with the numerator 1 and the denominator 4, representing the fraction 1/4. The red line is a horizontal line indicating the equality of the numerator and denominator, showing that 1 is equivalent to 4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula can be written as follows:\n\n$$\\text{r} = \\frac{1}{2}\\left(\\frac{1}{3} + \\frac{1}{4}\\right)$$\n\nwhere $\\text{r}$ is the result.",
        "gt_answers": "\\frac { a } { a - 1 } = a - 1\n",
        "image_path": "./data/HME100K/test_images/test_964.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is not shown, as it is only a representation of the number x1.",
        "gt_answers": "9 x - 4 x = 6 + 3 + 2\n",
        "image_path": "./data/HME100K/test_images/test_967.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear, so I cannot write out the expression.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$\\frac{1}{2}\\cdot x^{2}+\\frac{1}{4}\\cdot x^{4}=ax^{2}+bx^{4}$\n\\end{center}\n\nWhere $a=\\frac{1}{2}$ and $b=\\frac{1}{4}$.",
        "gt_answers": "z _ { 1 } + z _ { 2 } = - \\frac { b } { - a } = 2 p\n",
        "image_path": "./data/HME100K/test_images/test_969.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is not provided in the image. Please provide the formula for the expression in the image for me to write it out using LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the given image:\n\n\\begin{center}\n$\\begin{aligned}\n  f(x) &= \\frac{1}{2}x^2 + 3x - 4 \\ \\ \\text{for } x \\in \\left[-3, 3\\right]\n\\end{aligned}$\n\\end{center}\n\nNote: The function $f(x)$ is defined on the interval $[-3, 3]$.",
        "gt_answers": "( 1 ) 4 ( 2 x - 1 ) < 3 ( 4 x + 2 )\n",
        "image_path": "./data/HME100K/test_images/test_971.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX code for the given expression:\n\n$$\\begin{aligned}\n\\frac{1}{x^2} + \\frac{1}{y^2} &= \\frac{1}{r^2} \\\\\n\\frac{1}{x} + \\frac{1}{y} &= \\frac{1}{r}\n\\end{aligned}$$\nIn this equation, $x$ and $y$ represent the distances from the point $(0,0)$ to the points on the circle with radii $x$ and $y$,",
        "gt_answers": ": \\frac { m ( m + 1 ) } { ( m - 1 ) ^ { 2 } } \\cdot \\frac { m - 1 } { m } = \\frac { m + 1 } { m - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_973.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX formula for the expression:\n\n\\begin{center}\n$$\\frac{a+b}{2} = \\frac{b+c}{2} = \\frac{c+d}{2}$$\n\\end{center}\n\nThis formula is the equation of a straight line, where the slope is $\\frac{b-a}{c-d}$ and the y-intercept is $\\frac{b+c}{2}$.",
        "gt_answers": "\\frac { D G } { B A } = \\frac { A D } { A B } = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_974.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle can be written as follows:\n\narea = (1/2) \\* base \\* height\n\nIn LaTeX format, this can be written as:\n\narea = (1/2) \\* base \\* height\n\nHere, the variable 'base' represents the length of the base of the triangle and the variable 'height' represents the height of the triangle. The constant '1/2' is used to convert the length of the base into the area of the triangle.\n\nNote that the area formula is only applicable for right triangles, where one angle",
        "gt_answers": "S _ { 1 } = \\frac { V } { h } = 2 . 5 \\times 1 0 ^ { - 2 } m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_975.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: $\\frac{1}{\\sqrt{x^2 + 4x}}$.",
        "gt_answers": "x _ { 2 } = - \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_976.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:$$ f(x) = \\frac{4x^2 + 8x - 16}{x^2 - 4x + 16} $$",
        "gt_answers": "x _ { 1 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_978.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is given by the equation:$$ \\frac{3x^2+x+2}{x+2}=\\frac{3x^2+x+2}{x+2}$$This can be simplified by factoring the numerator and denominator as follows:$$ \\frac{3x^2+x+2}{(x+2)(x+2)}=\\frac{3x^2+x+2}{(x+2)(x+2)}$$which simplifies to$$ \\frac{3x^2+x+2}{x+2}=3x+",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\np(p \u2264 0.5) = 1 - \\frac{1}{2}\n\\end{center}\n\nThis formula can be read as follows: The probability of p being less than or equal to 0.5 is equal to 1 minus 1/2.",
        "gt_answers": "P ( A ) P ( B ) = \\frac { 1 } { 5 2 }\n",
        "image_path": "./data/HME100K/test_images/test_980.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 3x^2 + 2 = 3\\left(\\frac{x}{2}\\right)^2 + 2 $$\n\nwhich simplifies to:\n\n$$ x^2 + 2 = \\left(\\frac{x}{2}\\right)^2 + 2 $$\n\nThe left side of the equation represents the sum of the first two terms of the quadratic formula, which is given by:\n\n$$ x^2 + 2 $$\n\nThe right side of the equation represents the constant value that makes the equation",
        "gt_answers": "b = 3 - \\sqrt { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_981.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 3x + 4y = 14.\n\nThis formula can be derived from the given image by adding the values of the points in the image. The x-coordinate of the point at the bottom right is 3, and the y-coordinate is 4. The point in the upper left corner has coordinates (0,6), and the point in the lower left corner has coordinates (2,6). The sum of these points is (3,4) + (0,6) + (2,6) = (3+0+2,",
        "gt_answers": "5 \\div 8 = \\frac { 5 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_982.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $\\frac{1}{4}\\left(\\frac{a^2+b^2}{2}\\right)^2-\\frac{1}{2}(a-b)^2$",
        "gt_answers": "S _ { \\Delta } a b c = \\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_983.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\documentclass{article}\n\\usepackage{amsmath}\n\n\\begin{document}\n\nThe expression for the derivative of $f(x) = \\sin(x)$ is:\n\n$$ \\frac{d}{dx} \\sin(x) = \\cos(x) $$\n\n\\end{document}\n```",
        "gt_answers": "A E \\bot P N\n",
        "image_path": "./data/HME100K/test_images/test_984.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Select the text in the image, including the equations.\n2. Copy and paste the text into a new LaTeX document.\n3. Replace the image with a mathematical expression that represents the function of the image, such as a graph or diagram.\n4. Use LaTeX commands to format the expression, including variables, functions, and operators.\nFor the given image, the expression is:\nx^2 + 4x + 4 = 0x^2 + 4x +",
        "gt_answers": "x = 6 \\div \\frac { 2 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_986.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by A = \u03c0r^2, where r is the radius of the circle. In this image, the radius of the circle is given by r = 2. Therefore, the area of the circle is given by A = \u03c0(2)^2 = \u03c0(4) = 12.866.",
        "gt_answers": "\\sqrt [ 3 ] { ( \\sqrt { 2 a - 1 } ) } = 3 \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_987.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n$$ \\text{sin}\\left(\\frac{x}{a}\\right) = \\text{cos}\\left(\\frac{x}{b}\\right) $$\n\nwhere $a$ and $b$ are constants.",
        "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",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\left(\\frac{1}{3}+\\frac{1}{5}\\right)\\left(\\frac{1}{2}+\\frac{1}{4}\\right)\\left(\\frac{1}{4}+\\frac{1}{6}\\right)\\left(\\frac{1}{5}+\\frac{1}{7}\\right)\\left(\\frac{1}{6}+\\frac{1}{8}\\right)\\left(\\frac{1}{7}+\\frac{1}{9}\\right)\\left(\\frac{1}{8}+\\frac{1}{10}\\right)\\left",
        "gt_answers": "f ( x ) = \\frac { e ^ { 2 } x } { x } < 0\n",
        "image_path": "./data/HME100K/test_images/test_989.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Please provide a valid image so that I can assist you with your question.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as: \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "= 1 6 a ^ { 4 } - 8 1 b\n",
        "image_path": "./data/HME100K/test_images/test_992.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{1}{2} \\cdot \\frac{1}{4} \\cdot \\frac{1}{8} \\cdot \\frac{1}{16} = \\frac{1}{8} $$",
        "gt_answers": "x = k \\pi - \\frac { \\pi } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_993.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the number of electrons in an atom can be represented using LaTeX as follows:\n\nelectrons = 1\\*number of valence electrons + 8\\*number of shells + 8\\*number of valence electrons in each shell\n\nwhere the number of valence electrons is represented as n and the number of shells as m, and assuming that each shell contains 2 electrons.\n\nTherefore, for the given formula, the number of electrons would be:\n\nelectrons = 1*2 + 8*2 + 8*2 = 1 + 8",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\frac{x + 2}{x - 3} = \\frac{x - 3 + 2}{x - 3} = \\frac{x - 3 + 2}{x - 5} = \\frac{x - 5 + 2}{x - 5} = \\frac{x - 5 + 2}{x - 7} = \\frac{x - 7 + 2}{x - 7} = \\frac{x - 7 + 2}{x} =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Please provide the image so I can assist you.",
        "gt_answers": "6 + 1 = 7\n",
        "image_path": "./data/HME100K/test_images/test_996.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a fraction with the numerator 3 and the denominator 5. This fraction can be written in LaTeX format as: 3/5.",
        "gt_answers": "\\frac { 1 } { 3 } + \\frac { 1 } { 3 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_997.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} \\text{Image Content} \\end{aligned}$$",
        "gt_answers": "\\sqrt { a ^ { 2 } + 1 } = \\sqrt { ( 1 + a ) ^ { 2 } + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_998.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is written in the image is:\n\n$$E = mc^2$$\n\nwhere E is energy, m is mass, and c is the speed of light in a vacuum. This equation is known as the mass-energy equivalence principle and is a fundamental principle in physics that states that the energy of an object is equal to its mass multiplied by the speed of light squared.",
        "gt_answers": "C E = B E = 2 5 2\n",
        "image_path": "./data/HME100K/test_images/test_999.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{equation}\nP = \\frac{1}{4} \\cdot \\frac{1}{2} + \\frac{1}{4} \\cdot \\frac{1}{3} + \\frac{1}{4} \\cdot \\frac{1}{4} + \\frac{1}{4} \\cdot \\frac{1}{5}\n\\end{equation}\n\nwhere $P$ represents the probability of getting heads in four coin flips.",
        "gt_answers": "\\rightarrow d _ { A } \\rightarrow B C\n",
        "image_path": "./data/HME100K/test_images/test_1000.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I am not able to see the image as it appears to be broken or not available. Can you please provide another image or method to show me the expression?",
        "gt_answers": "9 6 \\div 6 0 = 1 \\cdots 3 6\n",
        "image_path": "./data/HME100K/test_images/test_1001.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{b - a}{c - h}$.",
        "gt_answers": "\\frac { B E } { A B } = \\frac { A E } { A C }\n",
        "image_path": "./data/HME100K/test_images/test_1002.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$m = \\frac{a^2 - b^2}{2ab}$$\n\nwhere $m$ is the midpoint of the line segment AB. The length of AB is given by $b - a$, so we can substitute that value into the formula to get:\n\n$$m = \\frac{(b - a)^2 - (b - a)^2}{2(b - a)}$$\n\n$$m = \\frac{0 - 0}{2(b - a)}$$\n\n$$m = \\frac{0}{2",
        "gt_answers": "m - 2 0 + 2 0 = 6 + 2 0\n",
        "image_path": "./data/HME100K/test_images/test_1004.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the equation in the image using LaTeX format is:$$\\frac{1}{4}\\cdot\\frac{1}{8} + \\frac{1}{2}\\cdot\\frac{1}{8} + \\frac{1}{4}\\cdot\\frac{1}{8} + \\frac{1}{2}\\cdot\\frac{1}{4} + \\frac{1}{2}\\cdot\\frac{1}{4} + \\frac{1}{4}\\cdot\\frac{1}{8} + \\frac{1}{4}\\cdot\\frac{1}{8} + \\frac",
        "gt_answers": "f ( - x ) = \\frac { 1 } { 2 ^ { x } } + 2 ^ { x } - 1\n",
        "image_path": "./data/HME100K/test_images/test_1006.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mi>h</mi><mo>+</mo><mspace width=\"1em\"></mspace><mi>t</mi></mrow><annotation encoding=\"application/x-tex\">\\frac{1}{2} m\\_0^2 \\_ {2} + m\\_1^2</annotation></semantics></math>\n\nwhere h is the Planck constant, m\\_0",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{a + b}{c + d}$.\n\nThis formula represents the ratio of two numbers, a and b, divided by another two numbers, c and d. The plus sign between the numbers indicates that they are added together. The division symbol (\\) separates the numerator (a + b) from the denominator (c + d).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression. It consists of a sum of two terms, where the first term is represented by the variable x and the second term is represented by the variable y. The expression is written as: f(x) = (x + 2y) \\* 3. This means that the value of the function f(x) is the result of multiplying x by 3 and adding 2y to it.\n\nIn LaTeX format, the expression would be written as: f(x) = (x + 2y) \\* 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{height} = \\text{width} \\times \\sqrt{\\frac{\\text{side}}{\\text{height}}}$$\n\nwhere $\\text{height}$, $\\text{width}$, $\\text{side}$ are the lengths of the three sides of the triangle, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$ E = \\frac{mgh^2}{4}$$where$m$is the mass of the object,$g$is the acceleration due to gravity, and$h$is the height from which the object is dropped.",
        "gt_answers": "\\frac { B D } { A B } = \\frac { A B } { B C }\n",
        "image_path": "./data/HME100K/test_images/test_1014.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is y = x2.\n\nIn LaTeX format, it would be written as:\n\n\\[ y = x^2 \\]",
        "gt_answers": "y = \\sqrt { 2 0 0 }\n",
        "image_path": "./data/HME100K/test_images/test_1015.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Can you please provide the image again or describe it in detail so I can assist you?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{5.3333}\\times\\frac{\\text{148}}{\\text{392}}=\\text{0.3594}$$",
        "gt_answers": "5 6 + 4 0 = 9 6 9 5 - 4 0 =\n",
        "image_path": "./data/HME100K/test_images/test_1017.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not written in LaTeX format. However, the image shows the equation for the formula for the area of a circle with a radius of 5 cm, which is \u03c0r^2. The formula is pi\\*r^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I don't see any image in your question. Could you please provide the image so I can help you with the expression of the formula?",
        "gt_answers": "\\cdot \\frac { x } { 3 } \\leq \\theta \\leq \\frac { 2 } { 3 } \\pi\n",
        "image_path": "./data/HME100K/test_images/test_1019.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is given by the formula:\n\n![Image Content](https://i.imgur.com/0oPxCtR.png)\n\nwhere A is the amplitude, w is the angular frequency, and t is time. The angular frequency w is related to the frequency f by the formula:\n\n![Image Content](https://i.imgur.com/0oPxCtR.png)\n\nwhere \u03c9 is the angular frequency and f is the frequency.\n\nIn LaTeX format, the equation can be written as:\n\n\\begin{align}",
        "gt_answers": "\\cos C = \\frac { \\sqrt { 3 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1021.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\text{R} = \\frac{V}{\\text{I}}$$\n\nIn words, this formula states that the resistance (R) of a material is equal to the ratio of the voltage (V) across it to the current (I) flowing through it.",
        "gt_answers": "R = \\frac { U } { I }\n",
        "image_path": "./data/HME100K/test_images/test_1023.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the derivative of a quadratic function is given by:$$\\frac{dy}{dx} = \\frac{2y}{x + y}$$This can be written in LaTeX format as:$$\\frac{dy}{dx} = \\frac{2y}{x + y}$$In the given image, the function f(x) = x^2 + 4x - 4 is a quadratic function with an x-intercept at x = -2 and a vertex at x = 2. The formula for the derivative of this function is given by the expression above.",
        "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",
        "image_path": "./data/HME100K/test_images/test_1024.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be expressed as:\n\n$$ 2x + 5y = 7 $$\n\nThe solution to this equation is:\n\n$$ x = 3, y = 2 $$\n\nTherefore, the image shows that if $x$ is equal to 3 and $y$ is equal to 2, then the equation is satisfied.",
        "gt_answers": "\\frac { 2 x ( - 1 ) - a } { 3 } - \\frac { - 1 - a } { 2 } = - 1 = - 1\n",
        "image_path": "./data/HME100K/test_images/test_1025.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the equation, we can write:$$\\text{k}=\\frac{\\text{m}\\times\\text{v}}{\\text{t}}$$where $k$ is the acceleration, $m$ is the mass, $v$ is the velocity, and $t$ is the time.\n\nThe above equation represents the acceleration of an object in terms of its mass and velocity. The numerator $m\\times v$ is the product of the mass and velocity of the object, while the denominator $t$ is the time taken for the object to accelerate from rest to its final velocity. The constant",
        "gt_answers": "k = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1026.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\begin{align}\nf(x) = \\frac{1}{x^2 + 4x - 4}\n\\end{align}\n```",
        "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",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n( 5x\u00b2 + 3x - 7 )( 2x + 3 ) = 2x\u00b2 + 11x + 21\n\nThis is a product of two binomials, ( 5x\u00b2 + 3x - 7 ) and ( 2x + 3 ), which are multiplied together. The expression inside the parentheses on the right side is evaluated first, and then the result is substituted into the expression on the left side. The binomials are multiplied together according to the distrib",
        "gt_answers": "\\frac { 4 } { 7 } \\times 5\n",
        "image_path": "./data/HME100K/test_images/test_1028.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2x^2 + 2x + 7.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{x^2 + y^2}{x - y}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: $\\frac{1}{2}x^2 + \\frac{1}{2}y^2 = \\frac{1}{2}(x + y)^2$. The image shows the equation of a circle in polar coordinates. The center of the circle is at the origin and the radius is $\\frac{1}{2}$ times the distance from the origin to the point on the circle's circumference where the radius intersects the x-axis.\n\nThe center of the circle is at the origin, denoted by (0,0), and the radius is half of the distance from",
        "gt_answers": "\\frac { 4 } { 2 4 } x = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1031.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n$$\\begin{aligned}x^2 + y^2 &= x^2 + y^2\\end{aligned}$$\n\nThis is simply the equation of a circle in the x-y plane with center at the origin and radius r.",
        "gt_answers": "( - \\frac { 1 } { n } ) ( - 2 ) = - 1\n",
        "image_path": "./data/HME100K/test_images/test_1032.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{100}\\% \\times \\frac{\\text{125 g}}{\\text{440 g}} = \\frac{\\text{100}\\% \\times \\text{125 g}}{\\text{440 g}} = \\text{50}\\%$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression on the image is given by:\n\n$$ \\text{a}\\_1 + \\text{b}\\_2 = \\frac{\\text{a}\\_1 + \\text{b}\\_2 + \\text{c}\\_3}{\\text{c}\\_3 + \\text{d}\\_4}$$\n\nThe variable names in this formula are defined as follows:\n\n* $\\text{a}\\_1$ is the first variable\n* $\\text{b}\\_2$ is the second variable\n* $\\text{c}\\_3$ is the third variable",
        "gt_answers": "\\frac { A D } { A E } = k\n",
        "image_path": "./data/HME100K/test_images/test_1034.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX format of the expression for the given formula:\n\n$$\\begin{aligned}&\\text{Battenfeld-Sorlie formula: } \\\\\\text{B = }&\\frac{\\text{V}\\times\\text{t}}{\\text{n}\\times\\sqrt{\\text{t}\\times\\text{n}}}\\\\\n&\\text{V} = \\text{Q}\\times\\text{t}\\end{aligned}$$\n\nIn this formula, B represents the bond energy, V represents the volume of the molecule, Q represents",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following code:\n\n\\begin{equation}\nsin(\\theta) = \\frac{opposite\\_side}{hypotenuse}\n\\end{equation}\n\nHere, the opposite side refers to the length of the opposite side of the triangle, and the hypotenuse refers to the length of the hypotenuse of the triangle.",
        "gt_answers": "\\sin a = - \\sqrt { 1 - \\cos ^ { 2 } a } = - \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1036.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:$$3x+5y=2$$This equation states that the sum of three times the x variable and five times the y variable is equal to two.",
        "gt_answers": "\\angle B A M = 2 2 . 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1038.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $ $ $\\frac{d\\frac{m}{d\\frac{c^2}}{dt} + \\frac{v}{d\\frac{c^2}}{dx}}{d\\frac{c^2}}{dt} - \\frac{a}{d\\frac{c^2}}{dx} = \\frac{F}{m}$$.\n\nThis formula represents the force acting on an object, where $F$ is the net force acting on the object, $m$ is the mass of the object, $a$ is the acceleration of the",
        "gt_answers": "6 c m = \\frac { 3 } { 5 } d m\n",
        "image_path": "./data/HME100K/test_images/test_1039.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is y = x^2.",
        "gt_answers": "x = \\frac { 1 } { 1 2 } \\div \\frac { 5 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1040.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ s\\_2 = \\frac{1}{2}\\left(\\frac{50}{49} + \\frac{30}{49}\\right) + \\frac{1}{4}\\left(\\frac{20}{49} + \\frac{30}{49}\\right) = \\frac{1}{2}\\left(\\frac{50}{49}\\right) + \\frac{1}{4}\\left(\\frac{20}{49}\\right) = \\frac{150}{49} +",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the volume of a cylinder with a radius of r and height of h.\n\nV = \u222b\u03c0r^2h\\\u222b \\pi r^2h\u222b\u03c0r^2h\u200bThe volume of the cylinder is the integral of the product of pi, the radius, and the square of the height. The height is given by h, and the radius is given by r. The volume of the cylinder is the integral of this product.",
        "gt_answers": "\\rho = \\frac { m } { V }\n",
        "image_path": "./data/HME100K/test_images/test_1042.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{c\\_0^2}{c\\_0^2 + c\\_1^2}$$\n\nwhere $c\\_0$ and $c\\_1$ are the coefficients of the quadratic expression $ax^2 + bx + c$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$C\\_6H\\_12O\\_6 + 6 O\\_2 \\rightarrow 6 CO\\_2 + 6 H\\_2O$$This is a chemical equation representing the combustion of glucose in the presence of oxygen to produce carbon dioxide and water.\n\nNote: This equation is written in the chemical notation, which uses symbols and formulas to represent chemical reactions.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a mathematical expression for the area of a right triangle.\n\nThe equation is:\n\nA = (1/2) x h x b\n\nWhere:\nA is the area of the triangle\nh is the height of the triangle\nb is the base of the triangle\nThe image shows the formula written in LaTeX format:\n\n\\frac{1}{2} h b\n\nThe image also includes a calculator, but it is not clear what the result of the calculation is.",
        "gt_answers": "1 8 \\times 2 = 3 6 m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1046.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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$$\\frac{1}{2}$$\n\nwhere the numerator is 1 and the denominator is 2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is $\\frac{10}{9}$+$\\frac{100}{91}$+$\\frac{1000}{911}$+$\\frac{10000}{9111}$+$\\frac{100000}{91111}$.",
        "gt_answers": "( 1 ) \\because A ( - 1 , 0 )\n",
        "image_path": "./data/HME100K/test_images/test_1048.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation for finding the sum of two numbers using the method of substitution. The equation is:",
        "gt_answers": "9 - 2 x + 6 = x - 3 - 6 x\n",
        "image_path": "./data/HME100K/test_images/test_1050.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: x = 3m.\n\nIn LaTeX format, this can be written as:\n\nx = 3m",
        "gt_answers": "3 x = \\frac { m } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1051.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is: x2 + 3x + 2 = 5x + 10.",
        "gt_answers": "3 b + \\frac { 5 } { 3 } \\times 2\n",
        "image_path": "./data/HME100K/test_images/test_1052.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression written in LaTeX format. It represents the formula for calculating the sum of two numbers. The expression is written as:$$\\frac{(a+b)}{2}$$\n\nThis formula calculates the average of two numbers, 'a' and 'b'. The numerator, $a + b$, represents the sum of the two numbers, and the denominator, $2$, represents the number of terms in the sum. The result is the average of the two numbers.\n\nNote that this formula is only valid for non-negative numbers. If either 'a' or 'b' is negative",
        "gt_answers": "x = - \\frac { 3 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_1053.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the given expression:\n\n$$a + b = c$$\n\nwhere a, b, and c are any real numbers.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\sqrt{x^2 + 9x + 36}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\begin{aligned} 4(x + 3) - 2x + 9 &= x^2 + 9x - 6x + 9 \\\\ &= x^2 + 8x - 6x \\\\ &= x^2 + 3x - 6x \\\\ &= x^2 + 3x - 2x^2 \\\\ &= x^2 - 3x + 2x^2 \\end{aligned}$$Note: This formula is written in LaTex format.",
        "gt_answers": "( 1 ) y = - \\frac { 4 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_1056.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\begin{aligned} x &= 3 \\\\ y &= 4 \\end{aligned} $$\n\nwhere x is the number of apples and y is the number of oranges.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "In LaTeX format, the formula for the area of a rectangle would be written as follows:\n\n$$A = b \\times h$$\n\nwhere $A$ is the area of the rectangle, $b$ is the base (or width) of the rectangle, and $h$ is the height of the rectangle. This formula is simply the product of the base and height of the rectangle, which gives the area of the rectangle.",
        "gt_answers": "- \\frac { 1 5 } { 4 } < - ( 6 - 2 ) ^ { 2 } + 4 \\leq 4\n",
        "image_path": "./data/HME100K/test_images/test_1058.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a formula for finding the average of a set of numbers. The formula is \u2211x / n, where x is the sum of the numbers in the set and n is the number of terms in the set.",
        "gt_answers": "\\frac { 6 5 } { 3 } = 2 1 \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1059.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[step=1cm,color=black] (0,0) grid (2,2);\n\\draw[thick,color=black] (0,0) -- (2,0) -- (2,2) -- (0,2);\n\\node at (1,1) {$$};\n\\end{tikzpicture}\n\\end{center}\n\nThis equation draws a square with sides of length 2 units and a black dot in the center",
        "gt_answers": "x = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1061.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a LaTeX formula for the formula in the image: \\frac{x^2 - y^2}{x - y}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Select the text in the image and copy it to your clipboard.\n2. Open a LaTeX editor, such as Overleaf or ShareLaTeX.\n3. Paste the copied text into the editor and format it as a mathematical expression.\n4. Use LaTeX commands to write the formula, such as \\frac, \\sum, and \\* for multiplication.\n5. Compile the document and display the formula in the image.\nHere is the formula written out in LaTeX format:",
        "gt_answers": "\\frac { x ( x + 1 ) } { 2 } = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_1063.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{align\\*}\na &= 40 \\times \\frac{3000 - 1000}{1000 + 200} \\\n   &= 40 \\times \\frac{2000}{1200} \\\n   &= 40 \\times \\frac{1}{3} \\\n   &= 40 \\times \\frac{1}{3} \\\n   &= 13.33\n\\end{align\\*}",
        "gt_answers": "A P = 4 0 + 3 0 ( \\sqrt { 3 } - 1 )\n",
        "image_path": "./data/HME100K/test_images/test_1064.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the formula for the image: $\\frac{1}{2}\\frac{1}{4}\\frac{1}{8}\\frac{1}{16}\\frac{1}{32}\\frac{1}{64}\\frac{1}{128}$\n\nIn LaTeX format, the formula would be written as:\n\n$$\\frac{1}{2}\\frac{1}{4}\\frac{1}{8}\\frac{1}{16}\\frac{1}{32}\\frac{1}{64}\\frac{1}{128}$$",
        "gt_answers": "\\angle O C F = \\frac { 1 } { 2 } \\angle A C D\n",
        "image_path": "./data/HME100K/test_images/test_1065.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 3x + 4y = 12. To write it in LaTeX format, we can use the following code:$$3x + 4y = 12$$\n\nThis formula is read as \"the sum of 3x and 4y is equal to 12\". The equals sign (=) indicates that the two expressions on either side of the equation are equal.",
        "gt_answers": "- 6 . 5 5 ) ] = 4 9 \\frac { 7 } { 1 0 } - [ - 2 3 \\frac { 3 } { 4 } + ( - 6 \\frac { 1 1 } { 2 0 } ) ]\n",
        "image_path": "./data/HME100K/test_images/test_1066.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$y = \\frac{2}{x}$",
        "gt_answers": "F e + H _ { 2 } S O 4 = H _ { 2 } \\uparrow + F e S O 4\n",
        "image_path": "./data/HME100K/test_images/test_1067.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the image you provided:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick, ->] (0,0) -- (2,0) node[right] {$x$};\n\\draw[thick, ->] (0,0) -- (0,2) node[above] {$y$};\n\\filldraw (1,1) circle[radius=2pt];\n\\end{tikzpicture}\n\\end{center}\n\nThis formula draws a point (1,1) on the Cartesian coordinate plane,",
        "gt_answers": "x = \\frac { 3 } { 4 } + \\frac { 1 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1068.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX expression for the formula in the image:$$\\text{mass of the cannonball} = \\frac{1}{2}mv^2 + \\frac{1}{2}mgd$$where $m$ is the mass of the cannonball, $v$ is its velocity, $g$ is the acceleration due to gravity, and $d$ is the height from which the cannonball is dropped.",
        "gt_answers": "1 0 \\times 2 = 2 0 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_1070.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format. Here is the LaTeX code for the expression:\n\n\\begin{equation}\ny = \\frac{100}{25}x + 5\n\\end{equation}\n\nThis is a linear equation in slope-intercept form, where the slope is $\\frac{100}{25}$ and the y-intercept is 5. The equation represents a line that passes through the point (0, 5) and has a slope of $\\frac{100}{25}$.",
        "gt_answers": "m c = 1 2 \\times 0 . 1 = 1 . 2 g\n",
        "image_path": "./data/HME100K/test_images/test_1071.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Im}(\\text{z}) = \\sqrt{2} \\cdot \\text{Im}(\\text{x} + \\text{y})$$\n\nNote that the imaginary unit, denoted by the letter \"i\", is used to represent the square root of -1. The formula is simply the product of the magnitude of the complex number z and the complex number x + y, where x and y are real numbers.",
        "gt_answers": "\\frac { x } { x + 1 } = - 2\n",
        "image_path": "./data/HME100K/test_images/test_1072.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\nwhere $\\omega$ is the angular frequency, $\\alpha$ is the angular amplitude, and $C$ is the capacitance of the capacitor. The formula is written in terms of the capacitance and the angular frequency of the signal.",
        "gt_answers": "\\angle E C D = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1073.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\text{Image Content}$$This is a mathematical expression that can be used to represent the image. The image is a mathematical expression that can be used to represent the image.",
        "gt_answers": "\\frac { 1 } { 2 } x ^ { 2 } + x y + \\frac { 1 } { 2 } y ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1074.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\begin{equation}\n     f(x) = \\frac{4}{x^2 + 4x + 4}\n\\end{equation}\n```",
        "gt_answers": "( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } ) ( 1 + 4 + 9 ) \\geqslant ( x + 2 y + 3 z ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1075.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$$\\text{d}t = \\frac{dx}{v}$$\n\nwhere $t$ is time, $x$ is the position of the car, $v$ is the velocity of the car, and $d$ is the time derivative operator. This formula represents the time rate of change of position with respect to time, which is also known as the velocity of the car.",
        "gt_answers": "D C D \\bot A D , D A \\bot A B\n",
        "image_path": "./data/HME100K/test_images/test_1076.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is fx(\u03b1+3x)=0.",
        "gt_answers": "f ( x ) = \\vert x - a \\vert + 3 x\n",
        "image_path": "./data/HME100K/test_images/test_1077.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 6x2 + 8x - 12.",
        "gt_answers": "\\frac { 5 } { 6 } \\textcircled { < } \\frac { 5 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1078.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written as follows using LaTeX format:\n\n$$\\ce{Fe + O2 -> Fe2O3}$$\n\nThis formula represents the reaction of iron with oxygen to form ferric oxide.",
        "gt_answers": "Z n + H _ { 2 } S O _ { 4 } = H _ { 2 } \\uparrow + Z n S O _ { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1079.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:\n\n$$\\frac{1}{2}(x - 3) + 1 = \\frac{1}{2}(2 - 3) + 1 = \\frac{1}{2}(1) + 1 = \\frac{1}{2}(1) + 1 = \\frac{1}{2}(1) + 1 = \\frac{1}{2} + 1 = 1$$",
        "gt_answers": "n = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1080.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not provided. Please provide the image for me to write out the expression.",
        "gt_answers": "V _ { a b } = V = \\frac { 2 m g \\cdot R } { 3 B ^ { 2 } l ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_1081.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by: \n\n$$ 3x^2 + 2x + 1 = 0 $$\n\nwhich can be solved using the quadratic formula:\n\n$$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} $$\n\nSubstituting the values of a, b, and c from the given image, we get:\n\n$$ x = \\frac{-(-2) \\pm \\sqrt{(2)^2 - 4(1)(3)}}{2(1)} $$\n$$ x = \\frac{2 \\",
        "gt_answers": ". x = 6 + 4 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1082.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 2m + 3m = 5m.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression written in LaTeX format. The expression is:\n\n$$\\frac{a+b}{c+d}=\\frac{ad+bc}{bd+cd}$$\n\nThis expression is known as the distributive property of multiplication over addition. It states that the product of two numbers is equal to the sum of their products.",
        "gt_answers": ". x ^ { 2 } + \\sqrt { 3 } t x + t ^ { 2 } - 1 = 0 .\n",
        "image_path": "./data/HME100K/test_images/test_1084.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given as:\n\n$a + b = c$\n\nWhere a, b, and c are variables that can take any value. The formula expresses the equality of a sum of two numbers, a and b, with a third number, c.",
        "gt_answers": "\\sin A = \\frac { a } { 2 R }\n",
        "image_path": "./data/HME100K/test_images/test_1086.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{2x}{x^2+2x+1}$. To write it out in LaTeX format, you would use the following code: $\\frac{2x}{x^2+2x+1}$.\n\nHere's how the image would be written out in LaTeX format:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=0.7]\n\\draw[->] (-2,0) -- (2,0) node[right] {$ x $};\n\\draw[->] (0,-1) -- (0",
        "gt_answers": "k ^ { 2 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1087.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression of the formula in the image:$$\\frac{200}{x^2 + 400}$$Note that the fraction has a numerator of 200 and a denominator of $x^2 + 400$.",
        "gt_answers": "x = \\frac { 2 2 0 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1089.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:\n\nA = l \\* w\n\nwhere l is the length and w is the width of the rectangle.\n\nTo calculate the area of the rectangle in the image, we can use the formula above with the given measurements:\n\nA = 4 \\* 2\n\nA = 8 square units\n\nTherefore, the area of the rectangle in the image is 8 square units.",
        "gt_answers": "1 4 4 \\div 2 = 7 2 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_1090.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format. Here's the formula:\n\n$$\\frac{3x+5}{x+2}=\\frac{3x+5}{x+2}$$\n\nThis formula is a ratio expression, where the numerator is 3x+5 and the denominator is x+2. When we simplify the expression using the distributive property of multiplication, we get:\n\n$$\\frac{3x+5}{x+2}=\\frac{3\\times(x+2)+5}{x+2}=\\frac{3",
        "gt_answers": "\\overrightarrow { P A } = ( - 6 - x _ { 1 } - \\sqrt { 2 0 ( 1 - \\frac { x ^ { 2 } } { 3 6 } ) }\n",
        "image_path": "./data/HME100K/test_images/test_1091.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is $\\text{A} = \\frac{1}{2}\\pi r^2$, where $r$ is the radius of the circle. The formula for the volume of a sphere is $\\text{V} = \\frac{4}{3}\\pi r^3$, where $r$ is the radius of the sphere. The formula for the volume of a cone is $\\text{V} = \\frac{1}{3}\\pi r^2h$, where $r$ is the radius of the cone and $h$ is the height of the cone. The formula for",
        "gt_answers": "a c = b c\n",
        "image_path": "./data/HME100K/test_images/test_1092.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is 1/(2x + 3y).",
        "gt_answers": "6 = \\frac { 8 } { 2 } h\n",
        "image_path": "./data/HME100K/test_images/test_1093.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the derivative of f(x) = 3x^2 + 2x - 5.\n\n$$ dy/dx = \\frac{d}{dx}(3x^2 + 2x - 5) = 6x + 2 $$",
        "gt_answers": "d _ { n } = \\frac { a _ { n } } { n ( n + 1 ) }\n",
        "image_path": "./data/HME100K/test_images/test_1094.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{b}{a+c} \\cdot \\sqrt{\\frac{a^2+bc}{a^2+ac}}$$Note that the formula is written in LaTex format, which is a mathematical notation language used for mathematical and scientific writing. The formula is written as a fraction, with the numerator being b and the denominator being a+c. The formula also involves the square root of a fraction, with the numerator being a^2+bc and the denominator being a^2+ac.\n\nThe LaTex format",
        "gt_answers": "\\Delta A B E \\cong \\Delta D B E\n",
        "image_path": "./data/HME100K/test_images/test_1095.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the image you provided:\n\n$$x=\\frac{3y+5z-2}{2y+4z-3}$$\n\nThe equation represents a linear equation in three variables, where x is the dependent variable, y and z are the independent variables, and the constant terms are -2, -3, and -5. The fraction form of the equation makes it easier to solve and manipulate.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by:",
        "gt_answers": "1 \\div 1 0 0 = 0 . 0 1 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_1097.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:x^2 + 2x + 1 = 0\\begin{aligned} x^2 + 2x + 1 &= 0\\end{aligned}x^2 + 2x + 1 = 0x^2 + 2x + 1 = 0The solution to the equation is given by:x = - 1 or x = 3\\begin{aligned} x &= -1 \\\\ x &= 3\\end{aligned}x = -1 or x = 3Therefore, the solutions to the equation are x",
        "gt_answers": "2 m - 3 + 5 - m = 0\n",
        "image_path": "./data/HME100K/test_images/test_1098.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\na &= \\frac{b}{c} \\\n&= \\frac{b}{2c} + \\frac{b}{2c} \\\n&= \\frac{1}{2} + \\frac{1}{2} \\\n&= \\frac{1}{2} + \\frac{1}{2} \\\n&= 1 \\\n&= 1 \\\n&= 1 \\\n&= 1 \\\n&= 1 \\\n&= 1 \\\n&= 1 \\\n&=",
        "gt_answers": "( 1 2 - 4 y ) ( 1 2 - 3 y ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_1099.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{equation}\nx = \\frac{4y}{3} + \\frac{2y}{3}\n\\end{equation}\n\nwhere x and y are variables.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\node[draw,circle,minimum size=2cm] (a) at (0,0) {$x$};\n\\node[draw,circle,minimum size=1cm] (b) at (2,0) {$y$};\n\\node[draw,circle,minimum size=1cm] (c) at (2,2) {$z$};\n\\draw[->,line width=1pt] (a)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The equation in the image is the slope of the tangent line to the curve at the given point. To write it in LaTeX format, we can use the following equation:\n\n$$\\frac{dy}{dx} = \\frac{5x^2 - 7x - 3}{2x^3 + 3x^2 - 5x + 2}$$\n\nThis equation represents the slope of the tangent line at the point where x = -3 and y = 5x^2 - 7x - 3. To find the slope",
        "gt_answers": "a + 1 5 - 1 5 = 2 5 - 1 5\n",
        "image_path": "./data/HME100K/test_images/test_1103.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is:\n\nA = \u03c0r^2,\n\nwhere A is the area of the circle, r is the radius of the circle, and \u03c0 is the mathematical constant that is approximately equal to 3.14159. To calculate the area of the circle in the image, we can use this formula with the given values:\n\nA = \u03c0(11.5^2)\n= \u03c0(128.25)\n\u2248 3.14159 \u00d7 128.25\n\u2248",
        "gt_answers": "A H \\bot B C\n",
        "image_path": "./data/HME100K/test_images/test_1104.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \\frac{5}{3} + 2 \\* \\frac{5}{6} - \\frac{3}{2}.",
        "gt_answers": "3 1 0 \\div 5 0 = 6 \\cdots 1 0\n",
        "image_path": "./data/HME100K/test_images/test_1105.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: $\\frac{a}{b}$.",
        "gt_answers": "\\therefore \\widehat { B D } = \\overline { C D }\n",
        "image_path": "./data/HME100K/test_images/test_1107.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{R}= \\frac{3\\sqrt{m^2 + 12b^2}}{m + \\frac{2b}{c}}$$\n\nWhere,\n\nm = 30\nb = 20\nc = 5",
        "gt_answers": "\\frac { 3 - 4 m } { 4 } \\leq 0\n",
        "image_path": "./data/HME100K/test_images/test_1108.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format of the expression in the image:\n\n\\begin{align\\*}\n\\frac{\\text{d} x}{\\text{d} t} = \\frac{v^2}{2} - \\frac{g}{m} x\n\\end{align\\*}\n\nThe image shows a graph with two curves, one representing the velocity of an object as a function of time, and the other representing the position of the object as a function of time. The equation shows the derivative of the position of the object with respect to time, which is equal to the velocity of the object squared",
        "gt_answers": "h _ { 1 } = t _ { 1 } \\cdot V = 5 S . 0 . 3 m / s = 1 . 5 m\n",
        "image_path": "./data/HME100K/test_images/test_1109.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\begin{equation}\n    \\frac{m1 + m2}{m1 + m2} = \\frac{m1 + m2}{m1 + m2}\n\\end{equation}\n```\nThis is a mathematical equation that states that the ratio of two quantities is equal to the ratio of those same quantities. It is a tautology, as the left-hand side and right-hand side are identical.",
        "gt_answers": "x ^ { 2 } - 5 x + 6 = 0\n",
        "image_path": "./data/HME100K/test_images/test_1111.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:$$x = \\frac{3y}{4}$$where x is the number of people and y is the number of days.",
        "gt_answers": "[ ( 5 6 + 4 4 ) \\div 2 ] \\times ( 5 6 - 4 4 ) = 6 0 0\n",
        "image_path": "./data/HME100K/test_images/test_1112.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ c\\_100 = \\frac{2}{5}\\cdot \\frac{1}{2} + \\frac{2}{5}\\cdot \\frac{2}{5} + \\frac{1}{2}\\cdot \\frac{3}{4} = \\frac{11}{20} $$",
        "gt_answers": "\\overrightarrow { C B } = 1 1 , 0 0\n",
        "image_path": "./data/HME100K/test_images/test_1113.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we need to follow the rules for mathematical expressions in LaTeX. Here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$2x^2 + 2x - 6 = 0$\n\\end{center}\n\nThis equation represents the parabola shown in the image, with the vertex at the origin and the axis of symmetry passing through the point (2, 2). The equation can be derived by completing the square for the left-hand side of the equation, as follows:",
        "gt_answers": "( \\sqrt { 5 } + 1 ) x \\cdot 2 x \\times \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1114.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n&#x2208;x+&#x2202;x&#x2202;y+&#x2202;x&#x2202;z=0\" role=\"presentation\">ax+ay+az=0ax+ay+az=0\\frac{a}{x}+\\frac{b}{y}+\\frac{c}{z}=0ax+ay+az=0\\frac{a}{x}+\\frac{b}{y}+\\frac{c}{z}=0\\frac{a}{x",
        "gt_answers": "( \\frac { 3 } { 2 } a + b ) ^ { 2 } _ { ; } \\geq 0\n",
        "image_path": "./data/HME100K/test_images/test_1115.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n$$\\frac{4\\times 100-5\\times 90+6\\times 80-3\\times 70+1\\times 60+5\\times 50-4\\times 40+3\\times 30-2\\times 20+1\\times 10+3\\times 0}{4\\times 5+3\\times 10+6\\times 9+5\\times 8+4\\times 7+",
        "gt_answers": "4 - 4 ( 2 k - 4 ) > 0\n",
        "image_path": "./data/HME100K/test_images/test_1116.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tabular}{c}\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\hline\n\\",
        "gt_answers": "\\frac { 1 } { 2 } x - 1 = 1\n",
        "image_path": "./data/HME100K/test_images/test_1117.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is $\\frac{2b}{2c+2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the expression: A = l \u00d7 b, where l is the length and b is the width. In the given image, the width is 15 and the length is 10. Therefore, the area of the rectangle is 15 \u00d7 10 = 150 square units.",
        "gt_answers": "A E = 3 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1121.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not provided, so I cannot write out the expression of the formula. Please provide the formula in the image.",
        "gt_answers": "- \\frac { 1 } { 2 } x - 3 x = 6 - 8 + 3\n",
        "image_path": "./data/HME100K/test_images/test_1122.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{1}{3}x^2 - \\frac{4}{9}x - \\frac{1}{3}$.",
        "gt_answers": "y = \\frac { 7 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1123.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ $\\frac{3x+5y}{4z+6}=\\frac{3x+y}{4z+6}+\\frac{x}{2z+3}$$. This expression is a rational expression, which means it is a ratio of polynomials. The numerator is a polynomial of degree 2 in x and y, and the denominator is a polynomial of degree 2 in z. The coefficients of the polynomials are 3, 5, 4, and 6, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $5x^2 - 7x + 3$.",
        "gt_answers": "\\frac { 4 } { 6 } < \\frac { 5 } { 6 } < 1 < \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1126.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for this image can be expressed as: $ 4x^2 + 12x - 6$. This is a second degree polynomial equation with three terms. The constant term is -6, the linear term is 12x, and the quadratic term is 4x^2. The solution set for this equation is all real numbers that make the equation true.\n\nIn LaTeX format, the formula would be written as:\n\n$$ 4x^2 + 12x - 6 $$",
        "gt_answers": "\\frac { x - 4 } { 3 } - 8 = - \\frac { x + 2 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1127.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\sqrt{3x^{2}+2x}$.\n\nHere is the image:\n\n![Img](https://i.imgur.com/8h5YiI7.png)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is $\\frac{x^2 - 3x - 2}{x - 1}$.",
        "gt_answers": "t = 0 . 5 s = 1 \\frac { 1 } { 4 } T\n",
        "image_path": "./data/HME100K/test_images/test_1129.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$3x^2+2x+1$$This is a quadratic equation in the form of a polynomial with three terms. The first term is $3x^2$, the second term is $2x$, and the third term is $1$. The coefficient of $x^2$ is 3, the coefficient of $x$ is 2, and the constant term is 1.",
        "gt_answers": "8 0 0 \\times 3 = 2 4 0 0 ( m )\n",
        "image_path": "./data/HME100K/test_images/test_1130.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\na &= 3x + 2y \\\nb &= 2x + 4y \\\nc &= 5x - 3y \\\nd &= 7x + 5y \\\n\\end{align\\*}\nwhere x and y are variables.",
        "gt_answers": "\\tan \\frac { \\theta } { 2 } = \\frac { \\sqrt { \\xi } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1131.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle with base 4 and height 6 is:\n\nA = (1/2)bh = (1/2) \\* 4 \\* 6 = 6\n\nTherefore, the area of the triangle is 6 square units.",
        "gt_answers": "B E = \\frac { 1 } { 2 } C E\n",
        "image_path": "./data/HME100K/test_images/test_1132.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression:\n\n\\begin{align}\n\\text{The number of moles of $\\ce{H2O}$ produced when 2.0 moles of $\\ce{CO2}$ are produced in a chemical reaction is}\\\n\\begin{aligned}\n\\text{2 moles.}\n\\end{aligned}\n\\end{align}\n\nNote: This is assuming that there is a 1:1 mole ratio between the reactants and products in the chemical reaction.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$\\text{a}+\\text{b}=\\text{b}+\\text{c}$, where $\\text{a}$ is the number in the first row, $\\text{b}$ is the number in the second row, and $\\text{c}$ is the number in the third row.",
        "gt_answers": "x = \\frac { 5 } { 3 } + k\n",
        "image_path": "./data/HME100K/test_images/test_1135.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\begin{align\\*} 4x^2 - 4x + 1 &= 0 \\Rightarrow 4x^2 - 4x - 1 = 0 \\Rightarrow 4x(x - 1) = 0 \\Rightarrow x = 1 \\end{align\\*}$$\n\nThus, the solution to the equation is x = 1.",
        "gt_answers": "4 \\times 8 \\times 2 = 6 4 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_1136.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not written in LaTeX format. However, assuming that the equation is written as: 2(5 + 3) - 1, it would be represented in LaTeX as: $ 2(5 + 3) - 1$.\n\nNote: The image appears to be a handwritten note with no equation or mathematical expression visible.",
        "gt_answers": "\\tan 6 3 . 4 ^ { \\circ } = \\frac { C E } { B E }\n",
        "image_path": "./data/HME100K/test_images/test_1137.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2 + 2 = 4.\n\nThe formula in the image is a simple arithmetic expression that adds the numbers 2 and 2 together to get 4. The equals sign (=) is used to indicate that the two expressions on either side of it are equal to each other. In this case, the left side of the equals sign is the sum of 2 and 2, and the right side is also 4, so the expression is true.",
        "gt_answers": "\\vert \\overrightarrow { a } + \\overrightarrow { b } \\vert = \\sqrt { 1 3 } .\n",
        "image_path": "./data/HME100K/test_images/test_1138.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{b} + \\text{n} = \\text{a} \\times \\text{c} $$\n\nwhere $\\text{b}$, $\\text{n}$, $\\text{a}$, and $\\text{c}$ are variables.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick] (0,0) -- (1,0) -- (1,1) -- (0,1) -- (0,0);\n\\filldraw (0.5,0.5) circle (2pt);\n\\node at (0.5,0.5) {ImageContent};\n\\end{tikzpicture}\n\\end{center}\n\nThis will produce the following image:\n\n![ImageContent](https://i.imgur.com",
        "gt_answers": "\\angle C P Q = \\angle B = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1140.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 3x + 2y = 6x - 4y.\n\nThe expression can be derived by solving the equation for y in terms of x: 2y = 6x - 3x, which simplifies to 2y = 3x. Substituting this expression back into the original equation, we get 3x + 2(3x) = 6x - 4(3x), which simplifies to 3x + 6x - 6x = 6x - 4",
        "gt_answers": "x _ { 4 } = - \\sqrt { 6 0 } - 2\n",
        "image_path": "./data/HME100K/test_images/test_1142.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula in the image using LaTeX format, we need to write the equation in the form of a mathematical expression.\n\nWe can use the following LaTeX code to express the formula in the image:\n\nThe formula in the image represents a mathematical expression for the volume of a sphere.\n\nUsing the formula, we can find the volume of a sphere with a radius of 3cm.\n\nTo find the volume of a sphere, we need to multiply the radius by itself and then multiply the result by 4/3.\n\nSo, the volume of the sphere is:\n\nV = (4",
        "gt_answers": "( m - n ) ^ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1144.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is: $\\frac{x}{2}+\\frac{y}{3}+\\frac{z}{4}=25$",
        "gt_answers": "\\angle A B C = \\angle A = 4 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1145.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX expression for the given formula:\n\n$$\\frac{x^2+y^2}{2}$$\n\nThis expression is simply the arithmetic mean of the squares of $x$ and $y$.",
        "gt_answers": "x = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1146.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is: $ x^2 - 3x + 2 $.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\nb = \u03b8tqbxxt\u22121b\u22121qbx\u22121t\u22121b\u22121tqb\u22121x\u22121t\u22121b\u22121x\u22121t\u22121b\u22121qb\u22121x\u22121t\u22121b\u22121tqbx\u22121t\u22121b\u22121qbx\u22121t\u22121b\u22121tqb\u22121x\u22121t\u22121b\u22121tqb\u22121x\u22121t\u22121b\u22121tqbx\u22121t",
        "gt_answers": "B = B _ { 0 } + k x\n",
        "image_path": "./data/HME100K/test_images/test_1148.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{align\\*}\ny &= 3x + 4 \\\n\\end{align\\*}",
        "gt_answers": "b = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1150.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the line given in the image is given by the equation:y = x + 1. The equation can be derived by finding the slope of the line and substituting it into the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept. The slope of the line in the image is m = 1, and the y-intercept is b = 1. Therefore, the equation of the line is y = x + 1.",
        "gt_answers": "y _ { 2 } = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1151.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n$$\\text{Length of the rectangle } = \\frac{12 \\times 8}{3} = 48$$\n\n$$\\text{Width of the rectangle } = 12$$\n\nThe area of the rectangle is:\n\n$$\\text{Area of the rectangle } = \\text{Length of the rectangle } \\times \\text{Width of the rectangle } = 48 \\times 12 = 576$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX code for the expression:\n\n$$ 3x - 5 = 2 $$\n\nThis equation represents the equation given in the image. The variable $x$ is on the left side of the equation, and the constant value 2 is on the right side. The operator $-$ is used to indicate the negative sign, and the operator $=$ is used to indicate equality.",
        "gt_answers": "\\frac { 1 } { 2 } x = 1 0 . 5\n",
        "image_path": "./data/HME100K/test_images/test_1153.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n$$ f\\_{x^2+y^2=1} = \\sqrt{\\frac{1}{2}} $$\n\nThis formula finds the minimum value of the function $f(x,y) = x^2 + y^2$ subject to the constraint $x^2 + y^2 = 1$. The solution to this problem is the minimum value of the function, which is $\\sqrt{\\frac{1}{2}}$.",
        "gt_answers": "F _ { 1 } L _ { 1 } = F _ { 2 } L 2\n",
        "image_path": "./data/HME100K/test_images/test_1154.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \n\n\u222b \u222b \u222b ( x 2 + 3 x + 1) dx = \u222b \u222b ( x 3 + 2 x 2 + x) dx + C1\u222b \u222b \u222b ( x + 1) dx = C2\u222b \u222b \u222b ( x 2 + 3 x + 1) dx + C1\u222b \u222b \u222b ( x 3 + 2 x 2 + x) dx + C2\u222b \u222b \u222b ( x + 1) dx + C",
        "gt_answers": "c d = 1 , m ^ { 2 } = 4\n",
        "image_path": "./data/HME100K/test_images/test_1156.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX expression for the given formula in the image:\n\n$$\\frac{\\text{bkg}}{\\text{dv}} = \\frac{\\text{bkg}}{\\text{dv}} \\cdot \\frac{\\text{bkg}}{\\text{dv}} \\cdot \\frac{\\text{bkg}}{\\text{dv}}$$\n\nIn LaTeX format, this would be written as:\n\n$$\\frac{\\text{bkg}}{\\text{dv}} = \\frac{\\text{bkg}}{\\text{dv}} \\cdot",
        "gt_answers": "6 0 k g \\times \\frac { 1 } { 6 } = 1 0 k g\n",
        "image_path": "./data/HME100K/test_images/test_1157.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the expression:\n\n\\begin{align\\*}\nx = \\frac{3}{5} \\\\\ny = \\frac{8}{15}\n\\end{align\\*}",
        "gt_answers": "3 . 1 4 \\times 2 \\times 1 . 8 \\div 3 \\times 1 . 8 = 1 3 . 5 6 4 8\n",
        "image_path": "./data/HME100K/test_images/test_1158.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the expression of the formula in the image using LaTeX format:\n\n$$\\text{sin}\\left(\\frac{\\text{tan}\\left(\\frac{\\text{x}}{\\text{6}\\right)}{3}\\right)}{\\text{cos}\\left(\\frac{\\text{x}}{\\text{2}\\right)}\\right)$$\nThis formula is used to calculate the slope of the tangent line at a point on a curve, where the point is at an angle of $60^\\circ$ from the x-axis, and the curve is defined by the equation $y=3x^2+2",
        "gt_answers": "6 > \\square\n",
        "image_path": "./data/HME100K/test_images/test_1159.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$5 - 3x - 4y = -1$$",
        "gt_answers": "x = \\frac { 2 4 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_1160.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle with sides of 3 and 4 is $\\frac{3 \\times 4}{2}=\\frac{3}{2}=\\frac{3}{2}=\\frac{3}{4}=\\frac{1}{2}=\\frac{1}{4}=\\frac{1}{3}=\\frac{1}{6}=\\frac{1}{8}=\\frac{1}{12}=\\frac{1}{24}=\\frac{1}{48}=\\frac{1}{96}=\\frac{1}{192}=\\frac{1}{384}=\\frac{1}{768}=\\",
        "gt_answers": "x ^ { 2 } - a x - 3 x + 3 = x ^ { 2 } - x\n",
        "image_path": "./data/HME100K/test_images/test_1163.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a quadratic equation in two variables x and y. The image shows an equation in the form of a parabola with a vertical axis of symmetry at the origin and a horizontal axis of symmetry at x = 2. The equation can be written in LaTeX format as follows:$$ax^2+bx+c=0$$where a, b, and c are constants. The constants can be determined by plugging in the given values for a, b, and c into the equation. For example, if a = 1, b = 3, and c = 4, the",
        "gt_answers": "\\angle A O C = 3 6 0 ^ { \\circ } - \\angle A O B - \\angle B O C\n",
        "image_path": "./data/HME100K/test_images/test_1165.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula using LaTeX format is:\n\n$$\\text{Image content}$$",
        "gt_answers": "\\frac { 1 } { 2 } x = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_1166.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression for the formula in the image using LaTeX format:\n\n$$\\begin{align\\*} 2x + 3y &= 10 \\\n\\begin{cases} x &= \\frac{10 - 3y}{2} \\\ny &= \\frac{2x + 10}{3} \\\n\\end{cases} \\\n\\begin{align\\*} 2x + 3y &= 10 \\\n\\begin{cases} x &= \\frac{10 - 3y}{2} \\\ny &= \\frac{2",
        "gt_answers": "y - \\frac { 2 } { y } - 1 = 0\n",
        "image_path": "./data/HME100K/test_images/test_1168.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression of the formula in the image:\n\n$$\\frac{a}{b}+\\frac{b}{c}+\\frac{c}{d}+\\frac{d}{e}+\\frac{e}{f}+\\frac{f}{g}$$",
        "gt_answers": "x _ { 1 } = a , x _ { 2 } = \\frac { a + 1 } { a - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_1169.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is $\\frac{1}{3} \\cdot 8 + \\frac{2}{3} \\cdot 6 = \\frac{1}{3} \\cdot 8 + \\frac{1}{3} \\cdot 6 = \\frac{22}{3}$",
        "gt_answers": "1 5 ) k = - 8\n",
        "image_path": "./data/HME100K/test_images/test_1170.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is d^3 - 5d^2 + 8d + 5. To write it in LaTeX format, use the following code:\n\n$$d^3 - 5d^2 + 8d + 5$$\n\nThe formula can be read as the third power of d minus five times the square of d plus eight times d plus five.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by: $\\text{f(x)} = \\text{x} \\sin\\left(\\frac{x^2}{2}\\right)$",
        "gt_answers": "P \\cdot 1 \\frac { 1 } { 2 } ( - 2 )\n",
        "image_path": "./data/HME100K/test_images/test_1172.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length l and width w is A = lw. In LaTeX format, this formula can be written as $\\text{A = } \\text{lw}$.\n\nHere is the LaTeX code for the formula:\n\n$$\\text{A = } \\text{lw}$$\n\nIn the image provided, the length of the rectangle is 4 and the width is 2. Therefore, the area of the rectangle is 4 x 2 = 8.\n\nHere is the LaTeX code for the calculation:\n\n$$\\text{A = }",
        "gt_answers": "\\frac { 4 } { 3 } x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1173.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n\\begin{align}\nx &= 4 \\\\\ny &= 10 \\\\\nz &= 2 \\\\\nA &= xy + z \\\n\\end{align}\n\nNote: In LaTeX, the `align` environment is used to align equations and expressions on the left margin. The `=` sign is used to separate the variables in the equation. The `\\` character is used to indicate the end of the line.",
        "gt_answers": "a _ { 0 } - a _ { 1 } + a _ { 2 } \\cdots - a _ { 9 } = 5 9\n",
        "image_path": "./data/HME100K/test_images/test_1174.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{100}{20 + 50}$.",
        "gt_answers": "x ^ { 2 } + 2 x - 6 = 0\n",
        "image_path": "./data/HME100K/test_images/test_1175.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{FOIL} \\left( \\frac{2x^2 + 4x - 5}{x - 1} \\right) = \\frac{2x^3 + 6x^2 + 4x - 5}{x - 1}$$",
        "gt_answers": "S _ { \\Delta A O F } = \\frac { 3 } { 2 } S _ { \\Delta B O F } = \\frac { 9 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1176.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent} = \\frac{1}{2} \\left(\\text{Red Ball} + \\text{Blue Ball}\\right)$$\n\nIn this formula, the variable $\\text{ImageContent}$ is defined as the average of the values of the variables $\\text{Red Ball}$ and $\\text{Blue Ball}$.",
        "gt_answers": "\\frac { I _ { 1 } } { I _ { 2 } } = \\frac { R _ { 2 } } { R _ { 1 } }\n",
        "image_path": "./data/HME100K/test_images/test_1177.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression:\n\n\\begin{align\\*}\n4x^2 + 4x - 8 &= 0 \\\n\\end{align\\*}",
        "gt_answers": "\\boxed { 1 1 } + 6 < \\frac { 9 + 9 } { 1 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1178.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be: $\\frac{1}{2} - \\frac{2}{5}$\n\nThis expression represents the difference between the sum of two fractions and the sum of two other fractions. To simplify this expression, we can combine the common denominators: $\\frac{1}{2}$ and $\\frac{5}{5}$ to get $\\frac{1}{2}$. We can then subtract $\\frac{2}{5}$ from $\\frac{1}{2}$ to get the result of $\\frac{1}{2} - \\frac{2}{5}$",
        "gt_answers": "a = \\frac { 2 } { 3 } \\cdot b = - \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1179.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$b = \\frac{c^2}{a^2 + b^2}$",
        "gt_answers": "\\angle B C D = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1180.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula is:\n\n\u222b[\u222b[x + y]dx + \u222b[2xy]dy]\n\nwhere the integral sign [\u222b] represents the definite integral.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format.\n\nHere is the LaTeX code for the given expression:\n\n\\begin{center}\n\\frac{\\frac{d^2x}{dt^2}}{\\frac{dx}{dt}}=\\frac{k\\_1^2-k\\_2^2}{k\\_1^2+k\\_2^2}\\\n\\end{center}\nThis formula represents the damping ratio of a second-order system with transfer function G(s) = k1/(1+k2s). The numerator of the",
        "gt_answers": "\\frac { b } { 3 a } + \\frac { a } { 2 b }\n",
        "image_path": "./data/HME100K/test_images/test_1182.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{3}{2}(x^2+y^2) - \\frac{1}{4}(x-y)^2$",
        "gt_answers": "2 \\sqrt { 4 2 } > 2 \\sqrt { 4 0 }\n",
        "image_path": "./data/HME100K/test_images/test_1184.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x^2 - 3x + 5.\n\nHere is the LaTeX code for the expression:\n```latex\n\\left(x^2 - 3x + 5\\right)\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the formula in the image:\n\n\\begin{align} x^2 + 4x + 4 &= 0 \\Rightarrow x = 2 \\ or \\ x = -2 \\end{align}\n\nNote that this is just one possible way to write out the formula using LaTeX.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format. Here is the expression:\n\n$$\\text{x} = \\frac{\\text{a}\\cdot\\text{b}\\cdot\\text{c}}{\\text{a}^{2}+\\text{b}^{2}+\\text{c}^{2}}$$\n\nIn this formula, $\\text{a}$, $\\text{b}$, and $\\text{c}$ are the lengths of the sides of the triangle. The formula calculates the x-coordinate of the center of gravity of the triangle.\n\nNote that the formula assumes that the",
        "gt_answers": "x _ { 1 } = 1 3\n",
        "image_path": "./data/HME100K/test_images/test_1188.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a power series expansion of the exponential function x^y with the constant term x = 2 and the variable x = y - 3.\n\nThe coefficient a is 1 and the exponent b is 2. The constant term x = 2 is added to the power series expansion to obtain the general formula for the function f(x) = ax^y + bx^y.\n\nThe constant term b represents the y-intercept of the parabola, which is the point at which the curve intersects the y-axis. The variable x is raised to the power of y in",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is x^2 - 4x + 5.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is d b c d c b d c d c.",
        "gt_answers": "B D ^ { 2 } = B C ^ { 2 } + D C ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1191.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by A = l \\* w, where l is the length and w is the width. The area of a rectangle is the amount of space inside it. To find the area of the rectangle in the image, we need to measure the length and width of the rectangle. The length is 4 cm and the width is 3 cm. The area of the rectangle is therefore 4 cm \\* 3 cm = 12 cm^2.\n\nAnother way to express this formula is to use LaTeX format:\n\nThe area of a rectangle is given by $",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is the product of two numbers, 2 and 4.\n\n\\begin{align\\*}\na \\times b &= 2 \\times 4 \\\n&= 8 \\\n&= 8 \\\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ucf54\ufffd",
        "gt_answers": "0 H = \\frac { 1 } { 2 } O C .\n",
        "image_path": "./data/HME100K/test_images/test_1194.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n$ (x+y)^2 = x^2 + 2xy + y^2 $\n\nThis formula can be derived by expanding the expression $(x+y)^2$ using the distributive property of addition over multiplication.",
        "gt_answers": "a = 4 c = 6\n",
        "image_path": "./data/HME100K/test_images/test_1195.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that.\n\nThe expression for the formula in the image using LaTeX format is:\n\n\\frac{3600}{\\frac{3000}{200}}\n\nThis formula can be used to find the average of 12 scores out of 300 scores.",
        "gt_answers": "a x + b y = 7 \\textcircled { 1 }\n",
        "image_path": "./data/HME100K/test_images/test_1196.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n\\begin{aligned}\na = \\frac{1}{2}x^2 + \\frac{1}{3}x^3\n\\end{aligned}\n\nThis expression is derived from the formula for the second derivative of a quadratic function, which is given by:\n\n\\begin{aligned}\na = \\frac{d^2y}{dx^2}\n\\end{aligned}\n\nWhen we substitute $y = x^2$ and $dy/dx = 2x$, we get:\n\n\\begin{aligned}",
        "gt_answers": "a c = 3 6 0\n",
        "image_path": "./data/HME100K/test_images/test_1197.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\text{p}= \\frac{mg}{v^2}$$where$m$ is the mass of the object being dropped, $g$ is the acceleration due to gravity, and $v$ is the initial velocity of the object. This formula is derived from the law of conservation of energy, which states that the total energy of a closed system remains constant.",
        "gt_answers": "3 . 1 4 \\times ( \\frac { 8 } { 2 } ) ^ { 2 } x - 1 2\n",
        "image_path": "./data/HME100K/test_images/test_1198.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$ \\text{c} = \\frac{\\text{d}}{\\text{b}+\\text{d}} $$\n\nwhere $c$ is the distance traveled, $d$ is the distance from the starting point to the current point, and $b$ is the distance from the starting point to the destination point.",
        "gt_answers": "C D = B D = A D = \\frac { 1 } { 2 } A B ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1200.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image using LaTeX format is:\n\n$ \\frac{x^{2}}{(x+1)(x-1)} $\n\nThis formula is derived by dividing the polynomial $x^{2}$ by the product of two polynomials, $x+1$ and $x-1$.",
        "gt_answers": "1 \\div 8 1 = \\frac { 1 } { 8 1 }\n",
        "image_path": "./data/HME100K/test_images/test_1201.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{m}{n}$.\n\nThe formula is a fraction with the numerator $m$ and denominator $n$. The variable $n$ is the denominator, which represents the number of people who have access to the database, and $m$ is the numerator, which represents the number of people who want to access the database.",
        "gt_answers": "y = \\pm 6\n",
        "image_path": "./data/HME100K/test_images/test_1202.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $ \\frac{r}{r^2 - 2r + 3} $\n\nHere is the LaTeX code for the expression:\n\n$$ \\frac{r}{r^2 - 2r + 3} $$\n\nTo display the image in LaTeX, you can use the following code:\n\n$$ \\begin{array}{c} \\begin{array}{cc} r & r^2 - 2r + 3 \\end{array} \\frac{}{} \\end{array} $$\n\nYou can then",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$ a + 2b + 3c = 7 $\n\\end{center}\n\nThis formula states that the sum of three variables (a, b, and c) is equal to 7.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation for the number of moles of a substance. The equation is written as: n = M \\* molar mass, where n is the number of moles, M is the mass of the substance, and molar mass is the molar mass of the substance. The equation can be used to determine the number of moles of a substance given its mass and molar mass.",
        "gt_answers": "C O = 6 0 - 2 0 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1205.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 3x2+5x+7=20. It is written in the LaTex format as $\\frac{3x}{2} + \\frac{5x}{1} + \\frac{7}{1}=20$.",
        "gt_answers": "\\frac { 2 3 } { 2 0 } > 1\n",
        "image_path": "./data/HME100K/test_images/test_1206.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center} $\\mathrm{d}x = \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot x^2 + \\frac{1}{3} \\cdot x^3$ \\end{center}\n\nNote: This is a simplified version of the formula and may not be accurate for all scenarios.",
        "gt_answers": "\\because \\angle C = \\angle C\n",
        "image_path": "./data/HME100K/test_images/test_1207.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I am unable to see the image provided. Can you please provide the image in a more visible format, such as a link to an image hosting site or an attachment?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$ \\frac{10}{11} + \\frac{11}{12} + \\frac{12}{13} + \\frac{13}{14} + \\frac{14}{15} + \\frac{15}{16} = \\frac{60}{66} $\n\nwhere each fraction represents the area of a rectangle with one side on the x-axis and the other side on the y-axis. The sum of the areas of all the rectangles is equal to the area of",
        "gt_answers": "\\angle A = 8 0 ^ { \\circ } \\angle C = 2 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1209.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula in the image is:\n\nf(x) = (x^2)/(x^2 + 1)\n\nwhich is the formula for the error function, also known as the mean squared error. This error function is used to measure the difference between the predicted and actual values of a function.",
        "gt_answers": "F = \\frac { w } { s }\n",
        "image_path": "./data/HME100K/test_images/test_1210.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is $\\frac{1}{2}x^2 + \\frac{1}{4}x - \\frac{3}{4}$.",
        "gt_answers": "\\frac { 2 \\pi } { w } = \\pi\n",
        "image_path": "./data/HME100K/test_images/test_1211.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows:\n\n\\begin{align\\*}\n\\frac{x^3+5x^2+3x+1}{x^3+4x^2+6x+2}\n\\end{align\\*}\n\nwhere x is the variable being solved for.",
        "gt_answers": "x _ { 8 } = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1213.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following steps:\n\n1. Choose the appropriate symbols for the variables in the formula, such as x, y, and z.\n2. Use the LaTeX syntax to write out the formula, including the multiplication symbol (x), addition symbol (+), and parentheses to group the terms.\n3. Use the correct syntax to display the formula in the desired size and style, such as using the \\large command to make the formula larger.\n4. Use the \\frac command to display the fractional values in the formula.",
        "gt_answers": "B G = B D = \\frac { 5 } { 2 } <\n",
        "image_path": "./data/HME100K/test_images/test_1215.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n$$ e^{a^2 + b^2} = \\left(\\frac{a^4 + b^4}{2}\\right) - \\left(\\frac{a^2b^2}{2}\\right) $$\n\nThis is a formula for the square root of the sum of the squares of two variables, a and b. The formula expresses the sum of the squares of the variables as a difference of squares, which is a common form of polynomials.",
        "gt_answers": "\\angle A E C = \\angle A C E = \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } - \\angle B A D )\n",
        "image_path": "./data/HME100K/test_images/test_1217.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Please provide a clear and legible image for me to work with.",
        "gt_answers": "\\frac { 1 } { C _ { 1 0 } ^ { 2 } } = \\frac { 1 } { 4 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1219.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{x^2}{x+2}$$",
        "gt_answers": "D ( - 5 , \\frac { 1 8 } { 2 5 } )\n",
        "image_path": "./data/HME100K/test_images/test_1220.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{3x^2+7x-5}{2x+1}=\\frac{3(2x^2+7x-5)+(2x+1)(x-5)}{2(2x+1)}$$\n\nExpanding the denominator:\n\n$$\\frac{3(2x^2+7x-5)+(2x+1)(x-5)}{2(2x+1)}=\\frac{3x^2+7x-5+2x(x-5",
        "gt_answers": "y = a ( x - x ) ( x + x )\n",
        "image_path": "./data/HME100K/test_images/test_1221.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: 4(x^2 - 3x + 1) = 0.",
        "gt_answers": "3 x + 2 x - 2 = 6\n",
        "image_path": "./data/HME100K/test_images/test_1222.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image can be expressed as follows:\n\n$latex$<img src=\"https://i.imgur.com/cF1b0Iu.png\" alt=\"Image of a circle and its inscribed square\"></img>\n\n$latex$This equation displays the image of a circle with its inscribed square, using the LaTeX math formatting system. The alt attribute provides a description of the image for screen readers and other assistive technologies.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{align}\nx^2 + 3x + 2 &= 3(2x + 1) \\\n\\end{align}\n\nThis equation is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 1$, $b = 3$, and $c = 2$.",
        "gt_answers": "\\frac { 1 3 } { 2 0 } x = 2 6\n",
        "image_path": "./data/HME100K/test_images/test_1225.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:\n\n\\begin{align\\*}\nx^2 + 3x - 4 &= 0 \\quad\\text{expanding the parentheses}\\n\nx^2 + 3x - 4 &= (x + 3)(x - 1) \\quad\\text{factoring}\\n\nx^2 + 3x - 4 &= x^2 - 3x + 4 \\quad\\text{simplifying}\\n\nx^2 + 3x - 4 &= (x - 2)^2 +",
        "gt_answers": "x = - 2 , y = 4 , x = 4 , y = - 5\n",
        "image_path": "./data/HME100K/test_images/test_1226.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n$$\\begin{aligned} \\text{ImageContent} \\end{aligned}$$",
        "gt_answers": "x = 5 \\sqrt { 4 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1228.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a width of 3.5 meters and a height of 2.2 meters is given by: A = l \\* w, where l is the length and w is the width. Using this formula, we can find the area of the rectangle in the image: A = 3.5 \\* 2.2 = 7.7 m^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 5cm is given by:A = \u03c0r^2, where r is the radius of the circle. Substituting r = 5cm, we haveA = \u03c0(5cm)^2 = 78.53 cm^2. Therefore, the area of the circle is 78.53 cm^2.",
        "gt_answers": "\\vert y - \\sqrt { x } \\vert = 0\n",
        "image_path": "./data/HME100K/test_images/test_1230.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n$x^2+y^2=r^2$\n\nwhere $x$ and $y$ are the coordinates of a point on the circle and $r$ is the radius of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $\\text{ImageContent}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the equation of the line given by the image, we can use the following steps:\n\n1. Determine the slope of the line:\nThe slope of the line is given by the ratio of the change in y to the change in x.\nTo find the slope, we can use the point-slope form of a line:\ny - y1 = m(x - x1)\nwhere m is the slope of the line and (x1, y1) is a point on the line.\nFrom the image, we can see that the line passes through the points (2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n$$y= \\frac{1}{2}x^2 + \\frac{3}{2}x + \\frac{1}{4}$$\n\nThe formula is a quadratic equation in the form of $y = ax^2 + bx + c$, where $a = \\frac{1}{2}$, $b = \\frac{3}{2}$, and $c = \\frac{1}{4}$.",
        "gt_answers": "x = \\frac { - 6 6 - 3 \\sqrt { 6 } } { 4 } = - \\sqrt { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_1238.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the equation in the image using LaTeX format is:$$\\frac{2x + 3y - 5}{x - 2y}$$",
        "gt_answers": "y = \\frac { 1 } { 5 } a\n",
        "image_path": "./data/HME100K/test_images/test_1239.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$ x + 3 = 7 $\n\\end{center}\n\nwhere $x$ is an arbitrary real number.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} = \\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} = \\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} = \\frac{1}{2} + \\frac{1}{4} + \\frac{",
        "gt_answers": "\\frac { 3 } { 4 } x = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1243.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given formula:\n\n\\begin{equation}\n\\frac{15\\left(10-\\frac{21}{2}\\right)}{3}\n\\end{equation}\n\nThis equation represents the ratio of the sum of 15 and the difference between 10 and 21/2, divided by 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "= \\frac { 3 } { 5 } = \\frac { B D } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_1246.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle with radius r is given by:\n\nA = \u03c0r^2\n\nwhere A is the area of the circle and r is its radius.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "1 + 3 = 4",
        "gt_answers": "x = 6 \\div \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1249.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX code for the expression in the image:\n\n\\begin{equation}\n\\text{y} = \\frac{1}{2}\\text{x}^2 + \\frac{1}{3}\\text{x} - \\frac{1}{4}\\text{x}^3\n\\end{equation}\n\nIn this equation, x represents the input variable and y represents the output variable. The coefficients in front of each power of x represent the constant terms in the equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as follows:\n\n$$e=\\sqrt{\\frac{1}{4}-\\frac{1}{2}\\sqrt{\\frac{1}{3}}-\\frac{1}{6}\\sqrt{\\frac{1}{5}}}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:$$ 2x + 3y = 7$$This can be represented in LaTeX format as:$$2x + 3y = 7$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given as follows:\n\n\u222b(a, b) f(x) dx = \u222b(a, b) f'(x) dx + C, where C is a constant.\n\nThe image shows the formula written out in LaTeX format:\n\n\u222ba^b f(x) dx = \u222ba^b f'(x) dx + C",
        "gt_answers": "( x + 7 ) .\n",
        "image_path": "./data/HME100K/test_images/test_1253.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 4x + 3 = 11 $$\n\nThis is a linear equation in one variable with a constant term of 3 and a linear term of 4x. The solution to this equation is x = 4, which is indicated by the red dot in the graph.",
        "gt_answers": "3 x - 2 = 9 + x + 3 - 6 \\sqrt { x + 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1254.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: 1 + 2 - 3 = 4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n<img src=\"https://i.imgur.com/2q3fHvX.png\" width=\"200\">Q=mgH</img>",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle can be written as:A=l\u00d7w\\text{A = l} \\times wA=l\u00d7wwhere l is the length of the rectangle and w is the width of the rectangle. The formula for the perimeter of a rectangle can be written as:P=2(l+w)\\text{P = 2(l+w)}P=2(l+w)where l is the length of the rectangle and w is the width of the rectangle.",
        "gt_answers": "x _ { 2 } = - \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1257.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n\\begin{aligned}\n\\frac{2048}{3592} - \\frac{1920}{3592} &= \\frac{112}{3592}\n\\end{aligned}\n\nwhere the numerator is the sum of the first three terms of the arithmetic sequence with first term 1 and common difference 2, and the denominator is the sum of the first four terms of the arithmetic sequence with first term 2 and common difference 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{center} $\\frac{a^2 + b^2}{a^2 - b^2} = 2 $\\end{center}\n\nThis expression represents the length of the hypotenuse of a right triangle with legs of length a and b. The value of 2 is the length of the hypotenuse.",
        "gt_answers": "\\frac { 3 } { 4 x - 3 } - 2 = - 1\n",
        "image_path": "./data/HME100K/test_images/test_1261.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\nm = g sin(\u03b8)cos(\u03b8) + 10cos\u00b2(\u03b8) - 5sin\u00b2(\u03b8)\n\nThis formula describes the motion of an object under the influence of gravity and centrifugal force. The variables in the equation are mass (m), acceleration due to gravity (g), angle of inclination (\u03b8), and centrifugal force (cos(\u03b8)). The equation can be used to calculate the acceleration of the object at any given angle of inclination.",
        "gt_answers": "m = \\frac { G } { g } = 1 0 ( k g )\n",
        "image_path": "./data/HME100K/test_images/test_1264.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x^4 + 3x^3 + 5x^2 + 5x + 4.",
        "gt_answers": "\\cdot y - 1 = k ( x - 4 )\n",
        "image_path": "./data/HME100K/test_images/test_1265.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written as follows using LaTeX format:\n\n$$\\frac{\\frac{1}{n}}{\\left(1-\\frac{1}{n}\\right)\\left(1-\\frac{1}{n+1}\\right)}$$",
        "gt_answers": "\\angle F O C = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1266.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}(x^2 + y^2) + \\frac{1}{2}(z^2 + w^2) + 10$.",
        "gt_answers": ". y = \\frac { k _ { 1 } } { x }\n",
        "image_path": "./data/HME100K/test_images/test_1267.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{\\text{100} + 200 - 300 + 400 - 500}{5}$$\n\nThis is a mathematical expression that calculates the average of the five numbers in the image. The expression uses the summation symbol $\\sum$ to represent the sum of each number, and divides the sum by 5 to obtain the average.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$$n=\\frac{100 \\* \\pi \\* r^2}{4}$$where $n$ is the number of people in the circle, $r$ is the radius of the circle, and $\u03c0$ is the mathematical constant pi, which is approximately equal to 3.14. This formula can be used to calculate the number of people in a circle based on its radius.",
        "gt_answers": "S _ { n } = n ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1269.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a diameter of x is given by:\n\nA = \u03c0r^2\\A = \\frac{\\pi}{r^2}A=\u03c0r2\u200bwhere r is the radius of the circle.\n\nThe diameter of a circle is the distance across the circle, passing through its center. It is equal to twice the radius. Therefore, we can write:\n\nd = 2r\\d = 2r\u00a0d=2r\u00a0where r is the radius of the circle.\n\nSince the area of a circle is proportional to the square of",
        "gt_answers": "B H = \\frac { 1 0 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1272.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula for a geometric series. The formula is written as follows:\n\n$x\\_n = \\frac{1}{2} - \\frac{1}{4} + \\frac{1}{8} - \\frac{1}{16} + \\frac{1}{32} - \\frac{1}{64} + \\frac{1}{128} - \\frac{1}{256} + \\frac{1}{512} - \\frac{1}{1024} + \\frac{1}{2048} - \\",
        "gt_answers": "1 2 \\times 4 \\times 5 = 2 4 0 c m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1273.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a function with the equation y = x^3 - x^2, where x is an independent variable and y is a dependent variable. The equation shows the relationship between x and y, with the slope of the tangent line being negative one.",
        "gt_answers": "( x + 2 y ) ( x - 2 y ) = 4 \\textcircled { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1274.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the equation of the line passing through the point (3, 4) and parallel to the x-axis, we can use the slope - intercept form of a line: y = mx + b. The slope of the line is - 1/3, and the y-intercept is 4. Substituting these values into the equation gives us:\n\ny = (-1/3)x + 4\n\nor, in slope-intercept form:\n\ny = mx + b\n\nwhere m = -1/3 and b = 4.\n\nThere",
        "gt_answers": "\\frac { 1 } { a } = \\frac { 3 - a . } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1275.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression in the image:\n\n\\begin{center}\n$ \\frac{a+b}{c+d} = \\frac{a}{c} + \\frac{b}{d}$\n\\end{center}\n\nThis is the formula for the addition-subtraction identity, which states that the sum of the fractions of two numbers is equal to the sum of the fractions of their sums. In other words, if we add the numerators and denominators of two fractions, the result will be the same as adding the numerators and denomin",
        "gt_answers": "A C = C D = 1 0 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1277.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize, but I cannot see the image you provided. Please provide a clear and legible image for me to perform the task.",
        "gt_answers": "\\frac { A F } { F B } = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1278.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the given expression:\n\n\\begin{center} $\\frac{7\\times10}{2\\times5}$ \\end{center}\n\nThis expression can also be written as:\n\n\\begin{center} $\\frac{7\\times 5}{2\\times 2}$ \\end{center}\n\nI hope this helps! Let me know if you have any other questions.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\text{sin}(\\frac{x}{2}) = \\frac{\\text{cos}\\left(\\frac{x}{2}\\right)}{2}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The image shows a formula for finding the sum of the first n positive integers. The formula is as follows: \u2211n=1n\\*i where n is the number of terms in the sum and i is the current term in the sum. The formula can be read as: starting with the first term in the sum, multiply each subsequent term by i and add up all the terms. This formula can be used to find the sum of any sequence of positive integers. Let me know if you have any further questions or if there's anything else I can help you with.",
        "gt_answers": "x = \\frac { 3 } { 2 } \\times \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1281.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\\begin{equation} \\text{CaCO} \\_{ 2} = \\frac{1}{2} \\times \\frac{40}{32} \\times \\frac{100}{96} \\times \\frac{16}{13} \\times \\frac{32}{25} \\times \\frac{48}{40} \\times \\frac{96}{80} \\times \\frac{32}{25} \\times \\frac{48}{40} \\times \\frac{100}{96} \\times \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is an equation in LaTeX format: $\\frac{a}{b}=\\frac{c^2}{d^2}$\n\nExplanation:\n\nThe above equation is a ratio of two fractions. It is saying that the ratio of the numerator of the first fraction to the denominator of the second fraction is equal to the ratio of the numerator of the second fraction to the denominator of the third fraction. In other words, it is a proportion.",
        "gt_answers": "x _ { 2 } = ^ { 4 } \\sqrt { 1 2 8 } - 1\n",
        "image_path": "./data/HME100K/test_images/test_1283.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$h^2 + 2x^2 + 2y^2 = k^2$$\n\nwhere h is the height of the prism, x and y are the lengths of its base and height respectively, and k is the volume of the prism.",
        "gt_answers": "x = \\frac { 5 a + 1 } { a }\n",
        "image_path": "./data/HME100K/test_images/test_1284.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is:$$y = x^2 + 3x - 5$$where $x$ is an integer variable and $y$ is the corresponding integer value.\n\nNote: This response is provided as a general guide and may not be applicable to all scenarios or equations.",
        "gt_answers": "x = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1285.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\text{100}\\times\\text{0.5} + \\text{50}\\times\\text{0.3} + \\text{30}\\times\\text{0.2} + \\text{20}\\times\\text{0.1} + \\text{10}\\times\\text{0.1} = 130$$\n\nwhere $\\text{100}\\times\\text{0.5}$, $\\text{50}\\times\\text{0.3",
        "gt_answers": "( 2 ) a _ { n } = 4 + ( - 1 ) ( n - 1 ) = 5 - n\n",
        "image_path": "./data/HME100K/test_images/test_1286.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n&#x2212;&#x2211;&#x2202;&#x2202;&#x2211;&#x2212;&#x2202;&#x2211;&#x2212;&#x2212;&#x2202;&#x2212;&#x2211;&#x2212;&#x2212;&#x2202;&#",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image:\n\n$$\\frac{a+b+c}{a+b}$$\n\nThis formula calculates the average of the three numbers a, b, and c. The denominator is the sum of the numerator and the subtraction of the smallest number from the sum. The numerator is the sum of the three numbers.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by the following LaTeX code:\n\n$$\\frac{a + b}{c}$$\n\nwhere $a, b, c$ are variables.",
        "gt_answers": "\\frac { A P } { A D } = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1290.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:$$\\frac{360}{560}=\\frac{6}{7}$$This equation can be simplified by canceling out the common factor of 2, which gives:$$\\frac{360}{560}=\\frac{12}{14}$$This simplifies to:$$\\frac{360}{560}=\\frac{2}{3}$$or$$\\frac{360}{560}=\\frac{1}{1.8}$$This means that the ratio of the circumference of the circle to its diameter is approximately 1 to",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following code:\n\n\\begin{align\\*}\nx + 5 &= 14 \\\nx - 5 &= 9 \\\nx &= 5\n\\end{align\\*}\n\nThe above code represents the equation in LaTeX format. The variable x is used to represent the unknown number in the equation, and the numbers 5 and 14 are used to represent the known values in the equation. The equal sign (=) is used to indicate that the two sides of the equation are equal.",
        "gt_answers": "x = \\frac { 1 7 } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1292.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{x^2+y^2}{2}$. This is a quadratic equation that can be solved using the quadratic formula: $\\frac{b\\pm\\sqrt{b^2-4ac}}{2a}$. To find the solution to the equation, you would plug in the values for a, b, and c from the formula and solve for x. The solution would be $\\frac{x}{2}$.",
        "gt_answers": "a ^ { 2 } - b ^ { 2 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_1293.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is:\n\n$$\\begin{aligned} \\text{Image Content} &= 7 + 4i - 3j \\ \\ \\ \\text{(mod 9)}\\\\ &= 7 + 4i - 3j + 9k \\ \\ \\ \\text{(mod 9)}\\\\ &= 16 + 9k \\ \\ \\ \\text{(mod 9)}\\\\ \\end{aligned}$$\n\nwhere $i$ and $j$ are the imaginary units, $k$ is a non-negative integer, and $\\mod$ denotes the modulus operator",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the expression for the formula in the image using LaTeX format:\n\n$$\\frac{1}{3} \\cdot \\frac{1}{4} \\cdot \\frac{1}{5} = \\frac{1}{15}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\ny = 3x + 5\n\\end{align\\*}\n\nThis equation represents a linear relationship between the variables x and y, where y is directly proportional to x with a slope of 3 and an intercept of 5.",
        "gt_answers": "\\frac { 1 } { x - y } = v\n",
        "image_path": "./data/HME100K/test_images/test_1296.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Could you please provide a different image or the text of the formula?",
        "gt_answers": "\\angle A E B = 4 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1297.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as follows in LaTeX format:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=0.7]\n\\draw[black,line width=2pt] (0,0) -- (3,0) node[below] {$x$};\n\\draw[black,line width=2pt] (0,0) -- (0,2) node[left] {$y$};\n\\filldraw (1,1) circle [radius=3pt];\n\\node[above] at (1,1) {$P$};\n\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n![ImageContent](https://cdn.imggl.com/misc/2018-12-26/cute-cat-sleeping-on-a-bed-8e507898457b.jpg)\n\nwhere:\n\n* I is the imaginary unit, denoted by the letter 'i'\n* C is the capacitance of the capacitor in the circuit\n* R is the resistance of the resistor in the circuit\n* V is the voltage across the capacitor\n* t",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: \u2211\\_{i=1}^{n} x\\_i = \u2211\\_{i=1}^{n} y\\_i.\n\nThis formula calculates the sum of all the values in the x\\_i and y\\_i series. The variable n is used as the index for both series, allowing the formula to calculate the sum of all values in both series. The result of the formula is the sum of the values in the x\\_i and y\\_i series.",
        "gt_answers": "3 . 5 g < 3 . 6 g < 5 g\n",
        "image_path": "./data/HME100K/test_images/test_1300.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear, as it is written in an unfamiliar mathematical notation. However, if we assume that the formula represents a quadratic equation, we can write it as follows:$$ax^2+bx+c=0$$where $a,b,c$ are constants. The solution to the equation is given by the quadratic formula:$$x=-\\bpm\\sqrt{b^2-4ac}$$where $\\alpha$ is the coefficient of the squared term and $\\beta$ is the coefficient of the linear term.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image is: x + 3y = 7x + 5y = 11x + y = 15x - 3y = 5.",
        "gt_answers": "x = \\frac { 1 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1302.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n$$\\text{csc}\\left(\\frac{\\text{t}}{\\text{2}}\\right) = \\text{sqrt}\\left(\\frac{\\text{15}}{\\text{4}}\\right)$$\n\nThis formula calculates the sine of half the angle of a right triangle, given the length of its hypotenuse, which is 15 units in the image. The hypotenuse is divided by 2 to find the angle, which is then converted to radians and the square root of 15 is taken to find",
        "gt_answers": ". B M = A B = \\frac { 1 } { 2 } B C\n",
        "image_path": "./data/HME100K/test_images/test_1304.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given below using LaTeX format.\n\n\\begin{center}\n\\begin{equation}\n\\frac{d^2x}{dt^2} + 2g\\sin(x) = m\\frac{dv}{dt}\n\\end{equation}\n\\end{center}\n\nHere, $x$ is the position of the object at time $t$, $v$ is the velocity of the object at time $t$, $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $\\sin(x)$",
        "gt_answers": "\\sin 4 5 ^ { \\circ } = \\frac { \\sqrt { 2 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1305.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a geometric sequence with a first term of 1 and a common ratio of 3. The formula for the nth term of this sequence is: an = 3\\*an\u22121, where an is the nth term and an\u22121 is the (n\u22121)th term. Using this formula, we can find the 5th term of the sequence: an = 3\\*5 = 15.\n\nThe formula for the sum of the first n terms of a geometric sequence is: S\\_n = a(1 - r^n)/(1 - r), where",
        "gt_answers": "\\frac { x } { 6 } - 4 x = 8\n",
        "image_path": "./data/HME100K/test_images/test_1306.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$ E = mc^2 $$\n\nwhere E is energy, m is mass, and c is the speed of light in a vacuum.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the formula:$$\\frac{a}{b}$$where a and b are integers. The fraction line is used to display the fraction as a ratio of two integers.\n\nHere is the LaTeX format for the formula:$$\\frac{a+b}{c+d}$$where a, b, c, and d are integers. The fraction line is used to display the fraction as a ratio of two integers.",
        "gt_answers": "x _ { 1 } = - 3 x _ { 2 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_1308.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is:\n\n$ f = \\frac{a\\_2^2 + b\\_2^2}{a\\_1^2 + b\\_1^2} $\n\nThis is the formula for calculating the probability of a coin landing on the same side as another coin that is flipped. The variables $a\\_1, b\\_1, a\\_2, b\\_2$ represent the probabilities of the two coins landing on different sides.",
        "gt_answers": "( 1 + 1 5 \\% ) x \\times 9 0 \\% = x = 7\n",
        "image_path": "./data/HME100K/test_images/test_1309.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$ 4x^2 + 12x - 16 = 0 $$In the image, the equation is written as $4x^2 + 12x - 16 = 0$. The equation represents a parabola with an x-intercept at the point (0, 16) and a y-intercept at the origin. The equation has two solutions, one real solution and one imaginary solution.",
        "gt_answers": "\\frac { 3 6 } { 9 } = 4\n",
        "image_path": "./data/HME100K/test_images/test_1311.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "1. The image shows an expression involving x^2 and x^3. 2. The image shows the multiplication of two binomials. 3. The image shows the multiplication of two binomials and the exponentiation of the result. 4. The expression is x^2\\*x^3=x^5. 5. The image is a mathematical expression involving x^2 and x^3.",
        "gt_answers": "x = \\frac { 2 } { a }\n",
        "image_path": "./data/HME100K/test_images/test_1312.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{2x+3y}{x+y}$.",
        "gt_answers": "( 9 1 - 6 ) \\times 5 = 7 5 ( d m )\n",
        "image_path": "./data/HME100K/test_images/test_1313.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the triangle in the image is $\\frac{1}{2}bh$, where b is the base length and h is the height.",
        "gt_answers": "x = 1 - \\frac { 1 } { 2 ^ { 1 0 0 } }\n",
        "image_path": "./data/HME100K/test_images/test_1314.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:$$\\frac{100-200\\times\\frac{40}{100}}{300+40}=\\frac{100-40\\times\\frac{40}{100}}{300+40}=40\\times\\frac{40}{100}}{300+40}=10\\times\\frac{40}{100}}{300+40}=\\frac{10\\times\\frac{40}{100}}{300+4",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{5}{3}$.",
        "gt_answers": "2 + \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1317.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the derivative of f(x) = x^3 with respect to x is given by: f'(x) = 3x^2.",
        "gt_answers": "\\tan A = \\frac { 3 } { 4 } = \\frac { a } { b }\n",
        "image_path": "./data/HME100K/test_images/test_1318.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression involving two variables x and y. The formula is written as follows:",
        "gt_answers": "\\angle E F C = 1 2 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1319.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by: 2x^2 - 2xy + y^2 = 2x^2 + y^2.",
        "gt_answers": "l x ^ { 2 } + y ^ { 2 } = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_1320.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: $ $\\frac{2\\times2 + 5\\times3 + 1\\times4}{6\\times7 + 3\\times4}$",
        "gt_answers": "\\frac { \\alpha } { y + 1 } = V\n",
        "image_path": "./data/HME100K/test_images/test_1321.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is not available for me to see. However, assuming the image is a mathematical expression, I can write out the formula in LaTeX format.\n\nThe formula is the product of two variables, i.e. y = x \\* z, where x and z are variables.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by: 3x - y = 4.",
        "gt_answers": "x = - 3 , y =\n",
        "image_path": "./data/HME100K/test_images/test_1323.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\begin{aligned}5 + 6 &= 11\\5 - 2 &= 3\\3 - 2 &= 1\\1 - 1 &= 0\\0 + 0 &= 0\\0 - 5 &= -5\\end{aligned}$$",
        "gt_answers": "\\frac { 1 2 } { 5 } x = \\frac { 1 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1324.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\nx\u00b2 + 5x + 6 = 0\n\nThis equation can be solved by the quadratic formula:\n\nx = (-b \u00b1 \u221a(b\u00b2 - 4ac)) / 2a\n\nPlugging in the values given in the image:\n\nx = (-(-5) \u00b1 \u221a((-5)\u00b2 - 4(1)(8))) / 2(1)\n\nx = (-5 \u00b1 \u221a(25 + 32)) / 2\n\nx = (-5 \u00b1",
        "gt_answers": "2 2 + x - 2 2 = 8 7 \\div 2 2\n",
        "image_path": "./data/HME100K/test_images/test_1325.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{1}{2} \\left(\\frac{x^2}{y}+\\frac{y^2}{x}\\right)\\left(\\frac{y}{x}+\\frac{x}{y}\\right)$$Note that the formula is written in LaTex format, which uses special characters and symbols to represent mathematical expressions. The formula is derived from the principle of conservation of energy, which states that the total energy of a closed system is constant over time.\n\nThe first term in the formula, $\\frac{1}{2} \\left(\\frac{",
        "gt_answers": "1 7 = y ^ { 2 } - 4 y + 5 + y ^ { 2 } - 2 y + 1 0\n",
        "image_path": "./data/HME100K/test_images/test_1327.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$\\frac{100 - 50}{10 + 5} = \\frac{50}{15} = \\boxed{3.3333} $$\n\nThe expression in the image is $\\frac{100-50}{10+5}$, which is equivalent to $\\frac{50}{15}$. The fraction $\\frac{50}{15}$ is simplified to $\\frac{5}{3}$, which is further simplified to",
        "gt_answers": "\\cdot b ^ { 2 } = a ^ { 2 } + c ^ { 2 } - 2 a c \\cdot \\cos B\n",
        "image_path": "./data/HME100K/test_images/test_1328.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a sum of two numbers.\n\n$$\\frac{a + b}{2}$$\n\nThis expression represents the average of two numbers $a$ and $b$. The numerator is the sum of $a$ and $b$, and the denominator is $2$.",
        "gt_answers": "\\frac { b } { A B } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1330.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$E = \\frac{1}{2}mv^2 + \\frac{1}{2}I\\omega\\_n^2$$\n\nwhere $E$ is the energy of the system, $m$ is the mass of the object, $v$ is the velocity of the object, $I$ is the moment of inertia of the object, and $\\omega\\_n$ is the angular frequency of the object.",
        "gt_answers": "\\cos a < 0 , \\tan a < 0 \\cot a < 0\n",
        "image_path": "./data/HME100K/test_images/test_1331.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format. It is written in a numerical format.",
        "gt_answers": "\\alpha 1 \\sim 2 3\n",
        "image_path": "./data/HME100K/test_images/test_1332.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation shown in the image is the equation of a circle. The equation is:\n\n(x - h)^2 + (y - k)^2 = r^2\n\nwhere (h, k) is the center of the circle and r is the radius of the circle.",
        "gt_answers": "= 1 0 4 0\n",
        "image_path": "./data/HME100K/test_images/test_1334.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is:$$\\text{area} = \\frac{1}{2}bh$$where $b$ is the base and $h$ is the height of the triangle. Using this formula, we can find the area of the triangle in the image:$$\\text{area} = \\frac{1}{2} \\times 8 \\times 12 = 384 \\sqrt{inches^2}$$Therefore, the area of the triangle in the image is 384 square inches.",
        "gt_answers": "P = \\frac { W } { t } = \\frac { 6 0 0 J } { 1 0 s } = 6 0 w\n",
        "image_path": "./data/HME100K/test_images/test_1335.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$n = \\frac{3}{2}$$\n\nThe numerator is the product of 2 and 3, and the denominator is the sum of 1 and 2.",
        "gt_answers": "s n = n 2\n",
        "image_path": "./data/HME100K/test_images/test_1336.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: (3x + 5) \\* (4y - 3z) = 18xy - 15yz + 9xz.",
        "gt_answers": "V ^ { \\prime } = \\frac { \\Delta x ^ { 2 } } { t } = \\frac { 0 . 0 6 } { 0 . 5 } = 0 . 1 2 . m / s\n",
        "image_path": "./data/HME100K/test_images/test_1338.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by:\n\narea = pi \\* radius^2\n\nwhere pi is a mathematical constant approximately equal to 3.14 and radius is the distance from the center of the circle to its edge.",
        "gt_answers": "A C \\bot B D\n",
        "image_path": "./data/HME100K/test_images/test_1339.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is shown below:\n\n$$\\text{sin}^{2}\\theta + \\cos^{2}\\theta = 1$$",
        "gt_answers": "\\angle 1 = \\frac { 1 } { 2 } \\angle B P Q , \\angle 2 = \\frac { 1 } { 2 } \\angle C Q P\n",
        "image_path": "./data/HME100K/test_images/test_1340.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{IQR}(x) = \\frac{75 percentile - 25 percentile}{100\\ text{percentile}}$$\n\nwhere $x$ is the variable for which IQR is being calculated.",
        "gt_answers": "\\Delta B D E \\sim \\Delta E D O\n",
        "image_path": "./data/HME100K/test_images/test_1341.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle can be written as:\n\nA = \u03c0r^2,\n\nwhere A is the area of the circle, \u03c0 is the mathematical constant pi (approximately equal to 3.14159), and r is the radius of the circle.",
        "gt_answers": "\\frac { 9 } { \\vert q \\vert } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1343.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the given image:\n\n$$\\frac{t}{2} = \\frac{3}{5} + \\frac{4}{5}$$\n\nwhere $t$ is the time taken to complete the job, and $t/2$ is half the time taken to complete the job. The first fraction on the right-hand side represents the time taken to complete half the job, while the second fraction on the right-hand side represents the time taken to complete the remaining half of the job.",
        "gt_answers": "F = \\frac { 1 } { 2 } G = \\frac { 1 } { 2 } \\cdot 2 0 0 N = 1 0 0 N .\n",
        "image_path": "./data/HME100K/test_images/test_1344.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a circle can be written as follows using LaTeX format:\n\n$$A = \\pi r^2$$\n\nwhere $A$ is the area of the circle, $r$ is the radius of the circle, and $\\pi$ is a constant that is approximately equal to 3.14.\n\nTo calculate the area of the circle in the image, we need to know the radius of the circle. We can do this by measuring the distance from the center of the circle to the edge of the circle. Let's assume that the radius of the circle is $r=",
        "gt_answers": "b > - 1 0\n",
        "image_path": "./data/HME100K/test_images/test_1345.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{align\\*} 4x^2 + 2x - 4 &= 0 \\ \\Rightarrow x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} \\ &= \\frac{-(-2) \\pm \\sqrt{(2)^2 - 4(1)(-4)}}{2(1)} \\ &= \\frac{2 \\pm \\sqrt{16 - 16}}{2} \\ &= \\frac{2 \\pm \\sqrt{0}}{2} \\",
        "gt_answers": "4 x + 2 x - 2 = 4\n",
        "image_path": "./data/HME100K/test_images/test_1346.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the rectangle in the image is:\n\nA = lw + 2lh = 4lw + 2lh = (4ln + 2lh)w = 4l2 + 2lh2 = 4ln + 2h2 + 2lh2 = 4ln + 2h2 + 2lh2 = 4ln + 2h + 2lh2 = 4ln + 2h + 2lh = 4l2 + 2h + 2lh =",
        "gt_answers": "2 0 0 \\times 2 = 4 0 0 k m\n",
        "image_path": "./data/HME100K/test_images/test_1347.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n&#x2220;&#x2212;&#x2212;&#x2220;&#x2212;&#x2212;&#x2220;&#x2212;&#x2220;&#x2212;&#x2212;&#x2220;&#x2212;&#x2212;&#x2220;&#x2212;&#x22",
        "gt_answers": "\\angle M C N = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1348.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:$$\\begin{aligned} \\frac{10 \\times 3}{2} &= 6 \\\\ 15 &= 2 \\times 6 \\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression of the formula in the image:\n\n$$\\frac{1}{2x^2 + 4x - 5} = \\frac{2x^2 + 4x - 5 - \\frac{1}{2x^2 + 4x - 5}}{\\frac{1}{2x^2 + 4x - 5}} = \\frac{x^2 + 3x - 2.5}{x - 2.5} = \\frac{x^2 + 3x - 2.5}{x - \\frac{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: $\\frac{5x^2}{2x+3}+\\frac{8x}{3x+1}$.",
        "gt_answers": "\\angle A C B = 7 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1353.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written on the blackboard is: $ \\frac{1}{1} + \\frac{1}{2} + \\frac{1}{4} = \\frac{3}{4} $\n\nThe formula written in LaTeX format is: $\\frac{1}{1} + \\frac{1}{2} + \\frac{1}{4}=\\frac{3}{4}$",
        "gt_answers": "x _ { 1 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1354.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX code for the expression:\n\n\\begin{align\\*}\n&\\text{The perimeter of the rectangle is } P = 2(l+w) \\\n&\\text{The area of the rectangle is } A = lw \\\n&\\text{The volume of the cube is } V = l^3 \\\n&\\text{The volume of the cylinder is } V = \u03c0r^2h \\\n&\\text{The volume of the sphere is } V = 4/3\u03c0r^3 \\\n&\\text{The volume of the cone is",
        "gt_answers": "- \\frac { 3 } { 1 6 } x = 1 6\n",
        "image_path": "./data/HME100K/test_images/test_1357.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{distance between the two points on the line given by the equation } x = 2y + 1$$The red line represents the equation x = 2y + 1, and the two points on the line are represented by the two red dots. The distance between the two points is given by the length of the red line.\n\nTo find the distance between the two points, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to",
        "gt_answers": "x = \\frac { 2 1 } { 2 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1358.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This image shows the multiplication of the number 4 and the fraction 1/2. To write the expression in LaTeX format, you can use the following code:\n\n$$\\frac{4}{2}=\\frac{4}{1}=\\frac{4}{1}=2$$\n\nIn LaTeX format, the fraction is written with a bar over the numerator, like this: $\\frac{a}{b}$. So, the expression can be written as:\n\n$$\\frac{4}{2}=\\frac{4}{1}=\\frac{4}{1}=2$$\n\nThis expression evaluates to 2,",
        "gt_answers": "\\frac { 2 } { 3 } x - \\frac { 1 } { 4 } x = \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_1359.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b \u222b \u222b \u222b \u222b (x^2 + y^2) dxdy = \u222b \u222b (x^2 + y^2) dxdy.",
        "gt_answers": "x = \\frac { - 4 \\pm 4 - \\sqrt { 2 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1360.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a geometric series with first term a and common ratio r.\n\nGiven a = 1 and r = 4, we can write the formula for the nth term of the sequence as:\nan = a(1 - r^n)/(1 - r)\n\nUsing this formula, we can find the value of the first 5 terms of the sequence:\n\nan = 1(1 - 4^n)/(1 - 4)\nan = 1 - 5n + 12n^2 + 22n^3 +",
        "gt_answers": "\\frac { 3 } { 5 } \\times \\frac { 5 } { 1 2 } x - \\frac { 3 } { 5 } \\times \\frac { 5 } { 6 } - \\frac { 3 } { 5 } \\times 5 + 4 = x\n",
        "image_path": "./data/HME100K/test_images/test_1361.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression for the formula in the image using LaTeX format:\n\n$$x = \\frac{400}{0.5 + 200\\left(1 - \\frac{400}{400 + 100}\\right)}$$\n\nThis formula calculates the percentage of time an employee takes to complete a task, given the time they take to complete 100 units of work and the time they take to complete 400 units of work. The formula uses the following steps:\n\n1. Calculate the average time taken to complete",
        "gt_answers": "x = \\frac { 4 0 . } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_1363.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below.\n\nLet the variable x be the age of a person in years. Then the formula is given by:\n\nThe probability that a person is alive at age x is given by the cumulative distribution function (CDF) of the Weibull distribution, which is defined as:\nP(x) = 1 - exp(-(lambda/k)x)\nwhere lambda and k are shape and scale parameters of the Weibull distribution, respectively.\nThe expected number of years until a person dies is given by the complement of the C",
        "gt_answers": "S _ { \\Delta } P C D = S _ { \\Delta } P O D = 1 . 5\n",
        "image_path": "./data/HME100K/test_images/test_1364.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in the image using LaTeX format, we can use the following code:\n\n$$\\frac{1}{\\sqrt{2}\\sqrt{2}}$$\n\nThis formula represents the area of a square with side length $\\sqrt{2}$.",
        "gt_answers": "\\alpha + \\beta \\in ( \\pi , 2 \\pi )\n",
        "image_path": "./data/HME100K/test_images/test_1367.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation of the formula in the image can be written as follows in LaTeX format:\n\n$$\\frac{3}{5}+\\frac{1}{4}=\\frac{8}{10}$$\n\nThis equation can also be written in a more general form as:\n\n$$\\frac{a+b}{c}+\\frac{d}{e}=\\frac{f+g}{h}$$\n\nwhere a, b, c, d, e, f, g, and h are any real numbers. This formula is known as the algebra equation of the addition of two fractions.",
        "gt_answers": "\\sqrt [ 3 ] { 6 \\frac { 6 } { 2 1 5 } } = 6 \\sqrt [ 3 ] { \\frac { 6 } { 2 1 5 } }\n",
        "image_path": "./data/HME100K/test_images/test_1368.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:$$\\frac{2x^2+3x-5}{x+2}$$",
        "gt_answers": "x _ { 2 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1369.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ f(x) = \\frac{3x^2 - 4x - 10}{x + 2}$$",
        "gt_answers": "8 0 \\times 1 0 0 = 8 0 0 0 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_1371.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression of the formula in the image using LaTeX format:\n\n$$\\begin{aligned} P(a \\in A) &= P(\\text{a}) \\cap P(\\text{A}) \\qquad \\text{(using the definition of } P(\\text{a}) \\text{ and } P(\\text{A})\\text{)}\\\\\n&= \\frac{1}{|A|} \\sum\\_{a \\in A} \\mathbf{1}\\left[\\text{a} \\in A\\right] \\qquad \\text{(using the definition of } P(\\text{a}) \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The image shows a mathematical expression for the formula of an ellipse. The equation is given by: x^2 + y^2 = a^2, where a is the semi-major axis of the ellipse. To find the equation of the line passing through two points, we can use the slope-intercept form of the equation: y = mx + b, where m is the slope and b is the y-intercept. Using this form, we can find the equation of the line passing through the two points (3, 4) and (5,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n$$\\text{image}=\\text{text in the image}$$\n\nwhere $\\text{image}$ is the image itself, and $\\text{text in the image}$ is the text written on the image.",
        "gt_answers": "x _ { 1 } = x x _ { 2 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_1374.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n\\begin{equation}\na\\_2 = \\frac{2 \\* r\\_2^2 + h\\_2^2 - r\\_1^2 - h\\_1^2}{2 \\* r\\_1^2 + h\\_1^2 - r\\_2^2 - h\\_2^2}\n\\end{equation}",
        "gt_answers": "\\angle A D B = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1375.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\sum\\_{i=1}^n x\\_i = 3$ where $n$ is the number of values in the array.\n\nIn LaTeX format, the expression can be written as: $\\sum\\_{i=1}^n x\\_i = 3$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format of the given expression:\n\n\\begin{center}\n5x + 4y = 20\n\\end{center}\n\nThis is a linear equation in two variables, where the constant term is 20 and the coefficients are 5 for x and 4 for y. The equation can be solved by using the elimination method or substitution method.",
        "gt_answers": "x _ { 3 } = \\frac { 1 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1377.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{equation}\na + b = c\n\\end{equation}",
        "gt_answers": "= 3 3 0 \\div 3\n",
        "image_path": "./data/HME100K/test_images/test_1378.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression for the derivative of a function f(x) with respect to x. The formula for the derivative is given by: d/dx f(x) = (4x - 5) / (x - 3).\n\nThe image also includes a numerical example of the formula in action, where the derivative of f(x) = x^3 at x = 4 is calculated to be 16.",
        "gt_answers": "\\angle C M N = \\arccos \\frac { \\sqrt { 3 } } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1379.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n$$\\frac{1}{3}\\left(\\frac{10}{11}\\right)^{4}\\left(\\frac{2}{3}\\right)^{5}\\left(\\frac{1}{4}\\right)^{3}$$\n\nThis can be derived by using the formula for the sum of a geometric series:\n\n$$\\frac{a}{1-r}$$\n\nwhere a is the first term and r is the common ratio. In this case, a = 10/11, r = 2/3, and n = 4. The sum",
        "gt_answers": "\\frac { 1 3 0 x - 2 6 } { 6 } =\n",
        "image_path": "./data/HME100K/test_images/test_1380.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$\\left[\\frac{3}{4}\\left(\\frac{x}{2}\\right)^2-\\frac{1}{2}\\left(\\frac{x}{2}\\right)^4\\right]^\\frac{2}{3}$",
        "gt_answers": "8 \\times 8 \\times 8 = 5 1 2 ( m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_1381.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I am sorry, I cannot see the image as I am a text-based AI language model and I cannot process image inputs. Can you provide the formula in LaTeX format?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by the equation:\n\nm = (1/2) \\* (2x - 4) \\* (3x + 1)\n\nwhere, x is the input value and m is the output value.",
        "gt_answers": "m = \\frac { \\sqrt { 2 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1383.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the image:\n\n\\begin{center}\n\\begin{tabular}{ccc}\n$\\frac{1}{4}$ & $\\frac{3}{4}$ & $\\frac{1}{4}$\\\n\\end{tabular}\n\\end{center}\n\nThe above formula represents the ratio of the areas of the three rectangles in the image. The first rectangle has an area of $\\frac{1}{4}$ of the image, the second rectangle has an area of $\\frac{3}{4}$ of the image, and the third rectangle has an area of $\\frac{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{Im}\\_\\text{aginary}\\_\\text{ part} = \\frac{1}{\\sqrt{2}}$$\n\nThis can be written in LaTeX format as:\n\n$$\\text{Im}\\_\\text{aginary}\\_\\text{ part} = \\frac{1}{\\sqrt{2}$$\n\nThe above expression represents the imaginary part of a complex number, which can be calculated by taking the square root of 2.",
        "gt_answers": "a c ^ { 2 } = b c ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1385.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\frac{100}{200 - 400}\\text{ ln}\\left(\\frac{100}{200 - 400}\\right)$$\n\nThe formula is a function of the input variables x and y. It calculates the natural logarithm of the ratio of x to y, scaled by 100 and subtracted from 200.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: $\\frac{(x+3)(x+4)}{2}$. This can be written as $\\frac{x+3}{2}+\\frac{x+4}{2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n$$\\text{Imaginary part of } \\zeta\\$\n\n$$\\begin{aligned}\n&\\text{Re}(i\\zeta) = \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} + \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} - \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{2} - \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is $\\pi r^2$ where $r$ is the radius of the circle.\n\nUsing the formula and the radius of the circle in the image, we can calculate the area of the circle. First, we find the radius of the circle by measuring the distance from the center to the edge of the circle.\n\nNext, we substitute the radius into the formula to find the area of the circle: $\\pi r^2$\n\nPlugging in the value for the radius, we get: $\\pi r^2$\n\nFinally, we evaluate the",
        "gt_answers": "V = \\frac { s } { t }\n",
        "image_path": "./data/HME100K/test_images/test_1393.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{\\text{Image Content}}{\\text{Initial Content}}$$This formula represents the change in the image content from its initial state to its current state.",
        "gt_answers": "\\angle P = \\angle A C P = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1395.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:$$(x+y)^2=x^2+y^2+2xy$$This is a quadratic equation, which means that it involves a variable (x) raised to the second power (squared) and another variable (y) raised to the second power (squared), as well as a constant term (2xy). The equation is saying that the sum of the squares of x and y is equal to the sum of x squared, y squared, and the product of x and y. In other words, the sum of x and y must be equal to the sum",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{t}{t+2}$$\n\nwhere $t$ is the time taken to complete the task.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{1}{x + \\frac{1}{y + 3}}$$",
        "gt_answers": "y _ { 3 } = - \\frac { 1 } { 3 } , y _ { 4 } \\cdot 3\n",
        "image_path": "./data/HME100K/test_images/test_1398.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression written in LaTeX format.\n\nThe expression is: (a + b)(c + d) = ac + bd + ad + bc\n\nThis is a product of two binomials, (a + b) and (c + d), which are combined using the distributive property of multiplication. The distributive property states that the product of two numbers a and b and the product of two numbers c and d can be combined using the distributive property, which is written as a \\* b + c \\* d.\n\nThe expression (a + b)(c + d",
        "gt_answers": "b ^ { 2 } + b - 2 = 0 \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_1399.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length 10cm and width 5cm is:\n\nA = l \u00d7 w\n\nA = 10 \u00d7 5\n\nA = 50 cm\u00b2\n\nThe formula for the area of a rectangle with length 5cm and width 4cm is:\n\nA = l \u00d7 w\n\nA = 5 \u00d7 4\n\nA = 20 cm\u00b2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not written in LaTeX format. It is written as follows:\n\n$$\\frac{3x^2 + 4x - 3}{x^2 - 6x + 8} = \\frac{x^2 - 6x + 8}{3x^2 + 4x - 3}$$\n\nThis equation can be rearranged into the form:\n\n$$\\frac{a}{b} = \\frac{b}{a}$$\n\nwhich is true for any two expressions that represent the same value.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:$$r=\\frac{2v^2}{r}$$where $r$ is the radius of the circle, $v$ is the velocity of the object at a certain time, and $r$ is the radius of the object's orbit.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{a}{b}$$\n\nwhere a and b are constants.",
        "gt_answers": "( a \\times b ) \\times c = a \\times ( b \\times c )\n",
        "image_path": "./data/HME100K/test_images/test_1403.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you can use the following LaTeX code:\n\n$$ \\text{Energy} = mc^2 \\left(\\frac{1}{2}mv^2 + V\\right) $$\n\nwhere $\\text{Energy}$ is the total energy of the system, $m$ is the mass of the object, $c$ is the speed of light, $V$ is the potential energy of the object at the top of the incline, and $mv^2$ is the kinetic energy of the object.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\\frac{5}{3} can be represented as follows: \\frac{5}{3}=\\frac{5}{3}\\frac{3}{2}=5\\frac{2}{1}=5\\frac{1}{0}=5. This equation shows that 5 is equivalent to 5 divided by 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$\\frac{\\frac{3\\cdot5\\cdot7}{4\\cdot6\\cdot9}}{\\frac{11\\cdot13\\cdot15}{12\\cdot14\\cdot16}} = \\frac{3}{4}\\cdot\\frac{5}{6}\\cdot\\frac{7}{9}\\cdot\\frac{11}{12}\\cdot\\frac{13}{14}\\cdot\\frac{15}{16}$\n\\end{center}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$ \\begin{aligned} x & = \\frac{5}{2} \\\\ y & = \\frac{11}{6} \\end{aligned} $$",
        "gt_answers": "1 \\frac { 1 } { 3 } x + \\frac { 1 } { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_1410.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a LaTeX expression for the equation of a parabola in two variables. The equation is y = 3x^2 - 4x + 2, which can be rewritten in the form y = mx^2 + bx + c. The equation represents a parabola that opens upwards and has its vertex at the origin. The y-intercept is 2 and the x-intercept is - 1/3.",
        "gt_answers": "\\frac { x + 1 } { 2 } = 1 - \\frac { 3 x - 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1411.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{2}{x^2 + 4x - 8}$$",
        "gt_answers": "k = - \\frac { \\sqrt { 3 } } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1412.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\documentclass{article}\n\\usepackage{amsmath}\n\\begin{document}\n\\begin{equation}\nF = \\frac{m}{r^2}\n\\end{equation}\n\\end{document}\n```",
        "gt_answers": ": x = \\sqrt { 2 } - 1 , y = \\sqrt { 2 } + 1\n",
        "image_path": "./data/HME100K/test_images/test_1413.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression with two unknowns. The equation is written as $2x^2 + 5x - 3 = 0$, which is a quadratic equation with solutions $(x=1)$ and $(x=-3)$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n$$\\text{b} = \\sqrt{\\frac{16(x - 1)^2 + 16(x - 2)^2 + 16(x - 3)^2}{24x + 18}}$$\n\nThis formula is used to calculate the equation of a parabola given its equation in vertex form. In this case, the vertex form of the parabola is given by the equation $y = ax^2 + bx + c$, where $a = 1",
        "gt_answers": "b c = ( - 1 ) \\times ( - 1 ) = 1\n",
        "image_path": "./data/HME100K/test_images/test_1415.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the image is:$$\\frac{5000\\times 1000}{2500}$$The expression for the volume of the image is:$$\\frac{5000\\times 1000\\times 500}{2500}$$These expressions represent the area and volume of a square with sides measuring 5000 cm and 1000 cm, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n\\begin{align\\*}\n    \\text{ImageContent}\n\\end{align\\*}",
        "gt_answers": "x ^ { 2 } + x ^ { 2 } + x = 2 ( x + 1 ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1417.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is written as:\n\n\u222b(1 - x\u00b2)dx = \u222b(2x)dx\n\nThe left-hand side of the equation is the indefinite integral of 1 - x\u00b2 with respect to x, and the right-hand side is the indefinite integral of 2x with respect to x. The two integrals are equal because the integral of a constant is equal to the constant itself. Therefore, the equation reduces to:\n\n\u222b(1 - x\u00b2)dx = 2x",
        "gt_answers": "x + y = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1419.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:\n\n\\begin{center}\n$\\frac{1}{n!}\\sum\\_{i=0}^{n} \\binom{n}{i}(-1)^i$\n\\end{center}\n\nwhere $n$ is a non-negative integer.",
        "gt_answers": "x + y = 1\n",
        "image_path": "./data/HME100K/test_images/test_1420.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in the image using LaTeX format, we can use the following equation: $\\frac{x+3}{x-3}=1$This formula represents the equation of a line in the x-y plane, where x is the independent variable and y is the dependent variable. The equation has a slope of 3 and passes through the point (0,0).",
        "gt_answers": "\\sqrt { 2 x - 3 } = 3 - x\n",
        "image_path": "./data/HME100K/test_images/test_1421.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 3. 141. This is derived from the equation 2(x + 1) = 5. Solving for x, we get x = 3. 141.",
        "gt_answers": "d = \\frac { m k } { \\sqrt { k ^ { 2 } + 1 } }\n",
        "image_path": "./data/HME100K/test_images/test_1422.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{4x^2 - 16x + 8}{2x + 4}$. This formula is derived from the given equation: $\\frac{x^4 - 4x^3 + 6x^2 - 4x + 1}{x + 2}$.\n\nTo derive the given formula from the given equation, we can use the following steps:\n\n1. Multiply both sides of the equation by $x + 2$ to get $x^4 - 4x^3 + 6",
        "gt_answers": "y = - ( x - 1 ) ^ { 2 } + 4 = - x ^ { 2 } + 2 x + 3\n",
        "image_path": "./data/HME100K/test_images/test_1425.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{b+2}{c-5}$$where $b$ and $c$ are constants and $a$ is the variable.",
        "gt_answers": "\\frac { 3 } { 8 } = \\frac { 6 } { 1 6 }\n",
        "image_path": "./data/HME100K/test_images/test_1426.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by: $y = \\frac{1}{x^2}$",
        "gt_answers": "y _ { 3 } = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1427.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the expression 5 + 3, which can be written as $\\frac{5 + 3}{10}$. This can be rewritten as $\\frac{5 + 3}{5}$, which is equivalent to $\\frac{5 + 3}{5}$. This can be rewritten as $\\frac{8}{5}$, which is equivalent to $\\frac{16}{10}$. This can be rewritten as $\\frac{16}{10}$, which is equivalent to $\\frac{16}{10}$. This can be rewritten as $\\frac{16}{10}$, which is",
        "gt_answers": "\\frac { 5 } { 6 } \\div \\frac { 5 } { 4 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1428.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nLaTeX: \n\n$ f(x) = \\frac{3x^2 - 5x + 2}{x - 2} $\n\n$$ f(x) = \\frac{3x^2 - 5x + 2}{x - 2} $$\n\n$$ \\frac{3x^2 - 5x + 2}{x - 2} = \\frac{3(x-2)^2 + 7(x-2) + 5}{x-2} $$\n$$ \\frac{3(x-2)^2",
        "gt_answers": "\\cos C = \\frac { 2 \\sqrt { 5 } } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1429.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula in the image using LaTeX format, we can write:\n\n\\begin{align\\*}\n\\text{BMI} &= \\frac{\\text{weight in kg}}{\\text{height in m}^2} \\\n   &= \\frac{68 \\text{ kg}}{182.88 \\text{ m}^2} \\\n   &= 0.392 \\\n   \\Rightarrow \\text{BMI} = 0.392\\_{}^{1} \\\n   \\text{kg/m}^2 \\\n   \\Rightarrow \\text{B",
        "gt_answers": "1 . 2 ( 1 1 0 y + 1 2 0 x ) = 9 7 2 0 0\n",
        "image_path": "./data/HME100K/test_images/test_1430.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression in the image:\n\n$$ 2x + 5y = 10 $$",
        "gt_answers": "2 N a O H + C O _ { 2 } = N a _ { 2 } C O _ { 3 } + H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_1431.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I am unable to see the image as it is not provided. Please provide the image so I can help you.",
        "gt_answers": "8 5 + 1 0 > 5 8 + 3 0 > 3 3 + 3 0 > 5 8 + 1 7 3 3 + 3\n",
        "image_path": "./data/HME100K/test_images/test_1432.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ $\\textstyle 1 + 2i$$Thus, the formula is $\\textstyle 1 + 2i$.",
        "gt_answers": "1 4 0 0 _ { m } = k 4 + k 4\n",
        "image_path": "./data/HME100K/test_images/test_1433.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n\\begin{align}\nL = \\frac{1}{2}mv^2 + mgh \\\n\\end{align}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n\\begin{center}\n$\\frac{\\text{1}}{\\text{3}\\left(\\frac{\\text{1}}{\\text{2}\\right)^2}+\\frac{\\text{1}}{\\text{2}\\left(\\frac{\\text{1}}{\\text{3}}\\right)^2}+\\frac{\\text{1}}{\\text{3}\\left(\\frac{\\text{1}}{\\text{4}}\\right)^2}}$\n\\end{center}\n\nIn the above expression, $\\text{1}$, $\\text{2}$, $\\text{3}$, and",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the derivative of the function f(x) = x^(2) - 2x + 1, we can use the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1). Applying this rule to our function, we get:\n\nf'(x) = 2x^(2) - 2 \\* 2x + 1 = 2x^1 - 4x + 1\n\nTo simplify this expression, we can factor out the x^1 term:\n\nf",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$ m = \\frac{n}{x} $$\n\n```",
        "gt_answers": "( m - 4 ) ( m + 1 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_1438.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:ax=b.\n\nThis equation is a simple algebraic equation that states that the value of x is equal to the value of b.",
        "gt_answers": "a ^ { 2 } x ^ { 2 } = a -\n",
        "image_path": "./data/HME100K/test_images/test_1439.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is x^2 + y^2 = r^2.\n\nThe formula is derived by adding the squares of x and y and then equating the result to the square of the radius, r. The equation represents a circle with center at the origin and radius r.",
        "gt_answers": ": 2 x ^ { 2 } + b x + 1 = 0 ( 2 , b , c \\in R )\n",
        "image_path": "./data/HME100K/test_images/test_1441.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\text{sin}\\left(\\frac{\\text{pi}}{4}\\right) + \\frac{1}{2}$$",
        "gt_answers": "\\frac { x } { x - 1 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_1442.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is $ f(x) = \\frac{1}{2} \\left( \\frac{x}{a} \\right)^2 + \\frac{3}{2}x + 4 $.",
        "gt_answers": "\\frac { 6 \\sqrt { 2 } } { A E } = \\frac { A E } { 2 \\sqrt { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_1443.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{Image Content} = \\text{Absolute Content} $$\n\nwhere $\\text{Image Content}$ is the formula in the image, and $\\text{Absolute Content}$ is the result of the formula in the image.",
        "gt_answers": "S _ { \\Delta A B C } = \\frac { 1 } { 2 } a b \\sin C\n",
        "image_path": "./data/HME100K/test_images/test_1444.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{a}{2b+c}=\\frac{b}{c}$$\n\nwhere $a,b,$ and $c$ are constants and $a,b,$ and $c$ are variables.",
        "gt_answers": "x ^ { 2 } - 4 + 2 ( x + 1 ) ( x + 2 ) = - 8 ( x + 1 )\n",
        "image_path": "./data/HME100K/test_images/test_1445.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression for the formula in the image:\n\n$$\\frac{3\\times5\\times6\\times7\\times9\\times11}{2\\times4\\times6\\times8\\times10}$$\n\nThis formula calculates the product of 3, 5, 6, 7, 9, and 11 multiplied by the reciprocal of 2, 4, 6, 8, and 10.",
        "gt_answers": "\\angle B O D = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1446.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{Sqrt}\\left(\\frac{\\text{1}}{2}\\right) + \\text{1} = \\sqrt{2} + 1 $$",
        "gt_answers": "S _ { \\Delta A O P } = 1 2\n",
        "image_path": "./data/HME100K/test_images/test_1447.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{Speed} = \\frac{300\\text{ ft}}{60\\text{ s}} = \\frac{5\\text{ ft}}{s}$$\n\nWhere,\n\n* 300 ft is the distance covered by the car in 60 s\n* 5 ft is the distance covered by the car in 1 s",
        "gt_answers": "\\frac { 4 0 0 } { 1 0 0 0 } = \\frac { 4 } { 1 0 } = \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1449.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we need to first identify the variables and constants involved in the formula. The formula is given as:\n\nx + 3y + 2z = 16\n\nThe variables in the formula are x, y, and z. The constant is 16. To write out the formula using LaTeX format, we can use the following code:\n\n$$\\begin{aligned} x + 3y + 2z &= 16 \\ \\\\ x + y + 2z &= 16 \\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: y = 2x + 4. This can be derived by substituting the values of the variables in the formula into the given values. The value of x is 5 and the value of y is 12, so the equation becomes 2(5) + 4 = 12.",
        "gt_answers": "x = - \\frac { 1 1 } { 3 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1451.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{3x^4 + 4x^3 + 6x^2 - 8x - 12}{4x^3 + 6x^2 - 12x + 9}$.",
        "gt_answers": "2 ( x + 5 ) - 6 < 3 ( 3 x + 2 ) ,\n",
        "image_path": "./data/HME100K/test_images/test_1452.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following steps:\n\n1. Identify the variables in the formula: x, y, and z\n2. Write the formula using the variables: x^2 + y^2 = z^2\n3. Simplify the formula by factoring out the common factors: (x + y)(x + z) = z^2\n4. Write the simplified formula in LaTeX format: $\\frac{(x + y)(x + z)}{z^2}$\n\nTherefore, the expression for the formula in the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\frac{a + b}{c - d} \\left(\\frac{e - f}{g + h}\\right)\\left(\\frac{i - j}{k + l}\\right)\\left(\\frac{m - n}{o + p}\\right)$$\n\nwhere $a, b, c, d, e, f, g, h, i, j, k, l, m, n, and o are constants and p is a variable.",
        "gt_answers": "F e _ { 2 } O _ { 3 } + 3 H _ { 2 } S O _ { 4 } = F e _ { 2 } ( S O _ { 4 } ) _ { 3 } + 3 H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_1455.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \u222b(1 + 2x)dx.\n\nIn LaTeX format, the integral sign is represented by the double integral sign, which is denoted by the double vertical bar, ||. The variable x is represented by the variable x, and the limits of integration are represented by the numbers 1 and 4. The constant 2 is represented by the number 2.\n\nTherefore, the LaTeX format of the formula in the image is: \u222b(1 + 2x)dx.",
        "gt_answers": "A F = A E + E F = 4 0 + 3 0 \\sqrt { 3 } - 3 0\n",
        "image_path": "./data/HME100K/test_images/test_1456.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2x - 4y + 5 = 0.",
        "gt_answers": "6 \\times 6 \\times 6 = 2 1 6 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_1457.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{C} = \\frac{\\text{A}}{\\text{B} + \\text{C}}$$\n\nwhere $\\text{A}$ is the length of the rectangle in the image, $\\text{B}$ is the width of the rectangle in the image, and $\\text{C}$ is the height of the rectangle in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, you would use the following code: $\\frac{3x^2}{x+5}+\\frac{4x}{x+3}$Note that the numerator and denominator have been simplified, and the radicals have been simplified using the distributive property.",
        "gt_answers": "\\sqrt { 3 } \\times \\frac { 1 } { \\sqrt { 3 } } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1459.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is: \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "P M = \\sqrt { 3 ^ { 2 } - 2 ^ { 2 } } = \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1461.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is $\\frac{1}{4}\\cdot x^2 + 3x - 5$, where x is a variable.\n\nThe image shows a graph of a parabola with an x-intercept at 1 and a y-intercept at 5. The vertex is at the point (0, 3). The equation of the parabola is given by y = ax^2 + bx + c, where a = 1, b = 3, and c = 5. The equation of the parabola is written as y = x^2 -",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula for the sum of two numbers, a and b, with the result being a+b. The formula is written in LaTeX format as follows: a+b.",
        "gt_answers": "3 - \\frac { 3 } { 2 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1463.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by: x^2 + 3x + 5 = 0, which is a quadratic equation. The solutions to this equation are x = 0 and x = 5, as the discriminant (b^2 - 4ac) is negative.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\frac{a}{b}=\\frac{4}{3}$",
        "gt_answers": "\\frac { 1 } { 2 } x = - \\frac { 7 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1465.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a LaTeX equation for the image: $\\frac{4+3+1}{2+3+1}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for this expression is: $\\frac{x^3+4x^2+5x-1}{x^2+3x-2}$",
        "gt_answers": "y = \\frac { 2 \\sqrt { 7 } } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_1467.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the formula for the given image using LaTeX format, we can use the following steps:\n\n1. Identify the variables in the image.\n2. Write the mathematical expression for each variable.\n3. Use LaTeX syntax to format the mathematical expressions.\n4. Write the LaTeX code for the entire formula.\n\nHere is the LaTeX code for the formula for the given image:\n\n\\begin{center}\n\\begin{align*}\nI = \\frac{Q}{t}\n\\end{align*}\n\\end{center}\n\nwhere\n\n* $I$ is the current",
        "gt_answers": "0 < x < \\frac { 2 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1469.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{\\text{Im}\\left(\\frac{1+i}{2}\\right)}{\\sqrt{\\left(\\frac{1+i}{2}\\right)^2 + 1}} = \\frac{1+i}{2}$$\n\nIn LaTex, the formula is written as:\n\n$$\\frac{\\text{Im}\\left(\\frac{1+i}{2}\\right)}{\\sqrt{\\left(\\frac{1+i}{2}\\right)^2 + 1}} = \\frac{1+i}{2}$$",
        "gt_answers": "1 1 x = \\frac { 2 2 } { 5 } \\times \\frac { 1 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_1470.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in LaTeX format for the given image is: $\\text{ImageContent}$.",
        "gt_answers": "A E = 3 0 \\sqrt { 3 } - 3 0 + 4 0 = 3 0 \\sqrt { 3 } + 1 0\n",
        "image_path": "./data/HME100K/test_images/test_1472.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \\frac{a^2 + b^2}{2a}\n\nThis formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.\n\nIn this case, the length of the hypotenuse is represented by the variable a, and the other two sides are represented by the variables b and c. Using the Pythagorean theorem, we can write",
        "gt_answers": "\\frac { 1 } { 6 } x = \\frac { 1 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1474.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$2x + 4y = 6$$",
        "gt_answers": "P = - 5 + 2 6 Q = 3 + t\n",
        "image_path": "./data/HME100K/test_images/test_1475.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written in the image is given below:\n\n$$\\frac{P\\_{ij}}{Q\\_{ij}} = \\frac{P\\_{i}}{Q\\_{i}} - \\frac{P\\_{j}}{Q\\_{j}}$$\n\nThis formula calculates the ratio of the pressure in cell ij to the pressure in cell i and j, respectively.",
        "gt_answers": "7 2 0 \\div 2 = 3 6 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1477.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the following LaTeX expression:\n\n$$A = l \\times w$$\n\nwhere $l$ is the length of the rectangle and $w$ is the width of the rectangle. The formula shows that the area of a rectangle is equal to the product of its length and width. This is a fundamental concept in geometry and is used to calculate the area of rectangles in a variety of contexts.",
        "gt_answers": "a = \\pm 2\n",
        "image_path": "./data/HME100K/test_images/test_1478.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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 the equation b = l fd.",
        "gt_answers": "\\angle B = \\angle F D C\n",
        "image_path": "./data/HME100K/test_images/test_1479.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is $\\frac{1}{2}x^2 + 3x - \\frac{1}{3}$.\n\nThe equation represents a parabolic function with a vertex at the origin, and a maximum value of $\\frac{1}{2}$ at the peak. The equation also has a minimum value of $3$ at the left end of the parabola. The equation is symmetric about the y-axis.",
        "gt_answers": "x _ { 1 } = \\frac { 3 + \\sqrt { 5 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1480.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{1}{2}$.",
        "gt_answers": "C \\equiv c - c - c - c \\equiv c\n",
        "image_path": "./data/HME100K/test_images/test_1481.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX format for the given expression:\n\n\\begin{center}\n$x^3+6x^2+11x+12$\n\\end{center}\n\nThis is the expression for a cubic equation with integer coefficients.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is: y = (x + 5) / (x - 3).",
        "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",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula written in LaTeX format with two variables, x and y, and a constant, k. The formula is: f(x) = kx^2 + 2x - 3y^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation for the number of positive integers that are greater than 5. The formula is: (5 + x) / 2, where x is a variable representing the number of positive integers. The image shows the equation for the number of positive integers that are greater than 5. The formula is: (5 + x) / 2, where x is a variable representing the number of positive integers.\n\nNote: This formula assumes that x is a positive integer. If x is not a positive integer, the result may not be correct.",
        "gt_answers": "x = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1485.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 12(x+5)2+6x32+12x23+x2\u221212x+52+5x2\u2212x2+5x\u2212152+5x2\u2212x2+5x\u2212152+5x2\u2212x2+5x\u2212152+5x2\u2212x2+5x\u2212152+5x2\u2212x2+5x\u2212152+5x2\u2212x2+5x\u2212152+5x2\u2212x2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you have provided as it is not accessible. Please provide a different image or make it accessible so that I can assist you.",
        "gt_answers": "\\angle E B C = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1487.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX format for the expression in the image:\n\n$$ \\text{16}\\times\\text{4} + \\text{3} = \\text{4}\\times\\text{16} + \\text{3} = \\text{64} + \\text{3} = \\text{67} $$\n\nWhere $\\text{16}$, $\\text{4}$, $\\text{3}$ are mathematical operators and $\\text{64}$, $\\text{67}$ are mathematical expressions.",
        "gt_answers": "1 3 + x = \\frac { 1 } { 2 } ( 4 7 + x )\n",
        "image_path": "./data/HME100K/test_images/test_1488.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is as follows:\n\n$$ 2(1/4) = 0.5 $$\n\nThe expression is in the form of a conditional statement, which is true only if the condition is true. In this case, the condition is that the expression 1/4 is greater than or equal to 0, which is true. Therefore, the entire expression is true and evaluates to 0.5.",
        "gt_answers": "\\therefore D E = x\n",
        "image_path": "./data/HME100K/test_images/test_1490.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$ 2 + 2 = 4 $$\n\nThe formula is a simple arithmetic expression that adds two numbers together to get four. The equation shows that two plus two equals four, which is a basic mathematical principle. The LaTeX format is used to write mathematical equations in a clear and concise manner, making it easier to read and understand the formula.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{d \\left( \\frac{a + b}{c + d}\\right)}{e - f}$ where a, b, c, d, e, and f are constants.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x}{2}$.",
        "gt_answers": "2 ( a _ { 0 } + a _ { 2 } + \\cdots + a _ { 1 0 } )\n",
        "image_path": "./data/HME100K/test_images/test_1493.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the expression of the formula in the image using LaTeX format:\n\n\\begin{align}\nx^2 + 6x - 8 &= 0 \\\n\\end{align}\n\nThe equation is a quadratic equation in the form of $ax^2 + bx + c = 0$. To solve it, we use the quadratic formula:\n\n\\begin{align}\nx = (-b \u00b1 \u221a(b^2 - 4ac)) / 2a\n\\end{align}\n\nPlugging in the values of $a = 1$,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is written in LaTeX as follows:\n\n$$m = \\frac{1}{2}m\\_0 - \\frac{1}{4}k\\_1 + \\frac{1}{2}k\\_2$$\n\nwhere m is the mass of the object, m\\_0 is the initial mass of the object, k\\_1 is the spring constant of the first spring, k\\_2 is the spring constant of the second spring, and the minus signs indicate the direction of the spring force.",
        "gt_answers": "y = \\frac { W } { Q }\n",
        "image_path": "./data/HME100K/test_images/test_1495.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression written in LaTeX format. The formula is shown below:\n\n$$ \\frac{m\\_{1}+m\\_{2}}{2m\\_{1}+m\\_{2}} $$\n\nThis is the formula for the average of two measurements. The numerator is the sum of the two measurements, while the denominator is their sum. The result is the average of the two measurements.",
        "gt_answers": "m ^ { 2 } - ( 2 \\cos \\alpha + 6 3 i n \\alpha ) m + 6 = 0\n",
        "image_path": "./data/HME100K/test_images/test_1496.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$E = mc^2$$\n\nwhere E is the energy of the object, m is its mass, and c is the speed of light.",
        "gt_answers": "x ^ { 2 } + 2 x = 3\n",
        "image_path": "./data/HME100K/test_images/test_1497.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am unable to see the image you provided. Can you please provide the image or a different question?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=1.5]\n\\draw (0,0) -- (1,0) node[midway, above] {$ 3$};\n\\draw (0,1) -- (1,1) node[midway, left] {$ 4$};\n\\draw (0,2) -- (1,2) node[midway, right] {$ 5$};\n\\draw (1,0) -- (1,1) node[midway, above]",
        "gt_answers": "\\frac { 5 } { 6 } < \\frac { 5 } { 7 } < \\frac { 5 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1499.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for finding the median of a data set, with the median represented by the middle value in the set of numbers. To calculate the median, you need to find the middle value in the set of numbers, which can be done by sorting the data in ascending order and finding the middle value. The median is then represented by the middle value in the set of numbers.",
        "gt_answers": "\\frac { 1 } { a _ { 1 } - 1 } = 1 ,\n",
        "image_path": "./data/HME100K/test_images/test_1500.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: m = 1/(1+x2)2x1.",
        "gt_answers": "m = - \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1502.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is:\n\nA = \u03c0r^2,\n\nwhere A is the area, \u03c0 is the mathematical constant, r is the radius, and ^2 denotes exponentiation.",
        "gt_answers": "\\frac { A D } { B D } = \\frac { B D } { D C }\n",
        "image_path": "./data/HME100K/test_images/test_1503.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is not clear from the provided image. Please provide a clearer image or more information on the equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n$ $ \\frac{1}{2} $ $ \\frac{2}{3}$ $\\frac{4}{5} $ $\\frac{6}{7} $ $\\frac{8}{9} $ $\\frac{10}{11} $ $\\frac{12}{13}$ $\\frac{14}{15} $ $\\frac{16}{17}$ $\\frac{18}{19} $ $\\frac{20}{21} $ $\\frac{22}{23} $ $\\frac",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in LaTeX format is: $\\frac{x}{y+z}$",
        "gt_answers": "x = 1 . 3 5 \\times \\frac { 1 0 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_1508.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given as: $\\frac{4\\times 3 + 5\\times 2}{2\\times 5 + 3\\times 4}$\n\nThe image shows the formula written as:\n\n$\\frac{4x + 3y + 5z}{2w + 3v}$\n\nwhere x, y, z and w are variables and x, y, z and v are constants.",
        "gt_answers": "( 4 + 2 ) \\times ( 4 - 1 ) \\neq 0\n",
        "image_path": "./data/HME100K/test_images/test_1509.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the expression in the image:\n\n\\frac{(4)(16)(15)(30)(30)}{(16)(30)(14)(4)(16)} \\cdot \\frac{(16)(30)(24)(25)(26)}{(16)(30)(24)(1)(30)} \\cdot \\frac{(16)(15)(24)(30)(30)}{(16)(15)(24)(30)(16)} \\cdot \\frac{(30)(30)(",
        "gt_answers": "4 ( 2 ) . A H = P H\n",
        "image_path": "./data/HME100K/test_images/test_1510.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given formula:\n\n$$\\begin{aligned}3\\times 4 + 2\\times 5 &= 3\\times 9 + 2\\times 10\\end{aligned}$$\n\nExplanation:\n\n* The expression given is $\\frac{3\\times 4 + 2\\times 5}{3\\times 9 + 2\\times 10}$.\n* To simplify the expression, we can use the distributive property of multiplication over addition, which states that $\\frac{a\\times b + c}{",
        "gt_answers": "\\frac { 8 } { 1 3 } > \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1511.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by: 64x - 32y + 42 = 0",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not provided, as it is unclear what the formula represents. Please provide the formula so that I can assist you with the LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image you provided is:\n\n$$ f(x) = \\frac{2}{x+2} $$",
        "gt_answers": "a _ { n } = \\frac { n + 1 } { n }\n",
        "image_path": "./data/HME100K/test_images/test_1516.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{4}{9} + \\frac{1}{4} = \\frac{3}{12}$\n\nThis equation is derived by adding the fractions $\\frac{4}{9}$ and $\\frac{1}{4}$, which represent the number of heads and tails in the image, respectively. The result is then simplified by dividing both numerator and denominator by $4$, which gives the final fraction $\\frac{3}{12}$",
        "gt_answers": "\\frac { 1 5 } { 7 } = 2 \\frac { 1 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_1517.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the image:\n\n\\begin{center}\n\\begin{equation}\n2x^2 + 2 = 6\n\\end{equation}\n\\end{center}\n\nThe equation is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 2$, $b = 2$, and $c = 6$. To solve the equation, we can use the quadratic formula:\n\n$$x = \\frac{-b \u00b1 \\sqrt{b^2 - 4ac}}{2a",
        "gt_answers": "a = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1518.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{x^3+x^2-6x+5}{x^3-6x^2+11x+5} $$",
        "gt_answers": "l y _ { 2 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1519.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:\n\n\\begin{equation}\na + 2b = 5\n\\end{equation}",
        "gt_answers": "B F = y . = 1 2 \\sqrt { 2 } = E F\n",
        "image_path": "./data/HME100K/test_images/test_1520.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: 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 + 18",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{a + b}{c + d}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$$ \\frac{1}{2} \\left( \\frac{1}{2} + \\frac{1}{4}\\right)$$In LaTeX format, the equation can be written as:$$\\frac{1}{2}\\left(\\frac{1}{2}+\\frac{1}{4}\\right)$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the derivative of f with respect to x is given by:",
        "gt_answers": "A B = 6\n",
        "image_path": "./data/HME100K/test_images/test_1526.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the triangle in the image is: A = (1/2)bh, where b is the base of the triangle and h is the height. This is a special case of Heron's formula for the area of a triangle, which states that the area of a triangle is equal to 1/2 the sum of its sides. In this case, the base of the triangle is 6 and the height is 8, so the area of the triangle is 8 + 6 = 14.\n\nNote that this is a Heron's formula for a right triangle",
        "gt_answers": "2 x = \\frac { 1 } { 2 0 } \\times 8\n",
        "image_path": "./data/HME100K/test_images/test_1527.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical formula written in LaTeX format. The formula is: $\\frac{a}{b+c}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX formula for the expression in the image:\n\n$$\\begin{aligned}\n\\frac{\\frac{a}{b}+\\frac{c}{d}}{e}+\\frac{f}{g}+\\frac{h}{i}+\\frac{j}{k}+\\frac{l}{m}+\\frac{n}{o}+\\frac{p}{q}+\\frac{r}{s}+\\frac{t}{u}+\\frac{v}{w}}{x}+\\frac{y}{z}\n\\end{aligned}$$\n\nThis formula is a sum of products of fractions with",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}3x^2+2x-5\\end{aligned}$$",
        "gt_answers": "x = \\frac { 1 3 } { 1 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1530.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is:\n\nwhere:\n\nm is the mass of the manure\ng is the acceleration due to gravity\nh is the height of the manure\n\nThis equation is the formula for the work done by gravity on an object. The work done by gravity on the manure as it falls from the top of the pile to the bottom is equal to the energy expended by the manure as it falls through the air.\n\nTo calculate the work done by gravity, we need to find the force of gravity acting on the manure, which is equal to the mass of the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am not able to see the image that you have provided. Please upload the image or provide a description of the image so I can assist you.\n\nHere is the LaTeX formula for the expression on the image, assuming the variables are x and y:\n\n$x^2 + 2y^2 = 1000$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 3x^2 + 2x + 1 = 0 $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{10}{5\\sqrt{3}}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Select the formula and copy it to the clipboard.\n2. Open a LaTeX editor, such as Overleaf, and create a new document.\n3. Paste the formula into the document and format it using LaTeX syntax.\n4. Compile the document to see the formula in its LaTeX format.\n\nHere is the LaTeX code for the formula:\n\n$$\\frac{x\\left(\\frac{3}{x+5}\\right)^2}{x+1}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "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$$\\text{ImageContent}\\text{ ImageContent} = \\text{ImageContent}\\left( \\frac{\\text{ImageContent}}{\\text{ImageContent}} \\right) \\text{ ImageContent}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: m = 3i - 5j + 4k.\n\nThis formula is derived from the image, where the coefficients of the monomials are given as 3, -5, and 4, respectively. The constant term is -5i, and the leading coefficient is 1. Therefore, the equation can be written as follows:\n\nmx + b = 0\n\nwhere m = 3i - 5j + 4k and b = -5i. This is a system of linear equations in three variables, which can be solved using the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\nn & = & 2k+1 \\\\\nx & = & \\frac{2}{2k+1} \\\\\ny & = & \\frac{2k-1}{2k+1} \\\\\nz & = & \\frac{k}{2k+1}\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The chemical formula for chlorine is Cl2.\n\nThe subscript indicates that there are two atoms of chlorine in the compound.\n\nThe superscript indicates that the compound is a diatomic molecule, meaning it has two atoms that are chemically bonded together.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX format for the expression of the formula in the image:\n\n\\begin{equation} \\text{The area of the image is } \\frac{1}{2}\\pi r^2.\\end{equation}\n\nIn this equation, $r$ is the radius of the circle, which is equal to $10$ cm.\n\nTo calculate the area of the image, we use the formula $\\text{A = \u03c0r^2}$:\n\n\\begin{equation} \\text{A = \u03c0r^2} \\Rightarrow \\text{A =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:<latex>p=&#x2212;&#x2212;(k/r)2&#x2212;mgh</latex>Where,p is the pressure, k is the spring constant, r is the radius of the spring, m is the mass of the object attached to the spring, and g is the acceleration due to gravity.",
        "gt_answers": "A O B C = ( A O + B\n",
        "image_path": "./data/HME100K/test_images/test_1544.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\\begin{align} we & = x^2 + 3x - 2 \\\n\n we & = \\frac{x^2 + 3x - 2}{x^2 + 2x - 3} \\\n\n we & = \\frac{x^2 + 3x - 2}{(x + 1)(x + 2)} \\\n\n we & = \\frac{x^2 + 3x - 2}{x^2 + 2x - 3} \\\n\n we & = \\frac{2x^2 + 3x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: 100 + 50x + 30x^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n\\begin{center}\n\\begin{align}\nx &= 2 \\times 3 - 4 \\times 5 \\\n&= 2(3-5)+5(3-4) \\\n&= 2(3-2)+5(2-4) \\\n&= 2+5 \\\n&= 7\n\\end{align}\n\\end{center}\n\nI hope that helps!",
        "gt_answers": "O B = B D = C D = O C\n",
        "image_path": "./data/HME100K/test_images/test_1547.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $ $ \\frac{x}{y} = 1 $ $\\frac{y}{x} = 4$ $\\frac{x+y}{x} = 3$ $\\frac{y+x}{y} = 4$ $\\frac{x}{y+x} = \\frac{1}{4}$ $\\frac{y}{x+y} = \\frac{4}{3}$ $\\frac{x}{y+x+x} = \\frac{1}{4}$ $\\frac{y}{y+x+y} =",
        "gt_answers": "\\frac { 1 } { 3 y + 4 } = b\n",
        "image_path": "./data/HME100K/test_images/test_1549.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image provided. Please provide a different image for me to work with.",
        "gt_answers": "\\angle H \\angle C = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1550.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for finding the length of the hypotenuse of a right angled triangle is given by the Pythagorean theorem: c^2 + b^2 = a^2, where c is the length of the hypotenuse, b is the length of the other leg, and a is the length of the third leg. In this case, the length of the hypotenuse is 20 cm. The length of the other leg is 15 cm, and the length of the third leg is 10 cm. Therefore, the length of the hypotenuse is 20 cm.##",
        "gt_answers": "\\frac { x ^ { 2 } - 2 } { x + 3 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_1551.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:$$\\frac{256}{10}$$This formula calculates the number of seconds in a day.\n\nNote that the formula in the image has a syntax error, as there is a missing multiplication symbol between the numerator and denominator. The correct formula would be:$$\\frac{256\\times 10}{10}$$This formula calculates the number of seconds in a day.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that.\n\nThe equation in the image is:\n\ny = a - bx\n\nwhere 'a' and 'b' are constants, and 'x' is the independent variable.\n\nNote that this is a linear equation, which means that the graph of the equation is a straight line.\n\nThe slope of the line is given by 'b', which represents the rate at which the value of 'y' changes as 'x' changes. The y-intercept is given by 'a', which represents the value of 'y' when 'x' is equal",
        "gt_answers": "( y - 1 ) ^ { 2 } + 2 y ^ { 2 } - 1 = 0\n",
        "image_path": "./data/HME100K/test_images/test_1553.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n\\begin{center}\n\\begin{equation}\n3x^2 + 4x - 5 = 0\n\\end{equation}\n\\end{center}\n\nThis equation represents a quadratic equation in standard form with coefficients 3, 4, and -5. The solutions to this equation can be found using the quadratic formula:\n\nx = (-b \u00b1 \u221a(b^2 - 4ac)) / 2a\n\nwhere a, b, and c are the coefficients of the quadratic equation:",
        "gt_answers": "W = \\frac { 2 \\pi } { 1 6 } = \\frac { \\pi } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1554.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:\n\n$$\\frac{x^2 + (2n+1)x + 2n^2 - (n+1)^2}{2x + (n+1)}$$\n\nThis is a quadratic formula with the variable x and the parameter n. The numerator is the sum of the square of x and a polynomial in x and n with degree 2. The denominator is the sum of 2x and a polynomial in x and n with degree 1.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the image:\n\n$$\\frac{3+3}{2}$$\n\nThis formula evaluates to 6.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the resistance of a wire is given by R = (V/I) where V is the voltage across the wire and I is the current flowing through the wire. Using this formula, we can find the resistance of a wire with a voltage of 120 V and a current of 5 A.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is $\\frac{x^2 + 3x - 4}{x + 2}$.",
        "gt_answers": "\\frac { 9 0 } { x } = \\frac { 1 3 5 } { x + 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1558.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe given formula in the image is\n\n$$ \\begin{aligned} x &= \\frac{a}{b} \\\n&= \\frac{c}{d} \\\n&= \\frac{e}{f} \\\n&= \\frac{g}{h} \\\n&= \\frac{i}{j} \\\n&= \\frac{k}{l} \\\n&= \\frac{m}{n} \\\n&= \\frac{o}{p} \\\n&= \\frac{q}{r} \\\n&= \\frac{s}{t} \\\n&= \\frac{u}{v} \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n\u222bdA/dt = \u222bd(\u222bdx dy) / dt = \u222b(\u222bdy dx) / dt = \u222b dy dx = yx - y - xy + C\n\nThe constant of integration (C) can be determined by applying the fundamental theorem of calculus to each integral.\n\u222bCdx = C\n\u222bCdy = C\n\u222bCdx dy = \u222bCdy dx + \u222bCdx dy\n\nThe integral of each differential is a constant, so the constant of integration (C) can be evaluated by solving for",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n\\begin{align}\na + b = c\n\\end{align}\n\nThis formula is a simple arithmetic expression that states that the sum of two numbers is equal to a third number. The letters a, b, and c represent the numbers being added together, and the equation symbol \"=\" indicates that the two sides of the equation are equal.\n\nNote that this formula could represent any number of different mathematical expressions, depending on the values of a, b, and c. For example, if a = 2, b =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle with length a and width b can be written as:\n\nA = ab\n\nwhere A is the area and a and b are the length and width, respectively.",
        "gt_answers": "x \\geq \\frac { 5 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1563.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\text{ImageContent} = \\frac{1}{\\sqrt{1^2 + (200 - 1)^2}}$$\n\nwhere $\\text{ImageContent}$ is the value of the expression.",
        "gt_answers": "C u O + H _ { 2 } S O _ { 4 } = C u S O _ { 4 } + H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_1564.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression given in the image is:\n\n$$\\frac{x^4 + x^3 - 5x^2 + 4x - 2}{x^2 - 2x + 1}$$\n\nThis can be simplified by factoring the numerator and denominator:\n\n$$\\frac{(x + 1)(x^3 + x^2 - 5x + 4)}{(x - 1)(x^2 - 2x + 1)}$$\n\nThe simplified expression is a rational function with a single pole at x = 1.",
        "gt_answers": "( a - 1 ) x \\vert a \\vert + 1 - 3 x + 2 = 0\n",
        "image_path": "./data/HME100K/test_images/test_1565.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length $l$ and width $w$ can be written as $A = lw$. This formula can be derived from the definition of area, which is the measure of the amount of space inside a two-dimensional shape. In this case, the rectangle's area is the product of its length and width.",
        "gt_answers": "x = \\frac { 2 } { a }\n",
        "image_path": "./data/HME100K/test_images/test_1568.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}x^2 + \\frac{1}{2}x - 1$.",
        "gt_answers": "y _ { 3 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1569.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{1}{x}+\\frac{1}{x^2}=\\frac{2}{x^2}$$This can be simplified to:$$\\frac{2}{x^2}=\\frac{1}{x}+\\frac{1}{x^2}$$This is a quadratic equation that can be solved using the quadratic formula:$$x=\\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$$where a, b, and c are the coefficients of the quadratic equation. For this particular formula, the coefficients are a =",
        "gt_answers": "x _ { 1 } = \\frac { - 2 + \\sqrt { 4 - 4 a } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1571.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the expression of the formula in the image using LaTeX format:$$\\sum\\_{i=1}^n a\\_i \\cdot x\\_i$$where n is the number of terms in the sum, and ai and xi are the values of the terms.",
        "gt_answers": "1 + 2 n - 3 = a n \\Rightarrow a n = 2 n - 2\n",
        "image_path": "./data/HME100K/test_images/test_1572.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$y = \\frac{3x^2 - 5x + 2}{x^2 - x + 2}$$\n\nThis can be simplified to:\n\n$$y = \\frac{3x^2 - 5x + 2}{x - 1}$$\n\nNote that the denominator is a quadratic equation, which can be factored using the quadratic formula.",
        "gt_answers": "a = \\frac { L } { I } = \\frac { 2 } { 1 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_1573.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX code for the given expression:\n\n\\begin{align\\*}\na &= \\frac{b}{c} \\\n     &= \\frac{b}{d} \\\n     &= \\frac{b}{e} \\\n     &= \\frac{b}{f}\n\\end{align\\*}\n\nIn this expression, the variable `a` is defined as the result of dividing `b` by `c`, `d`, `e`, and `f`. Each division is a fraction with the same numerator (`b`) and denominator (`c`, `d`,",
        "gt_answers": "A P ^ { 2 } = \\frac { 2 0 } { 3 } - \\frac { 1 6 } { 3 } \\cdot \\sin ( 2 \\theta + \\frac { 5 } { 6 } \\pi )\n",
        "image_path": "./data/HME100K/test_images/test_1574.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a mathematical expression for the slope of a line. The slope is represented by the symbol (slope) and is calculated as the change in y divided by the change in x.\n\nIn the given image, the slope is represented by the symbol (slope) and is equal to (rise) / (run). To write this equation in LaTeX format, we can use the following code:\n\n\\(m = \\frac{rise}{run}\\)\n\nwhere'm' represents the slope, 'rise' represents the vertical change in the line, and 'run",
        "gt_answers": "x _ { 1 } = \\frac { 7 } { 2 } , x _ { 2 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_1575.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} x &= \\frac{2y+3z}{x+2y-z} \\ \\ \\\\ y &= \\frac{4x+6z}{2x+3y-z} \\ \\ \\\\ z &= \\frac{6x+9y}{3x+6y} \\ \\ \\end{aligned}$$",
        "gt_answers": "\\log _ { x } ^ { y } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1577.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: x + y + z = 5.",
        "gt_answers": "- x = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1578.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX expression for the formula in the image:\n\n$$x = \\frac{a}{b} + \\frac{c}{d}$$\n\nThe variables $a, b, c, d$ are defined as follows:\n\n$a = \\frac{m}{n}$\n\n$b = \\frac{p}{q}$\n\n$c = \\frac{r}{s}$\n\n$d = \\frac{t}{u}$\n\nwhere $m, n, p, q, r, s, t, u$",
        "gt_answers": "\\alpha - \\pi = \u3002 \\alpha - \\pi = a v c \\sin \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1579.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression for the formula in the image using LaTeX format:\n\n$$\\text{The final formula is:}$$\n$$\\text{Both formulas are the same.}$$",
        "gt_answers": "k = - \\frac { 1 } { 4 } \\cdot \\frac { 3 2 } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1580.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the given image:\n\n\\begin{center}\n\\begin{equation}\n\\frac{5x^4+6x^3+8x^2+10x+12}{2x^3+3x^2+5x+7}\n\\end{equation}\n\\end{center}\n\nThis expression is a rational function with the numerator being a polynomial of degree 4 and the denominator being a polynomial of degree 3. The fraction is the quotient of these two polynomials.",
        "gt_answers": "( 2 x + n ) ^ { 2 } = 4 x\n",
        "image_path": "./data/HME100K/test_images/test_1581.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the equation for the probability density function of a Poisson distribution. It can be written as:\n\nP(x) = (e^(-\u03bb) \\* \u03bb^x) / x!\n\nwhere x is the number of events and \u03bb is the expected number of events in a given time interval.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is given by the formula: A = (b / 2) \\* h, where b is the base and h is the height. To derive this formula, we can consider a right triangle with sides of length a and h, and hypotenuse of length b. The area of the triangle is then equal to (1/2) \\* a \\* h, which can be simplified using the Pythagorean theorem to give the above formula.",
        "gt_answers": "\\because \\angle C B A = 4\n",
        "image_path": "./data/HME100K/test_images/test_1583.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am unable to see the image you have provided as it appears to be broken. Can you please provide the image again so that I can assist you with your question?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula is as follows:\n\n$$ \\frac{\\partial^2 E}{\\partial t^2} = \\frac{\\partial E}{\\partial t} $$\n\nIn LaTeX format, this can be written as:\n\n$$ \\frac{\\partial^2 E}{\\partial t^2} = \\frac{\\partial E}{\\partial t} $$\nThis formula describes the second derivative of the energy of an object with respect to time. The left side of the equation represents the second derivative of the energy, while the right side represents the first derivative of the energy with respect to time.",
        "gt_answers": "_ { 1 } D E ^ { 2 } = D O \\cdot D B\n",
        "image_path": "./data/HME100K/test_images/test_1585.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the circle with radius 2 can be written as:\n\n$$A = \\pi r^2$$\n\nwhere $r$ is the radius of the circle. Substituting $r=2$ gives:\n\n$$A = \\pi (2)^2 = 4\\pi$$\n\nTherefore, the area of the circle is 4\u03c0 square units.",
        "gt_answers": "1 4 \\times 1 4 = 1 9 6 ( c m ^ { 2 } ) 5 6 \\times 4 2 = 2 3 5 2 ( c m ^ { 2 } ) .\n",
        "image_path": "./data/HME100K/test_images/test_1586.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as:\n\nA = \u03c0r^2\n\nwhere A is the area, r is the radius, and \u03c0 is the mathematical constant pi (approximately equal to 3.14).",
        "gt_answers": "3 . 1 4 \\times 5 ^ { 2 } = 7 8 . 5 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_1587.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is given below.\n\n$$\\text{f}=\\frac{mg}{L}\\left(\\frac{V}{r}\\right)^2\\left(1-\\frac{V^2}{r^2}\\right)$$\n\nIn this formula,\n\n* m is the mass of the object\n* g is the acceleration due to gravity\n* L is the distance between the center of gravity of the object and the point where the object is released from\n* V is the velocity of the object at the time it is released\n* r is the radius of",
        "gt_answers": "x = \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1589.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a mathematical expression using LaTeX format to represent the formula for the sum of two numbers:2+3=523525+32355235+53323553552355235235235235523523523523523523523523523523523523523523523523523523523523523",
        "gt_answers": "\\frac { 3 + 2 } { 3 } = \\frac { 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1591.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is shown in the image. It represents the sum of two numbers and their squares.\n\nFor example, if the number is 3, the expression would be 3 + 3 = 6 and 3^2 = 9.",
        "gt_answers": "x ^ { 2 } - 3 x + ( \\frac { 3 } { 2 } ) ^ { 2 } = - 2 + ( \\frac { 3 } { 2 } ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1592.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{3x + 4y}{2x + 5y}$.\n\nIn this formula, $\\frac$ represents the fraction operation, and the numerator and denominator are written as $3x + 4y$ and $2x + 5y$, respectively. The division bar ($$) is used to separate the numerator and denominator.",
        "gt_answers": "x = \\frac { 2 1 } { 2 8 } - \\frac { 8 } { 2 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1593.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression for calculating the sum of the infinite series: \u2211 (n=1 to infinity) 1/n. This expression can be written in LaTeX format as follows:\n\n\\begin{align\\*}\n\\sum\\_{n=1}^{\\infty} \\frac{1}{n}\n\\end{align\\*}\n\nThis expression represents the sum of an infinite series of terms, each equal to 1/n, where n ranges from 1 to infinity. The notation $\\sum\\_{n=1}^{\\infty}$ indicates that the sum is taken over all integers greater than or",
        "gt_answers": "= \\frac { C D } { C B } = 0 . 6\n",
        "image_path": "./data/HME100K/test_images/test_1594.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a quadratic equation in x. It can be written as:x^2+3x+1=0This equation has two solutions, one positive and one negative. The positive solution is x=1 and the negative solution is x=-3.",
        "gt_answers": "l \\cdot \\frac { 2 } { 5 } x = 3\n",
        "image_path": "./data/HME100K/test_images/test_1595.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 5 - 2x2 + 4x3. This can be written in LaTeX format as follows:\n\n$$ 5 - 2x^2 + 4x^3 $$\n\nThe image shows the equation written on a piece of paper with the variable x in the denominator. This equation represents the equation of a parabolic function with a focus at the origin and a directrix with equation 2x^2 + 4x^3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{align\\*}\nf(x) = \\frac{1}{2} x^2 - \\frac{5}{4} x + \\frac{3}{2}\n\\end{align\\*}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} x &= \\frac{1}{4} \\cdot 3 + \\frac{1}{2} \\cdot 1 + \\frac{1}{4} \\cdot 2 \\\n&= \\frac{1}{4} \\cdot 3 + \\frac{1}{2} \\cdot 1 + \\frac{1}{4} \\cdot 2 \\\n&= \\frac{3}{2} + \\frac{1}{2} + \\frac{1}{4} \\cdot 2 \\",
        "gt_answers": "\\frac { 1 } { 3 } x - \\frac { 1 } { 3 } - \\frac { 1 } { 5 } x = 1 2\n",
        "image_path": "./data/HME100K/test_images/test_1598.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image in LaTeX format is:\n\n$$\\frac{m\\_1 + m\\_2}{2} \\leq \\frac{3m\\_1 + 4m\\_2}{5} \\leq \\frac{2m\\_1 + 3m\\_2}{3} \\leq m\\_1 + 2m\\_2$$\n\nThe inequality states that the average of the two measurements of a physical quantity is less than or equal to the upper bound of the interval, which is less than or equal to the lower bound of the interval. In this case, the measurements of some physical quantity are",
        "gt_answers": "\\angle A B D + \\angle A B C = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1599.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe equation in the image is:\n\nd / dt (m) = (k * m - (m^2)) / m^2\n```",
        "gt_answers": "\\frac { - 1 } { 1 6 } > \\frac { 1 } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1600.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the sum of an arithmetic series is given by:\n\n$$\\sum\\_{i=1}^{n} i = \\frac{n(n+1)}{2}$$\nwhere n is the number of terms in the series. For the given image, the sum of the series would be $\\frac{10\\times 11}{2}=55$.",
        "gt_answers": "x > - \\frac { 7 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1601.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$ E = mc^2 $\n```",
        "gt_answers": "O _ { 2 } + 4 e ^ { - } + 2 H _ { 2 } O = 4 O H ^ { - }\n",
        "image_path": "./data/HME100K/test_images/test_1602.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:$$\\frac{a}{b} = \\frac{c}{d}$$This formula expresses the ratio of two fractions, with $a$ and $b$ on the left and $c$ and $d$ on the right.",
        "gt_answers": "\\angle B O C = 9 0 - 2 0 = 7 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1603.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$\\begin{aligned}x^2 + 3x + 5 &= 0\\quad \\Rightarrow \\quad x = - \\frac{3}{2} \\lor x = \\frac{5}{2}\\end{aligned}$$\n\nThis equation is obtained by solving the quadratic equation $x^2 + 3x + 5 = 0$ for $x$. The solution is obtained by using the quadratic formula: $x = -b \\pm \\sqrt{b^2",
        "gt_answers": "\\frac { 5 } { 6 } = \\frac { 5 \\times 3 } { 6 \\times 3 } = \\frac { 1 5 } { 1 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1605.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the volume of a cylinder is given by:V = (r\u00b2h). In this case, the radius of the cylinder is 1.5 feet, the height is 6 feet, and the volume is 9.314 cubic feet.",
        "gt_answers": "S 2 x ^ { 2 } - y ^ { 2 } - 7 = 0 \\textcircled { 1 }\n",
        "image_path": "./data/HME100K/test_images/test_1606.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression of the formula in the image using LaTeX format:\n\n$$\\frac{x\\_{1}}{x\\_{2}} = \\frac{1 + \\frac{3}{2} - \\frac{1}{4}}{1 + \\frac{3}{4}} = \\frac{7/4}{5/4} = \\frac{14}{20} = 0.70$$",
        "gt_answers": "\\Delta B D E \\sim \\Delta E D O\n",
        "image_path": "./data/HME100K/test_images/test_1607.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$c(2H\\_4)+c(2H\\_6)\\rightarrow c(2H\\_6)+c(2H\\_4)$",
        "gt_answers": "C u ( O H ) _ { 2 } + 2 H C l = C u C l _ { 2 } + 2 H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_1608.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\nx^2 - (a^2 + b^2) = (a - b)(a + b)\n\nwhere a and b are the lengths of the two sides of the triangle.",
        "gt_answers": "\\frac { 1 0 0 x + 2 0 0 } { 2 5 } + \\frac { 1 0 x } { 5 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1610.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$x^2+y^2=r^2$$where x and y are the coordinates of the point on the circle and r is the radius of the circle.",
        "gt_answers": "\\therefore \\tan \\alpha = - \\frac { 2 \\sqrt { 2 } } { 1 } = - 2 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1612.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the expression in the image is:\n\n![Equation in LaTeX format](https://latex.codecogs.com/svg.image?%5C%5C%5C%5C3%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%",
        "gt_answers": "2 \\angle 3 + 2 \\angle 4 = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1614.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is 2x+4y=12. It can be written in LaTeX format as:\n\n$$ 2x + 4y = 12 $$\n\nThe equation represents a line in the x-y plane, with a slope of 2 and an y-intercept of 4. The equation is a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.",
        "gt_answers": "A E = \\sqrt { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_1615.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{a+b}{c+d}$$where a, b, c, and d are the integers in the image. The expression can be rearranged to get the same result:$$\\frac{a-c}{b-d}$$",
        "gt_answers": "y + 3 \\cdot \\frac { 1 } { y } = 4\n",
        "image_path": "./data/HME100K/test_images/test_1616.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by:\n\nA = \u03c0r\u00b2\n\nwhere \u03c0 is the mathematical constant approximately equal to 3.14.\n\nThe expression can also be written in LaTeX format as:\n\nA = \\pi r^2",
        "gt_answers": "c = \\sqrt { 6 } + \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1617.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \u2211\\_{i=1}^{n} (x\\_i - x\\_{i+1}) \\* (y\\_i - y\\_{i+1}) + c, where x\\_1, x\\_2,..., x\\_n are the data points and y\\_1, y\\_2,..., y\\_n are the corresponding error terms. The constant c represents the intercept of the line of best fit.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is given by: $\\text{c} = \\frac{1}{2}\\text{v}^2$. This formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Applying this theorem to the image, we have $\\text{c} = \\frac{1}{2}(\\text{v} + \\text{u})^2$. Solving for $\\text{c}$ gives $\\text{",
        "gt_answers": "C _ { n } ^ { 0 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1619.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n<LaTeX code>\n$$ f(x) = \\frac{1}{x} $$\n</LaTeX code>\n\nThis formula states that the derivative of x with respect to x is equal to 1 divided by x.",
        "gt_answers": "B r _ { 2 } > C N _ { 2 } > I _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1620.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is:$$ x^4 + 4x^3 + 6x^2 + 4x + 1 = 0$$This equation represents a fourth degree polynomial equation with four terms. The coefficients of the equation are $1, 4, 6, 4,$ and $1$, respectively.",
        "gt_answers": "\\frac { 4 - a ^ { 2 } } { a ^ { 2 } - 2 a } = \\frac { ( 2 + a ) \\times ( 2 - a ) } { a ( a - 2 ) } = - \\frac { 2 + a } { a }\n",
        "image_path": "./data/HME100K/test_images/test_1621.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{n(n+1)}{2}$. This can be written in LaTeX format as $\\frac{n(n+1)}{2}$.",
        "gt_answers": "7 \u3001 5 7 0 0 \\times 2 4 0 = 1 3 6 8 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_1625.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the number of integers less than 100 that are multiples of 5 can be written as follows:\n\nnumber of integers less than 100 that are multiples of 5 = (number of integers less than 100 that are multiples of 2) x (number of integers less than 100 that are multiples of 20) x (number of integers less than 100 that are multiples of 50) x (number of integers less than 100 that are multiples of 100)\n\n= (",
        "gt_answers": ": \\frac { 1 2 } { 6 0 } = 2 0 9 0\n",
        "image_path": "./data/HME100K/test_images/test_1626.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n$$\\begin{aligned} \\text{ImageContent} \\ &= \\frac{1}{2}(2x + 3y) - \\frac{1}{4}(x^2 + y^2) \\ &= \\frac{1}{2}x + \\frac{5}{4}y \\ &= x + \\frac{5}{2}y \\ &= x + \\frac{5}{4}y + \\frac{1}{4}x^2 + \\frac{1}{4}y^2 \\ &=",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the sum of the two fractions. To write it out in LaTeX format, you can use the following code:\n\n\\begin{align\\*}\n2(x^2 + 2x) - 5x + 3 &= 2x^2 + 2x - 5x + 3\\\n&= 2x(x + 1) - 5x + 3\\\n&= 2x - 5x + 3 + x(x + 1)\\\n&= x^2 - 5x + 3 + x(x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{10 - 4}{2}$.",
        "gt_answers": "\\frac { 7 } { 1 0 } = \\frac { 2 8 } { 4 0 }\n",
        "image_path": "./data/HME100K/test_images/test_1630.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is as follows:\n\n\\begin{aligned}\n\\frac{1}{2}x^2 + 10x - \\frac{1}{3} &= \\frac{100}{9} \\\n\\end{aligned}\nThe above equation represents the equation of a parabola with vertex at the origin and passes through the point (0, 20). The equation can be graphed using the x- and y-intercepts and the given point. The x-intercept is found by setting x equal to zero in the equation,",
        "gt_answers": "7 \u3001 \\sqrt { \\frac { 4 } { 9 } } = \\pm \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1631.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{x^2+y^2}{2x}=\\frac{x^2+y^2}{2x}$$\nThis is a true statement because it is equivalent to the original equation, which is true.",
        "gt_answers": "x = \\frac { 1 } { a - 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1632.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by:$$ \\text{Image Content} = 2\\times 100 + 3\\times 500 + 5\\times 3000 + 8\\times 1000 + 10\\times 5000 + 15\\times 10000 + 20\\times 20000 + 25\\times 50000 + 30\\times 100000$$This is the sum of the areas of the rectangles in",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">f</mi><mi mathvariant=\"normal\">(</mi><mi>x</mi><mi mathvariant=\"normal\">,</mi><mi>y</mi><mi mathvariant=\"normal\">)</mi><mo>=</mo><mfrac><mn>0</mn><mn>0</mn></mfrac><mi mathvariant=\"normal\">.</mi",
        "gt_answers": "O B = \\frac { 1 } { 2 } A C = A O\n",
        "image_path": "./data/HME100K/test_images/test_1635.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The expression for the formula in the image is:$$ \\frac{2\\sqrt{x^2 + 4y^2}}{x + y}$$The image shows a graph of this function with the equation x = 0. I can also provide the LaTeX code for the formula if you need it. Let me know if you have any questions or if there's anything else I can help with.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{dv}{dt} = \\frac{F}{m}$$where $v$ is the velocity of the object, $t$ is time, $F$ is the force applied to the object, and $m$ is the mass of the object.",
        "gt_answers": "x _ { 4 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1638.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:$\\sqrt{\\frac{x^2+y^2}{2}}$\\. The formula represents the distance between two points in a two-dimensional space. The numerator is the sum of the squares of the x and y coordinates of the two points, and the denominator is the square root of the sum of the squares of the x and y coordinates of the two points.",
        "gt_answers": "8 \\times 1 2 = 9 6 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_1639.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you have provided. Please make sure the image is in a format that can be displayed, such as a.png or.jpeg file.",
        "gt_answers": "8 2 0 < 8 0 0\n",
        "image_path": "./data/HME100K/test_images/test_1640.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a triangle with base angle 45 degrees and height h is given by:\n\nA = (1/2)bhsin\u03b8\n\nwhere b is the base of the triangle and \u03b8 is the angle between the base and the height.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:$$\\frac{1}{2}\\left(\\frac{5\\times 3}{x^2}+\\frac{2\\times 7}{x}\\right)$$where x is the variable.\n\nThe image shows a graph of a quadratic function with a maximum point at x = 5 and a minimum point at x = -1. The graph opens upward and has a vertex at x = 0. The quadratic function has a constant term of 2x^2, a linear term of 5x, and a linear term of 7.\n\nThe vertex of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the triangle can be written as:\n\nA = (1/2) \\* (2)(2)(3) \\* 2 = 36\n\nThe perimeter of the triangle can be written as:\n\nP = 3 + 4 + 5 = 12\n\nAnd the height can be written as:\n\nh = 5",
        "gt_answers": "4 \\times 3 \\times 3 = 3 6 ( c m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_1645.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\documentclass[12pt,a4paper]{article}\n\\usepackage{graphicx}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{center}\n\\begin{tikzpicture}\n\\node at (0,0)[inner sep=0pt, outer sep=0pt, anchor=center, font=\\Large\\sffamily]\n{\\includegraphics[width=0.5\\textwidth]{image.png}};\n\\end{tikzpicture}\n\\end{center}\n\n\\end{document}\n```",
        "gt_answers": "y = - \\frac { \\sqrt { 1 0 } } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1646.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\n$$x = \\frac{y}{2} - \\frac{z}{2}$$\n\nThis is the equation for a line that passes through the points $(0, 0, 1)$ and $(1, 1, 1)$.",
        "gt_answers": "\\frac { 2 5 } { 9 } x ^ { 2 } = 1 6\n",
        "image_path": "./data/HME100K/test_images/test_1648.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the formula for the derivative of f(x) = x^2, which is 2x.",
        "gt_answers": "y _ { 3 } = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1650.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $\\sin^2\\theta + \\cos^2\\theta = 1$. This can be derived from the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two sides is equal to the square of the length of the hypotenuse. In this case, the hypotenuse is $\\sin\\theta$ and the two sides are $\\cos\\theta$ and $\\cos\\theta$.\n\nTo derive this formula from the Pythagorean theorem, we first write out the theorem:\n\n$$c^2",
        "gt_answers": "+ y ^ { 2 } + y ^ { 2 } - 6 y + 1 0 = 1 0 .\n",
        "image_path": "./data/HME100K/test_images/test_1651.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we need to identify the variables and apply the given rules to the formula. Here is the LaTeX expression for the formula:\n\n&x\\mathrm{A}\\mathrm{B}\\mathrm{C}\\mathrm{D}\\mathrm{E}\\mathrm{F}x^2+(\\frac{1}{2}\\mathrm{B}^2-\\frac{1}{2}\\mathrm{A}\\mathrm{C}^2-\\frac{1}{2}\\mathrm{D}\\mathrm{F}^2)+(\\frac{1}{3}\\mathrm{A}^",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with base 4 and height 3 can be written as:\n\narea = base x height\narea = 4 x 3\narea = 12 square units\n\nTherefore, the area of the rectangle is 12 square units.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is showing the formula for the area of a rectangle with length l and width w. The formula for the area of a rectangle is A = lw, where l is the length and w is the width. The formula is written in LaTeX format as: A = l \\* w.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: f(x) = 3x - 2. To write it in LaTeX format, you can use the following code:$$f(x) = 3x - 2$$This will give you the equation in the format you specified.\n\nNote: I assumed that the equation in the image is in the form of a function. If it is not, you can modify the equation accordingly.",
        "gt_answers": "1 - x + \\vert 1 2 x + m \\vert \\leq 3 - 2 x\n",
        "image_path": "./data/HME100K/test_images/test_1656.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$E = \\frac{1}{2}mv^2$$\n\nwhere $E$ is the energy of the object, $m$ is the mass of the object, and $v$ is the velocity of the object.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{5\\times 4\\times 1000\\times 0.50}{12\\times 1000\\times 0.50\\times 1000}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Write out the equation in LaTeX format using the equation editor.\n2. Include the image file using the following command:\n```less\n\\begin{center}\n\\includegraphics[width=5cm]{image.png}\n\\end{center}\n```\n3. Replace 'image.png' with the actual file name of the image.\n4. Use the following LaTeX code to write out the equation:\n```css\n\\begin{center}\n\\begin{tikzpicture}",
        "gt_answers": "x > \\frac { 1 } { 8 \\sqrt { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_1659.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image using LaTeX format is: 2 \u00d7 3 \u00d7 4 \u00d7 5 \u00d7 6 = 60.",
        "gt_answers": "\\frac { 2 + 1 3 } { 2 } + 2 - m = 0\n",
        "image_path": "./data/HME100K/test_images/test_1660.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize, but it appears that the image you provided is not displaying properly. Please provide a different image for me to work with.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length l and width w is A = lw.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\frac{a+b+c}{2}$$\n\nThis formula calculates the average of the numbers a, b, and c.",
        "gt_answers": "\\frac { B D } { B A } = \\frac { O E } { A C }\n",
        "image_path": "./data/HME100K/test_images/test_1664.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am unable to see the image you provided. Could you please give me the expression of the formula in the image using LaTeX format?",
        "gt_answers": "x _ { 2 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1665.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $ \\frac{2 \\* z}{a+b}$",
        "gt_answers": "Z n ( N O _ { 3 } ) _ { 2 } + C u = C u ( N O _ { 3 } ) _ { 2 } + Z n\n",
        "image_path": "./data/HME100K/test_images/test_1666.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:p = x + 5y - 3z2p = x + 5y - 3z2p = x + 5y - 3z2p = x + 5y - 3z2p = x + 5y - 3z2p = x + 5y - 3z2p = x + 5y - 3z2p = x + 5y - 3z2p = x + 5y - 3z2p = x + 5y -",
        "gt_answers": "P ( 2 ) = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1667.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given formula:\n\n$$\\frac{1}{3} - \\frac{2}{5} = \\frac{2}{15}$$\n\nIn this formula, we have two fractions with different numerators and denominators. We can combine them into one fraction by using the distributive property of multiplication, which states that we can multiply the numerators and denominators of the fractions together:\n\n$$\\frac{1}{3} \\cdot \\frac{2}{5} = \\frac{2}{3}\\cdot \\frac{5}{3}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of the trapezoid is given by: A = (h \\* w1) + (w2 \\* h2) - h \\* w2, where h is the height of the trapezoid and w1 and w2 are the widths of the trapezoid.\n\nIn the given image, the height of the trapezoid is h = 8 cm and the widths of the trapezoid are w1 = 4 cm and w2 = 5 cm.\n\nTherefore, the area of the trapezoid is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by $A = \u03c0r^2$ where $\u03c0$ is the constant value of pi and $r$ is the radius of the circle. In LaTeX format, the formula would be written as $A = \\pi r^2$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:$$x^2+y^2=r^2$$where x and y are the coordinates of the point on the sphere and r is the radius of the sphere.",
        "gt_answers": "x = \\frac { 5 \\sqrt { b a ^ { 4 } } } { a }\n",
        "image_path": "./data/HME100K/test_images/test_1673.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation for the formula for the area of a triangle. The formula for the area of a triangle is: A = (1/2)bh, where b is the base of the triangle, h is the height of the triangle, and A is the area of the triangle.",
        "gt_answers": "\\frac { 1 } { x - y } = b\n",
        "image_path": "./data/HME100K/test_images/test_1675.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear enough to determine the expression. Can you please provide a clearer image?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} \\text{Image Content} = \\frac{5}{6} \\times \\frac{4}{5} + \\frac{3}{4} \\times \\frac{4}{5} + \\frac{2}{3} \\times \\frac{4}{5} + \\frac{1}{2} \\times \\frac{4}{5} \\end{aligned}$$\n\nThe image shows a set of algebraic expressions arranged in a grid, each expression involving the multiplication of two fractions. The values of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is:\n\n$$\\begin{aligned} f(x) &= x^4 - 4x^3 + 6x^2 - 4x + 1 \\ \\? \\end{aligned}$$",
        "gt_answers": "\\therefore \\Delta = ( - 1 ) ^ { 2 } - 4 ( a - 1 ) \\leq 0\n",
        "image_path": "./data/HME100K/test_images/test_1679.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 0. 006x + 0. 018y + 0. 029z - 0. 112x - 0. 024y - 0. 036z - 0. 108x + 0. 022y - 0. 033z - 0. 080x + 0. 015y + 0. 027z + 0. 100x +",
        "gt_answers": "c = - 6\n",
        "image_path": "./data/HME100K/test_images/test_1681.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by the formula:$$\\frac{100}{x+2y}$$where x and y are integers.",
        "gt_answers": "a + b = 1 5 \\times 2 = 3 0\n",
        "image_path": "./data/HME100K/test_images/test_1682.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 4\\*sin(45)\\*sin(30)\\*sin(60) = 0.3416.",
        "gt_answers": "\\angle 2 = 4 2 ^ { \\circ } ( p i v e n )\n",
        "image_path": "./data/HME100K/test_images/test_1684.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of the triangle in the image is:\n\nA = 0.5 \\* base \\* height\n\nThe base of the triangle is 5 units and the height is 6 units, so the formula is:\n\nA = 0.5 \\* 5 \\* 6\nA = 15 square units\n\nTherefore, the area of the triangle is 15 square units.",
        "gt_answers": "A C = A E + C E = 5 + 5 = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_1685.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 5 cm is:\n\nA = \u03c0r\u00b2\n\nwhere r is the radius of the circle.\n\nTherefore, the area of the circle is:\n\nA = \u03c0(5 cm)\u00b2\n= \u03c0(12.5 cm\u00b2)\n= 3.14159 cm\u00b2\n= 3.14159 square centimeters.",
        "gt_answers": "C O _ { 3 } C = 1 \\cos C = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1686.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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\\begin{align\\*}\nV = \\frac{1}{2}RC\n\\end{align\\*}\n\nwhere V is the voltage across the capacitor, R is the resistance of the resistor, and C is the capacitance of the capacitor.",
        "gt_answers": "O E \\bot D C\n",
        "image_path": "./data/HME100K/test_images/test_1688.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for calculating the speed of an object in motion.\n\nThe speed of an object in motion is given by the formula:\n\nv = \u0394x/\u0394t\n\nwhere \u0394x is the change in position of the object and \u0394t is the change in time.",
        "gt_answers": "\\angle E B F = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1690.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{a\\*h\\_1+b\\*h\\_2+c\\*h\\_3+d\\*h\\_4+e\\*h\\_5+f\\*h\\_6}{a+b+c+d+e+f}$$The variable names are h\\_1, h\\_2, h\\_3, h\\_4, h\\_5, and h\\_6.\n\nIn LaTeX format, the formula would be written as:$$\\frac{a\\*h\\_1+b\\*h\\_2+",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the number of integers greater than 1000 in the image is: n(x > 1000).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $x = \\frac{m\\_{2} - m\\_{1}}{m\\_{1}}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation for the number of electrons in a copper wire. The equation is: x = 4 \\* (1 + 0.001) - (1 + 0.0008) \\* x^2. This equation shows that the number of electrons in the wire is proportional to the number of electrons that would be present if the wire were completely filled with copper atoms.\n\nQuestion: What is the value of x in this equation?\nAnswer: The value of x in this equation is 3.4062.\n\nQuestion: What is the value",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}y &= x^2 - 2x + 1\\end{aligned}$$\n\nThis formula is a quadratic equation in the form of $y = ax^2 + bx + c$, where $a = 1$, $b = -2$, and $c = -1$. The solutions to this equation are the values of $x$ that make the equation true. In this case, the solutions are the roots of the equation, which are the values of $x$ that make the equation equal",
        "gt_answers": "\\sin \\beta = \\frac { \\sqrt { 1 0 } } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_1697.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\frac{x+y}{2}=\\frac{x+z}{2} + \\frac{y+z}{2}\n```",
        "gt_answers": "x = \\frac { 2 0 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_1698.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image can be written as follows:\n\n$$r=\\sqrt{\\frac{35^2+44^2}{2}}=\\sqrt{2184+1785}=2184+1785\\frac{1}{2}=1092.5$$\n\nHere, the numerator is the sum of the squares of the lengths of the two sides of the rectangle, and the denominator is half the sum of the squares of the lengths of the rectangle's two diagonals. The expression simplifies to half the sum of the squares",
        "gt_answers": "R = \\frac { V } { 2 } = \\frac { 3 V } { 0 . 2 5 A } = 1 2 \\Omega\n",
        "image_path": "./data/HME100K/test_images/test_1699.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n$ x = \\frac{a}{b} $\n\nwhere $a$ and $b$ are constants.",
        "gt_answers": "( x - 2 y ) ( x - y ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_1700.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:\n\n$$\\frac{12 - 6}{3 - 1} = \\frac{6}{2} = 3$$",
        "gt_answers": "x = \\frac { 2 5 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1701.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\nThe expression for the area of the circle with a radius of 3.5 cm is given by:\n\nA = \u03c0r^2\n= \u03c0(3.5 cm)^2\n= 3.14159 x (3.5 cm)^2\n= 3.14159 x 12.25 cm^2\n= 37.5676 cm^2\n```",
        "gt_answers": "5 d m = ( 5 0 )\n",
        "image_path": "./data/HME100K/test_images/test_1702.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} A &= \\frac{P\\_{f}}{\\rho\\_{f}} \\\\ B &= \\frac{P\\_{g}}{\\rho\\_{g}} \\\\ C &= \\frac{P\\_{h}}{\\rho\\_{h}} \\end{aligned}$$\n\nwhere $P\\_f$, $\\rho\\_f$, $P\\_g$, $\\rho\\_g$, and $P\\_h$, $\\rho\\_h$ are the pressure and density of fluid $f$, $g$, and $h$, respectively.",
        "gt_answers": "\\angle O A C = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1703.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by A = \u03c0r^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{a}{b}+\\frac{b}{c}+\\frac{c}{d}+\\frac{d}{e}+\\frac{e}{f}+\\frac{f}{g}+\\frac{g}{h}+\\frac{h}{i}+\\frac{i}{j}+\\frac{j}{k}+\\frac{k}{l}+\\frac{l}{m}+\\frac{m}{n}+\\frac{n}{o}+\\frac{o}{p}+\\frac{p}{q}+\\frac{q}{r}+\\frac{r}{s}+\\frac{s}{t}+\\",
        "gt_answers": "3 ( x - 2 ) - ( x - 1 ) = x ^ { 2 } - 4\n",
        "image_path": "./data/HME100K/test_images/test_1705.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{t^2}{2} + \\frac{t^4}{4} + \\frac{t^6}{6} + \\frac{t^8}{8}$",
        "gt_answers": "a = \\frac { 9 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1706.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image using LaTeX format is: x^2 + 5x + 6. This can be written as: $\\left ( x \\right )^2 + 5x + 6$.\n\nHere, the variable 'x' is being raised to the power of 2, and the constants 5 and 6 are added to the expression. The result is the value of the expression evaluated for the value of 'x' equal to 4. So, the value of the expression for 'x' = 4 is 42 + 20 + 6",
        "gt_answers": "\\frac { 5 x - 1 3 } { 5 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_1707.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle with base 4 and height 3 can be written as:\n\nA = lw = 4 \\* 3 = 12 units squared\n\nThe area of the rectangle is 12 square units.",
        "gt_answers": "( x - 4 y - 5 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_1709.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{a+b+c}{3}=\\frac{a}{b}+\\frac{b}{c}+\\frac{c}{a} $$\n\nIn this formula, a, b, and c are the lengths of the sides of a right triangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula for solving a quadratic equation. The equation is represented by the formula:2x^2 + 2x - 5 = 0, where x is the variable. The solution to this equation is given by the formula:x = - b / 2a, where a and b are the coefficients of the equation.",
        "gt_answers": "y - \\frac { 6 } { y } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1711.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: sin (x)cos (x) + cos (x)sin (x) = cos (x).",
        "gt_answers": "- \\frac { 1 } { 2 } \\leq \\sin \\alpha < \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1712.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is an image of a person holding a sign that reads, \"I love math\" in red letters. The person is standing in front of a black background.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is the equation of a line in the x-y plane, given by the equation: y = mx + b. This equation can be represented in LaTeX as follows:y=mx+b. The slope of the line is represented by the parameter m, and the y-intercept is represented by the parameter b.",
        "gt_answers": "A B = \\sqrt { A E ^ { 2 } - R E ^ { 2 } } = 5\n",
        "image_path": "./data/HME100K/test_images/test_1714.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $\\text{y} = \\text{b} \\times \\text{x} + \\text{c}$.",
        "gt_answers": "k 1 4 m + b n - 4 9\n",
        "image_path": "./data/HME100K/test_images/test_1715.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the given expression:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\node[draw, rectangle, minimum width=2cm] at (0,0) {$x$};\n\\node[draw, rectangle, minimum width=1cm] at (1.5,0) {$y$};\n\\node[draw, rectangle, minimum width=2cm] at (0,1.5) {$z$};\n\\node[draw, rectangle, minimum width=1cm] at (1.5,1.5) {$w$};\n\\draw[line",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\begin{aligned}\n\\frac{1}{2}x^2 + \\frac{1}{4}x - \\frac{1}{8} &= \\frac{1}{2}y^2 + \\frac{1}{4}y - \\frac{1}{8} \\\n\\frac{2x}{3} + \\frac{4y}{9} &= \\frac{4}{3}x + \\frac{6}{9}y \\\n\\frac{1}{4}(x - 2y) &= \\frac{1}{4}(2x -",
        "gt_answers": "3 \\cdot 6 x = 2 . 4 \\times 0 . 6\n",
        "image_path": "./data/HME100K/test_images/test_1718.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 3x^2 - 4x + 1.",
        "gt_answers": "\\Delta h = \\frac { 3 0 } { 1 9 } \\approx 1 \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_1720.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the derivative of the function f(x) = x^2.\n\nIn LaTeX format, the formula is:\n\n$$\\frac{d}{dx}x^2$$\n\nThis formula calculates the derivative of the function f(x) = x^2 with respect to x.",
        "gt_answers": "x ^ { 2 } = \\frac { 1 } { 1 6 }\n",
        "image_path": "./data/HME100K/test_images/test_1721.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle with sides a = 5 cm, b = 6 cm, and c = 8 cm can be written as:\n\nA = (1/2) \\* a \\* b \\* c\n\n= (1/2) \\* 5 \\* 6 \\* 8\n= (1/2) \\* 30\n= 15 cm^2\n\nTherefore, the area of the triangle is 15 cm^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=0.5]\n\\coordinate (a) at (0, 0);\n\\coordinate (b) at (3, 2);\n\\coordinate (c) at (2, 4);\n\\draw (a) -- (b) -- (c) -- cycle;\n\\filldraw (b) circle (2pt);\n\\filldraw (c) circle (2pt);\n\\filldraw (a) circle (2pt);\n\\",
        "gt_answers": "( - 2 a ^ { 2 } b ^ { 3 } ) ( - 3 a )\n",
        "image_path": "./data/HME100K/test_images/test_1723.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\frac{5\\times4\\times6\\times3\\times8}{2\\times6\\times4\\times1\\times3\\times5\\times4}\n\\end{center}\n\nThis expression evaluates to 1480.",
        "gt_answers": "\\frac { 4 } { 9 } ( 1 0 ^ { n } - 1 )\n",
        "image_path": "./data/HME100K/test_images/test_1724.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{2x^2 - 2x - 1}{x - \\frac{1}{2}} = 4x - 2$$",
        "gt_answers": "\\frac { 4 } { 3 } a = 1\n",
        "image_path": "./data/HME100K/test_images/test_1725.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{\\text{sin}\\left(x\\right)}{\\text{cos}\\left(x\\right)}$",
        "gt_answers": "F _ { 1 } = \\frac { F _ { 2 } l _ { 2 } } { l _ { 1 } } = \\frac { 3 0 } { 2 } = 1 5 N\n",
        "image_path": "./data/HME100K/test_images/test_1726.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\nThe equation is written in Japanese, which is read as: \"3 + 5 = 8\".\n```",
        "gt_answers": "\\frac { 1 } { 7 } ( 3 x - \\frac { 2 } { 3 } x - 4 ) = \\frac { 7 } { 3 } ( x - 3 )\n",
        "image_path": "./data/HME100K/test_images/test_1727.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><msup><mi mathvariant=\"normal\">a</mi></msup><mi mathvariant=\"normal\">b</mi></mrow><mrow><mrow><mfrac><mrow><msup><mi mathvariant=\"normal\">c</mi></msup><mi mathvariant=\"normal\">d</mi></mrow></mfrac><mi math",
        "gt_answers": "\\cos B = \\frac { B D } { B F }\n",
        "image_path": "./data/HME100K/test_images/test_1728.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{1}{\\sqrt{2}} \\times \\frac{1}{4} \\times \\sqrt{2} = \\frac{1}{8\\sqrt{2}}$$\n\nNote: The expression assumes that the variable `d` is defined as the diameter of the circle, and the variable `r` is defined as the radius of the circle.",
        "gt_answers": "C _ { 1 } C = D C , \\angle C _ { 1 } C D = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1730.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ \\frac{a}{b}$$This formula represents the ratio of a to b.",
        "gt_answers": "( 1 0 \\times \\frac { 3 } { 5 } )\n",
        "image_path": "./data/HME100K/test_images/test_1731.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:\n\nA = l \\* w\n\nwhere l is the length and w is the width.\n\nUsing the given image: <Img>ImageContent</Img>, we can calculate the area of the rectangle as follows:\n\nl = 10 cm\nw = 5 cm\n\nTherefore, the area of the rectangle is:\n\nA = l \\* w = 10 cm \\* 5 cm = 50 cm2\n\nSo the area of the rectangle is 50 cm2.",
        "gt_answers": "\\angle P E F = \\frac { 1 } { 2 } \\angle B E F\n",
        "image_path": "./data/HME100K/test_images/test_1732.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is given below in LaTeX format:\n\n$$\\text{d} x = \\frac{\\text{d} t}{\\sqrt{\\text{d} t^2 + \\text{d} x^2}}$$\n\nwhere $\\text{d} t$ and $\\text{d} x$ are infinitesimal changes in time and position, respectively, and the speed of light $c$ is set equal to 1.",
        "gt_answers": "0 . 6 4 < x < 0 . 7 6\n",
        "image_path": "./data/HME100K/test_images/test_1733.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a linear equation with slope -3/4 and y-intercept 5/4. The equation is represented by the following LaTeX expression: $ y = -3/4x + 5/4 $.",
        "gt_answers": "y = - \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1734.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image can be written as follows:\n\nLet the equation be y = x + 3.\nThe point on the curve with x-coordinate x1 and y-coordinate y1 is given by the equation:\nx1 = (y1 - 3) / 2\ny1 = x1^2 + 9\nSubstituting the point (x1, y1) into the equation for the curve, we get:\ny = (x1 - 3) / 2 + 9\nSimplifying the equation, we get:\ny = (x",
        "gt_answers": "y = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1735.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write out the expression of the formula in the image using LaTeX format.\n\nThe formula in the image is: y = 3x^2 - 5x + 2.\n\nIn LaTeX format, this formula would be written as:\n\ny = 3x^2 - 5x + 2\n\nThis formula is a polynomial equation of degree 2. It represents a parabola that opens upwards and has a vertex at the origin. The equation y = x^2 + x + 1 is the standard form of the quadratic equation.",
        "gt_answers": "\\frac { x - 1 } { 4 } - 1 = \\frac { 2 x + 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_1737.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\ce{Ca3(PO4)2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\text{sacado o cedo}\\_\\text{d}$ where $\\text{sacado}$ means'sacred'and $\\text{cedo}$ means'died'. The meaning of the expression is'the sacredness of death'.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length 5 and width 3 is:\n\nA = l \\* w\n\nwhere l is the length and w is the width. Plugging in the given values, we get:\n\nA = 5 \\* 3\n\nTherefore, the area of the rectangle is 15 square units.\n\nThe formula for the perimeter of a rectangle with length 5 and width 3 is:\n\nP = 2l + 2w\n\nwhere l is the length and w is the width. Plugging in the given",
        "gt_answers": "= ( a + b i ) ( a - b i ( a + b ) ( a - b )\n",
        "image_path": "./data/HME100K/test_images/test_1740.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format of the expression in the image:\n\n\\begin{equation}\nE = mc^2\n\\end{equation}\n\nwhere $E$ is the energy of the object, $m$ is its mass, and $c$ is the speed of light in a vacuum.",
        "gt_answers": "1 8 - 9 \\textcircled { = }\n",
        "image_path": "./data/HME100K/test_images/test_1741.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula written in LaTeX format. The formula is:$$\\frac{5x^2}{2}-\\frac{10xy}{3}+\\frac{7y^2}{2}=\\frac{5x^2+7y^2-10xy}{3}$$This formula represents a quadratic equation in the form of $ax^2+bx+c=0$, where $a=5$, $b=10y$, and $c=-5x^2+7y^2+10xy$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is $\\sqrt{2x^2 + 4x - 8}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$x = \\frac{4\\sqrt{10}}{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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can follow the following steps:\n\n1. Select the formula from the image and copy it to the clipboard.\n2. Open a LaTeX editor, such as Overleaf or Microsoft Word with LaTeX add-on.\n3. Paste the formula into the editor and format it using the appropriate LaTeX commands.\n4. Compile the document to generate a PDF file.\n\nHere's the LaTeX code for the formula in the image:\n\n\\begin{center}\n\\begin{align}\ny &= mx + b",
        "gt_answers": "7 \\times 7 = 4 9 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_1745.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is: (x + y) \\* (x - y) = x^2 - y^2.",
        "gt_answers": "y = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1746.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The formula in the image appears to be a mathematical expression for calculating the surface area of a cube. The formula is written in kanji characters, which makes it difficult to interpret. However, based on the shape of the cube in the image, we can see that it has a square base with sides of length 3 and a height of 4. Therefore, the formula is likely to be: A = 3 \\* 4 = 12. This is the surface area of the cube.\n\nIt's worth noting that the image appears to be a piece of",
        "gt_answers": "t \\overrightarrow { n } \\cdot \\overrightarrow { n } + \\overrightarrow { n } ^ { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_1747.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the formula is not visible in the image you provided. Without a clear and legible expression, it's difficult to write out the formula in LaTeX format. Can you please provide a clearer image or formula?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression:\n\n\\begin{center}\n\\begin{equation}\n5 + 2\\times 2 + 1 = 11\n\\end{equation}\n\\end{center}\n\nThis expression represents the sum of 5 and 2 times 2 plus 1, which equals 11.",
        "gt_answers": "\\angle A + \\angle B = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1749.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a triangle with sides a, b, and c can be written as:A= (1/2)\\*b\\*c. In LaTeX format, this expression would be written as:A = (1/2) \\* b \\* c.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{2x^2+3x+1}{x^2-x+2}$. To write it in LaTeX format, you would use the following code: $\\frac{2x^2 + 3x + 1}{x^2 - x + 2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Can you please provide the image so I can assist you in writing out the expression of the formula in LaTeX format?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you can follow these steps:\n\n1. Type ` $\\left( \\frac{2}{3} \\right) x 4 + 5$' to get the formula in LaTeX format.\n2. Replace the numbers in the formula with the corresponding variables from the image: $\\left( \\frac{2}{3} \\right) x 4 + 5$ becomes $\\left( \\frac{2}{3} \\right) x 4 + 5$\n3. The expression is now in LaTeX format: $\\left(",
        "gt_answers": "2 x + y - 4 = 0 . 1 2 . 5 1 1\n",
        "image_path": "./data/HME100K/test_images/test_1753.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is not provided, so I cannot write it out in LaTeX format. Please provide the expression.",
        "gt_answers": "\\angle P M O = \\arctan \\frac { \\sqrt { 1 0 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1754.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not shown in LaTeX format. It appears to be a mathematical expression written in regular text. However, to write it in LaTeX format, it would need to be encoded in LaTeX code.\n\nHere is the LaTeX format of the expression:\n\n$ c\\_2 = \\frac{-b} {2a} $\n\nNote that the variable names and coefficients are enclosed in dollar signs and the equation is enclosed in parentheses.",
        "gt_answers": "c = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1757.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 1 + 1 = 2.\n\n![](https://i.imgur.com/6C3D2NH.png)",
        "gt_answers": "A F = \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1758.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Can you please provide the image so I can assist you with the LaTeX format?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\begin{align\\*} 9600 - 600 = 9000 \\\\ 9000 \\* 5 = 45000 \\\\ 45000 - 7000 = 40000 \\end{align\\*}$$",
        "gt_answers": "9 8 0 0 \\div 1 4 0 = 7 0\n",
        "image_path": "./data/HME100K/test_images/test_1760.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{x + 2} + \\frac{3}{x - 4}$\n\nThis is a simple algebraic expression that can be used to find the value of the formula when x = 2. The expression is in the form of a sum of two fractions, where the numerators are polynomials in x and the denominators are polynomials in x. The constants of integration are arbitrary and do not affect the value of the integral. The integral is evaluated by substituting the value of x for which the expression is to be evaluated and evaluating the expression",
        "gt_answers": "\\frac { 6 } { A B } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1761.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I am unable to see the image as it is not provided. Can you please provide the image so I can assist you?",
        "gt_answers": "x _ { 2 } = - \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1764.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n\\begin{center}\n\\frac{2x^2+3x-5}{x^2+2x-3}\n\\end{center}\n\nwhere x is the variable.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n\\begin{center}\n$\\text{T} = \\frac{1}{2}mv^2 + \\text{W} + \\text{Q}$\n\\end{center}\n\nwhere $\\text{T}$ is the total energy, $m$ is the mass, $v$ is the velocity, $\\text{W}$ is the work done by the external force, and $\\text{Q}$ is the heat transferred to or from the system.",
        "gt_answers": "\\Delta D E B \\sim \\Delta E B C\n",
        "image_path": "./data/HME100K/test_images/test_1767.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is A = l \\* w, where l is the length and w is the width. In the image, the length is 5 units and the width is 4 units. Therefore, the area of the rectangle is A = 5 \\* 4 = 20 units.",
        "gt_answers": "x = 1 \\frac { 7 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1768.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThere is no LaTeX code for this image, as it is not a mathematical expression. The image appears to be a symbol or letter, but it is unclear what it represents without further context.\n```",
        "gt_answers": "\\frac { 2 } { 6 } = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1769.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as: f(x) = x^2 + 2x - 5.",
        "gt_answers": "m = - \\frac { 8 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_1770.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{400}{400} + \\frac{500}{400} = 1 + \\frac{500}{400} = 1.25$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is: $\\frac{\\frac{a}{b}+\\frac{c}{d}}{\\frac{b}{d}+\\frac{c}{a}}$.",
        "gt_answers": "C B = \\frac { 1 } { 2 } A B\n",
        "image_path": "./data/HME100K/test_images/test_1772.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\n$$\\begin{aligned} \\frac{x^2 - 4x + 2}{x - 2} = \\frac{2x^2 - 6x + 4}{x - 2} \\end{aligned}$$",
        "gt_answers": "y _ { 1 } = 0 y _ { 2 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1773.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it appears to be broken. Can you please provide a different image or a description of the equation you would like me to write out in LaTeX format?",
        "gt_answers": "x - 3 x + 1 \\leq x + 2\n",
        "image_path": "./data/HME100K/test_images/test_1774.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 1 + 3 + 2 = 6.\n\nTo write out the expression in LaTeX format, you can use the following code:\n\n$$ 1 + 3 + 2 = 6 $$\n\nThis will display the equation with the correct syntax and formatting.",
        "gt_answers": "O P ^ { 2 } = x ^ { 2 } + ( - x + 6 ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1775.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the formula for a circle with a radius of 6 cm:\n\n$$r = 6 cm$$\n\nThis formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the legs.\n\nIn this case, we can write the hypotenuse as $r$ and the legs as $x$ and $y$, as shown in the diagram below:\n\n[Diagram of right triangle with hypotenuse $r$ and legs $x$ and $y$",
        "gt_answers": "\\frac { 1 . 4 6 g } { 1 4 6 g } = 0 . 1 = 1 0 \\%\n",
        "image_path": "./data/HME100K/test_images/test_1776.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\ub9ce\uc740 \ud589\ub3d9\uc774 \uc788\uc2b5\ub2c8\ub2e4. \ud2b9\ud788 \ud2b9\ud788 \ub9ce\uc740 \uc21c\uc11c\uc758 \ud589\ub3d9\uc774 \uc788\uc2b5\ub2c8\ub2e4. \ub2e4\ub978 \uc21c\uc11c\ub85c \ud589\ub3d9\uc744 \ucde8\ud558\uc2ed\uc2dc\uc624. \ud589\ub3d9\uc740 \uc54c\uc544\uc694?\n\n\ubc88\uc5ed\uacb0\uacfc\uc21c\uc11c \uc5c6\ub294 \ud589\ub3d9\uc774",
        "gt_answers": "\\frac { 1 } { 2 } \\cdot \\vert y \\vert \\cdot 2 = 4\n",
        "image_path": "./data/HME100K/test_images/test_1777.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ f(x) = \\begin{cases} x^3 - 3x^2, & \\text{if } x \\leq 1 \\leq x^2 + 2x - 1 \\\\ 0, & \\text{otherwise} \\end{cases} $$",
        "gt_answers": "x = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1778.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![Img](https://i.imgur.com/vvC1dqx.png)\n\n![Img](https://i.imgur.com/vvC1dqx.png)\n\nIn LaTeX format, the formula would be written as:\n\n![Img](https://i.imgur.com/vvC1dqx.png)\n\nwhere the equation is written using the `equation` environment and the `frac` package to typeset the fraction.",
        "gt_answers": "2 x = \\frac { 5 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_1779.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{2x + 3y - 5z}{x - y + 3z}$.",
        "gt_answers": "m = \\frac { 5 \\cdot } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1780.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle with radius r is given by: A = (\u03c0r^2). To find the equation of the line passing through the center of the circle with radius r, we can use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope of the line and (x, y1) and (x1, y1) are the coordinates of the two points on the line. Let's call the coordinates of the center of the circle (0,0) and the coordinates of the point on the circle with",
        "gt_answers": "( 2 - a ) x = 5 - a\n",
        "image_path": "./data/HME100K/test_images/test_1781.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Convert the formula to LaTeX format. This can be done by writing the formula in a mathematical format, including all the symbols and operators, and then converting it to LaTeX format using an equation editor or a LaTeX compiler. For example, the formula in the image can be written as:\n\n\\frac{a + b}{c + d}\n\n2. Add the equation number to the formula. In LaTeX format, equation numbers can be added using the `\\eqno` command. For example, the",
        "gt_answers": "y _ { 1 } = 2 , y _ { 2 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_1783.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{d\\mathbf{x}}{dt} = \\mathbf{v}$",
        "gt_answers": "( b + c ) \u3001 ( a + c ) \u3001 ( b + a )\n",
        "image_path": "./data/HME100K/test_images/test_1784.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is A = l x w, where l is the length and w is the width.\n\nThe area of the rectangle in the image is A = (4 - 2) x (6 - 1) = 12 - 5 = 7 square units.\n\nThe length of the rectangle is 6 - 1 = 5 units.\n\nThe width of the rectangle is 4 - 2 = 2 units.\n\nSo, the formula for the area of the rectangle in the image is A = l x w, where l = 5",
        "gt_answers": "x = \\frac { 1 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_1785.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{3x + 2y - 5}{x + 2y - 5}$$",
        "gt_answers": "\\pm \\sqrt { c - 2 } = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1786.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\nr = -------------------r\n\nor, in LaTeX format,\n\n$$r = \\frac{2r}{r + 2r}$$\n\nThis formula states that the sum of the interior angles of a triangle is equal to 180 degrees, and is used to solve for the length of the sides of the triangle.",
        "gt_answers": "R _ { 1 } = \\frac { V _ { 1 } } { I _ { 1 } } = \\frac { 6 V } { 0 . 2 A } = 3 0 \\Omega\n",
        "image_path": "./data/HME100K/test_images/test_1787.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ E = \\frac{m}{2} \\left(\\frac{v^2}{r} - \\frac{GM}{r^2}\\right) $$\n\nwhere $E$ is the total energy of the system, $m$ is the mass of the satellite, $v$ is the velocity of the satellite, $r$ is the distance between the satellite and the center of the Earth, and $G$ is the gravitational constant.",
        "gt_answers": "9 0 \\times 6 0 = 5 4 0 0 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_1788.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent}$$\n\nThis formula is written in black ink on a white background. The word \"ImageContent\" is written in capital letters, and the formula is enclosed in curly brackets to indicate that it is an image.",
        "gt_answers": "D C \\bot A B\n",
        "image_path": "./data/HME100K/test_images/test_1789.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Please provide the image so I can assist you.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "\\frac { 1 } { 4 } : \\frac { 1 } { 9 } = \\frac { 1 } { 3 } : x\n",
        "image_path": "./data/HME100K/test_images/test_1791.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 2x2 + 4x - 5 = 6x - 5.\n\nThis formula represents the equation of a line in the coordinate plane. The slope of the line is 2/2, which is equal to 1, and the y-intercept is -5. The line passes through the point (0, -5) and has an equation of y = 2x + 5.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} f(x) &= \\frac{2}{x-2} \\quad \\text{for } -2 < x < 2 \\\\\\\\ f'(x) &= \\frac{2}{x-2} - \\frac{2}{2} = \\frac{2}{(x-2)^2}\\quad \\text{for } -2 < x < 2 \\\\\\\\ f''(x) &= \\frac{2}{(x-2)^2} - \\frac{2}{(x-2",
        "gt_answers": "y - \\frac { 3 } { 4 } = - \\frac { 1 } { 2 } ( x - 1 )\n",
        "image_path": "./data/HME100K/test_images/test_1793.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the probability of a point being on or above the line of best fit for a set of data. The formula is given by:P(x) = (1 - 2x) / (1 - 2x^2)where x is the value of the x variable in the data set. This formula is a probability density function that describes the probability of a point being on or above the line of best fit for a set of data.",
        "gt_answers": "y ^ { 2 } = \\frac { b ^ { 2 } ( a ^ { 2 } - 1 ) } { a ^ { 2 . } }\n",
        "image_path": "./data/HME100K/test_images/test_1794.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a quadratic equation of the form 2x^2 + 3x - 5 = 0.",
        "gt_answers": "\\frac { 3 a ^ { - 2 } } { 2 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_1795.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a trapezoid is given by the formula:$$A = (bh)\\_{1} + (ah)\\_{2}$$where $b$ is the length of the parallel sides and $h$ is the height of the trapezoid. In this case, $b = 10$ and $h = 5$, so the area of the trapezoid is $A = (10)(5) + (5)(10) = 50 + 50 = 100$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not provided, so I cannot write it out in LaTeX format. Can you please provide the formula so that I can write it out for you in LaTeX format?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is x + 4y - 3z = 10.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as:$$\\begin{align\\*}\\text{height} &= \\frac{\\text{width}}{\\text{2}}\\\\\\text{width} &= \\sqrt{\\frac{\\text{height}\\times\\text{length}}{\\text{2}}}\\\\\\text{length} &= \\sqrt{\\frac{\\text{width}\\times\\text{height}}{\\text{2}}}\\\\\\text{area} &= \\text{width}\\times\\text{length}\\end{align*}$$",
        "gt_answers": "x = \\frac { a - 5 } { a - 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1800.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n\\begin{center}\n$ 4x^2 + 4y^2 = 4 \\quad \\text{or} \\quad x^2 + y^2 = 1 $\n\\end{center}\n\nThis is the equation of a circle centered at the origin with radius $ 2 $.",
        "gt_answers": "4 5 9 + 8 6 = 5 4 5\n",
        "image_path": "./data/HME100K/test_images/test_1801.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a line segment AB with endpoints A(0, 0) and B(1, 2). The length of the line segment AB is given by the formula:\n\nLength of AB = \u221a((x2 - x1)2 + (y2 - y1)2)\n= \u221a(12 + 4)\n= \u221a16\n= 4\u221a2\n= 4\\*sqrt(2)\n= 4\u221a2\n= 4\u221a2\n\nSo, the length of the line segment AB is 4\u221a2 units.",
        "gt_answers": "x = \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_1803.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is 4x^2 + 4x - 8.",
        "gt_answers": "2 x - ( - 7 . 8 ) = - \\frac { 4 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1804.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x + 2y - 3z = 6xyz - 3zx - 2y2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 3x^2 + 2x - 5.\n\nHere is the LaTeX code for the formula:\n\n\\begin{align\\*}\n3x^2 + 2x - 5\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\frac{2x + 3y - 7z}{x + 2y - 3z} = \\frac{2(3x + 2y - 7z) - (2x + 3y - 7z)}{(x + 2y - 3z) - 2(3x + 2y - 7z)} = 3x + 4y - 6z.\\",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1807.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the derivative of f(x) = x^3 at x = a, we can use the power rule of differentiation. The derivative of f(x) is given by:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is \\frac{b}{a}.",
        "gt_answers": "x = \\frac { 1 5 } { 1 6 }\n",
        "image_path": "./data/HME100K/test_images/test_1809.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![Img](https://latex.codecogs.com/svg.image?%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C%5B%5C",
        "gt_answers": "6 8 3 - 8 = 6 7 7 \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_1810.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$ 4 \\times 2 + 5 = 20 $$\n\nThis is a simple arithmetic expression that adds the values of the variables 4 and 2, and multiplies the result by 2, to obtain the final value of 20.",
        "gt_answers": "2 4 - 7 = 1 4 ( m )\n",
        "image_path": "./data/HME100K/test_images/test_1811.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: fdcos(60\u00b0) = 1.",
        "gt_answers": "\\frac { D F } { C E } = \\frac { O D } { D C }\n",
        "image_path": "./data/HME100K/test_images/test_1814.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image using LaTeX format is:$$\\frac{100\\times\\frac{x^2}{4}+x}{x^2+12}\\times\\frac{x^2-4x}{x^2-9}$$This expression can be read as the product of three terms:$$100\\times\\frac{x^2}{4}+x$$100\\times\\frac{x^2-4x}{x^2-9}$$100\\times\\frac{x^2-4x}{x^2-",
        "gt_answers": "\\frac { x } { 0 . 3 } - \\frac { 0 . 2 3 - 0 . 2 x } { 0 . 0 7 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1815.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$R = \\frac{V^2}{R+X}$\n\\end{center}\n\nThis formula represents a resistor divider circuit, where the output resistance $R$ is given by the ratio of the input voltage $V$ to the sum of the input resistance $R$ and the external resistance $X$.",
        "gt_answers": "R = \\frac { V } { I } = \\frac { 2 v } { 0 . 5 A } = 4 \\Omega\n",
        "image_path": "./data/HME100K/test_images/test_1816.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n\\text{F} &= \\frac{\\text{m} \\cdot \\text{a}}{\\text{b} \\cdot \\text{c}} \\\\\n&= \\frac{\\text{m} \\cdot \\text{a}}{\\text{b} \\cdot \\text{c}} \\\\\n&= \\frac{\\text{mass} \\cdot \\text{acceleration}}{\\text{force} \\cdot \\text{gravity}}\n\\end{align\\*}\nwhere\n\\begin{align\\*}",
        "gt_answers": ". 1 . 3 . 1 4 \\times 4 ^ { 2 } \\times 1 2 = 6 0 2 . 8 8 l m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1817.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression:\n\n$$ \\frac{x^2 + 4x + 2}{x + 2} = \\frac{x^2 + 4x + 2}{x + 2} $$\n\nThis expression represents a rational expression in which the numerator is a quadratic polynomial with variable x and the denominator is a linear polynomial with variable x. The constant value 2 is added to the denominator.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{a^2 + b^2}{2ab}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not shown as it is not clear what the image represents. However, assuming that the image is a representation of the formula for a vector with magnitude 6 and angle 30 degrees, then the formula would be:</br>r = 6sin30\u00b0</br>where r is the magnitude of the vector.",
        "gt_answers": "\\frac { F C } { C N } = \\frac { D F } { D N }\n",
        "image_path": "./data/HME100K/test_images/test_1820.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{x + 2y}$.",
        "gt_answers": "y _ { 2 } = 4 y _ { 4 } = - 4\n",
        "image_path": "./data/HME100K/test_images/test_1821.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:2x^2+3x-5.\n\nThis formula is derived by taking the derivative of the given equation with respect to x. The derivative is 2x+3, which when substituted into the given equation results in the formula in the image.2x^2+3x-5\n\nThe derivative of a quadratic equation is the slope of its graph at any point on the graph, which can be calculated by finding the slope of the tangent line to the graph at that point. In this case, the derivative is 2x",
        "gt_answers": "\\frac { 2 } { 3 } = \\frac { 8 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1824.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX format for the expression in the image:\n\n\\begin{equation} x + 3 = \\frac{4}{5} \\times 3 \\end{equation}\n\nIn this equation, x is the variable, 3 is the constant and 4/5 is the fraction. The fraction is multiplied by 3 to get the value of x. The equation is solved by plugging in the value of x, which is 6, into the equation. This gives us the value of x, which is 6.\n\nPlease",
        "gt_answers": "- \\frac { 3 } { 1 4 } - \\frac { 4 } { 1 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1825.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```markdown\n\n$$\\text{sin}\\left(\\frac{\\pi}{6}\\right) = \\frac{1}{2}$$\n```",
        "gt_answers": "x + 2 \\sqrt { x + 4 } + x + 4 - 2 x - x = 0\n",
        "image_path": "./data/HME100K/test_images/test_1826.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n\\begin{align\\*}\n\\frac{x}{2}\\left(\\sqrt{4x^2 + 9} - 3x\\right) &= \\frac{1}{2}x\\left(\\sqrt{4x^2 + 9} - 3x\\right) \\\\\n&= \\frac{1}{2}x\\sqrt{4x^2 + 9} - \\frac{1}{2}x^2 \\\\\n&= \\frac{1}{2}x\\sqrt{4x",
        "gt_answers": "( 8 0 ) - 4 0 = 4 0 . ( 8 0 ) + 3 0 = 5 0\n",
        "image_path": "./data/HME100K/test_images/test_1827.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n$$ \\begin{aligned}\n    5x^2 + 9xy + 3y^2 &= 7x + 5y \\\n    5x^2 - 9xy + 3y^2 &= 7x - 5y \\\n    5x^2 + 9xy - 3y^2 &= 7x - 5y \\\n    5x^2 - 9xy - 3y^2 &= 7x + 5y \\\n    5x^2 + 9xy + 3y^2 &=",
        "gt_answers": "3 - \\frac { 2 x - 1 } { 5 } = \\frac { x + 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1828.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by: $\\text{C} = \\frac{\\text{m}}{\\text{V}} + \\frac{\\text{V}}{\\text{n}}$.",
        "gt_answers": "S _ { \\Delta B E } = 9 s = 2 2 5\n",
        "image_path": "./data/HME100K/test_images/test_1829.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a quadratic function of the form: y = ax^2 + bx + c, where a, b, and c are constants. The values of a, b, and c can be determined by solving the equation for x. For example, if x = 3, the equation becomes 3y = 12 - 6y + 10. By solving for y, we find that y = 3. Therefore, the equation is y = ax^2 + (3a - 6)x + 10.",
        "gt_answers": "y - 3 = \\frac { 1 8 } { y }\n",
        "image_path": "./data/HME100K/test_images/test_1830.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by the equation $ A = \\frac { \u03c0r^2 }{ 4 } $. In LaTeX format, this can be written as $ A = \\frac{\\pi r^2}{4} $.",
        "gt_answers": "( y + 2 ) ^ { 2 } - y ^ { 2 } = - 6\n",
        "image_path": "./data/HME100K/test_images/test_1831.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->] (0,0) -- (2,0) node[right] {$x$};\n\\draw[->] (0,0) -- (0,2) node[above] {$y$};\n\\draw[line width=1.5pt,rounded corners] (1,1) -- (1,2) -- (2,2) -- (2,1);\n\\node[above right] at (1,1) {$\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a length of 5cm and a width of 3cm is:\n\nA = l x w\n\nwhere l is the length and w is the width.\n\nSo, the area of the rectangle is:\n\nA = 5cm x 3cm\n\n= 15cm\u00b2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: f(x) = x^4 + 2x^3 - 5x^2 + x + 1.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\text{F} = \\frac{\\text{m}\\cdot\\text{a}\\cdot\\text{g}}{\\text{h}^2 + \\text{k}^2}$$\n\nwhere $\\text{m}$ is the mass of the object, $\\text{a}$ is its acceleration, $\\text{g}$ is the acceleration due to gravity, $\\text{h}$ is the height of the object from the ground, and $\\text{k}$ is the constant that relates the force applied to the object to its disp",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n\\begin{center} $\\frac{1}{2} \\left(\\frac{3}{4}+\\frac{5}{6}\\right)$ \\end{center}\n\nThis expression evaluates to $\\frac{1}{2}\\left(\\frac{3}{4}+\\frac{5}{6}\\right) = \\frac{1}{2}\\left(\\frac{7}{12}\\right) = \\frac{7}{12}$.",
        "gt_answers": "v c = r A - 1 7 .\n",
        "image_path": "./data/HME100K/test_images/test_1836.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is 88 + 99.",
        "gt_answers": "3 8 \\div 8 8 = \\frac { 1 9 } { 4 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1837.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$$ f(x) = \\frac{1}{2} \\times x^2 + 3x + 1 $$",
        "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",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows:\n\n$$\\frac{a}{b} = \\frac{c^2}{d^2}$$\n\nwhere a and b are the lengths of the rectangle's parallel sides, c and d are the lengths of the rectangle's diagonal sides.\n\nNote that the length of the rectangle's diagonal sides is equal to the length of the rectangle's parallel sides, as both are equal to 3 units. Therefore, the expression simplifies to:\n\n$$\\frac{3}{3} = \\frac{3^2}{3^2",
        "gt_answers": "\\frac { 1 } { 1 2 } \\times 6 \\times \\vert y - 3 \\vert = b\n",
        "image_path": "./data/HME100K/test_images/test_1839.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$ P=\\frac{2^6\\times 10^6}{5!}\\left(\\frac{1}{2}\\right)^5 $\n\nor\n\n$ P=\\frac{2^6\\times 10^6}{5!}\\left(\\frac{1}{2}\\right)^5 $",
        "gt_answers": "E F \\bot A D : \\angle A P F = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1841.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX formula for the image:\n\n\\begin{align}\nf(x) = \\frac{x^2}{x+3}\n\\end{align}\nThis formula calculates the value of x^2 divided by x+3 for x>=-3. The domain of f(x) is all real numbers except -3. The range of f(x) is all real numbers.",
        "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",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is not available for me to view. Can you please provide a different image?",
        "gt_answers": "x < \\frac { 2 } { \\sqrt { 5 } - 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1843.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{1}{4}+\\frac{3}{8}+\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}+\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}+\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}+\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}+\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}+\\frac{1}{2}+\\frac{1}{4",
        "gt_answers": "1 3 + x = ( 4 7 + x ) \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1844.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$\\left(\\frac{x+3}{x-2}\\right)\\left(\\frac{y-5}{y+3}\\right)=\\left(\\frac{x+3}{x-2}\\right)\\left(\\frac{y+3}{y-5}\\right)$\n\nThe numerator of the fraction is the product of the two fractions $\\left(\\frac{x+3}{x-2}\\right)$ and $\\left(\\frac{y-5}{y+3}\\right)$.\n\nThe denominator of the fraction is the product of the two",
        "gt_answers": "\\frac { 9 } { 1 6 } - \\frac { 9 \\cdot } { 1 6 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_1846.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation for the sum of two numbers: x and y. The equation is written as follows:\n\nx + y = x + y\n\nThis equation simply states that the sum of two numbers is equal to the sum of those two numbers. It can be read as \"x plus y is equal to x plus y.\"",
        "gt_answers": "( b + 1 ) x ^ { 2 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_1847.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Image content} = \\frac{\\text{height}}{\\text{width}} \\times \\sqrt{\\frac{\\text{area}}{\\text{perimeter}}}$$\n\nwhere $\\text{height}$ and $\\text{width}$ are the dimensions of the image, and $\\text{area}$ and $\\text{perimeter}$ are the area and perimeter of the image, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is:\n\n$$ \\text{ln(2)} + \\frac{1}{2} \\times \\text{ln(x)} - \\text{ln(1 - x)} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$ $\\frac{a}{b+c}$ $=$ $\\frac{ab}{b+c}$\n\nThis formula is used to calculate the product of two binomials. In the image, the expression is written as $\\frac{a}{b+c} \\cdot \\frac{bc}{b+c}$. The result is $\\frac{ab}{b+c}$, which is equivalent to $\\frac{a(b+c)}{b+c}$ and can be simplified further to $\\frac{ab}{b}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: 5 - 3x + 2. The expression can be written as follows:\n\n(5 - 3x + 2)\n\nThis is a formula for the image that shows how to find the number of the image if you know the values of the variables x, y, and z.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{\\frac{2x}{x^2 - 4}}{x - \\sqrt{x^2 - 9}}$$",
        "gt_answers": "\\geq 2 \\sqrt { \\frac { 9 } { 1 } } = 6\n",
        "image_path": "./data/HME100K/test_images/test_1853.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not available as it is not shown in the image. Please provide the image for me to write out the expression.",
        "gt_answers": "S m = \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_1854.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{x^2 - 4x}{x - 2} = \\frac{x^2 - 2x - 8}{x - 2} = \\frac{x^2 - x - 8}{x - 2} = 4 - \\frac{x}{x - 2}$$\n\nAlternatively, the equation can be written as:\n\n$$\\frac{x^2 - 4x}{x - 2} = 4 - \\frac{x}{x -",
        "gt_answers": "\\frac { 6 } { 2 0 } = \\frac { 3 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_1855.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{5 + 3 \\times 6 - 10 + 1}{5 - 2} = \\frac{5 + 18 - 10 + 1}{5 - 2} = \\frac{23 - 10 + 1}{5 - 2} = 23 - \\frac{10}{5} + 1 = \\boxed{23 - \\frac{5}{2} + 1} = 23 - \\frac{5}{2} +",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression for the formula in the image using LaTeX format: $\\frac{3}{2}$x + $\\frac{1}{2}$y + $\\frac{1}{4}$z.\n\nThe formula in the image is a point in 3-dimensional space, with x, y, and z coordinates of 2, 1, and 4, respectively. The formula is therefore the sum of the point's x, y, and z coordinates.\n\nThe fraction notation used in the formula represents the sum of the point's x, y, and z coordinates. The fraction $\\frac{",
        "gt_answers": "3 y - 2 = 9 - 6 \\sqrt { y + 3 } + y + 3\n",
        "image_path": "./data/HME100K/test_images/test_1857.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$\\text{x + 3} = 5$$This can be read as: the value of x is equal to 3 plus 5.",
        "gt_answers": "\\frac { 3 } { 8 } \\times 5 = \\frac { 3 \\times 5 } { 8 . }\n",
        "image_path": "./data/HME100K/test_images/test_1858.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\frac{x^2+y^2}{r^2} = \\frac{a^2+b^2}{c^2} \\Rightarrow \\frac{x^2+y^2}{r^2} = \\frac{a^2+b^2}{c^2} \\Rightarrow \\frac{x^2+y^2}{r^2}=\\frac{a^2+b^2}{c^2}\n\nwhere $x$, $y$, $r$, $a$, $b$,",
        "gt_answers": "2 \\times \\frac { \\sqrt { 3 } } { 2 } \\times \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1860.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} 2x^2 + 4x + 2 = 0 \\Rightarrow x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} \\end{aligned}$$\n\nIn the above equation, $a = 1$, $b = 4$, and $c = 2$. So, the roots of the equation are:\n\n$$\\begin{aligned} x\\_1 &= \\frac{-4 \\pm \\sqrt{4^2 - 4 \\",
        "gt_answers": "- \\frac { b } { 2 a } = \\frac { 1 } { 3 } ( x - 2 ) ^ { 2 } + 5\n",
        "image_path": "./data/HME100K/test_images/test_1861.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I don't have access to the image you've provided. Please provide the image so I can assist you with your questions.",
        "gt_answers": "b _ { n } = 2 ( a _ { n } - 2 a _ { n - 1 } ) ^ { 1 } = 2 b _ { n - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_1862.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n\\begin{center}\n\\frac{1}{x^2+2x-2}\n\\end{center}\n\nThis expression evaluates to 0.5, as indicated in the image.",
        "gt_answers": "\\angle M G H = \\angle N H G\n",
        "image_path": "./data/HME100K/test_images/test_1863.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not clear as it is in a different language and requires knowledge of that language to read and understand. Can you please provide the image?",
        "gt_answers": "\\because \\angle O E D = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1864.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a square with side length $3$ can be written as:\n\n$$A = 3^2 = 9$$\n\nThe formula for the perimeter of a square with side length $3$ can be written as:\n\n$$P = 4 \\times 3 = 12$$\n\nThe formula for the area of a rectangle with length $5$ and width $3$ can be written as:\n\n$$A = L \\times W = 5 \\times 3 = 15$$\n\nThe formula for the perimeter of a rectangle with",
        "gt_answers": "x = \\frac { 1 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1865.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x \\* y + z \\* w + (a - b) \\* c + (d - e) \\* f = 0. Here, x, y, z, w, a, b, c, d, e, and f are variables.",
        "gt_answers": "1 3 + x = \\frac { 1 } { 2 } ( 4 7 + x )\n",
        "image_path": "./data/HME100K/test_images/test_1866.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is A = (bh)/2, where b is the base and h is the height. In this image, the base of the triangle is 4 and the height is 6. Therefore, the area of the triangle is A = (4\\*6)/2 = 6.",
        "gt_answers": "\\frac { 3 } { 2 } y - y ^ { 2 } - \\frac { 1 } { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_1867.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the product of its length and width. The formula for the area of a rectangle is A = l \\* w, where l is the length and w is the width.\n\nThe formula for the perimeter of a rectangle is given by the sum of its sides. The formula for the perimeter of a rectangle is P = 2(l + w), where l is the length and w is the width.\n\nThe formula for the volume of a rectangular prism is given by the product of its length, width, and height. The formula for the volume",
        "gt_answers": "f ( t + 1 ) = \\vert t + 1 \\vert\n",
        "image_path": "./data/HME100K/test_images/test_1868.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for solving a system of linear equations, which is given by the equation.\n\n$$x + 2y = 5 \\\n\nx - y = - 1$$\n\nTo solve the system, we use the substitution method, where we substitute the value of one variable in terms of the other. Let x = y - 1, then the system becomes:\n\n$$y - 1 + 2y = 5 \\\n\ny - 1 - y = - 1$$\n\nSimplifying the equations, we get:\n\n$$3y =",
        "gt_answers": "y = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1869.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX formula for the expression in the image:$\\frac{100}{10 + 2\\times 3}$",
        "gt_answers": "y _ { 1 } = 3 y _ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1870.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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\u222b[a, b] f(x) dx\n\n\u222b[a, b] f(x) dx is the definite integral of f(x) over the interval [a, b].",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\n$$ 500 + \\frac{1}{2}(100 - 20) = 550 $$\n\nThe expression can be simplified as follows:\n\n$$ 500 + \\frac{1}{2}(80) = 550 $$\n\nThis expression represents a linear equation with a slope of $\\frac{1}{2}$ and an y-intercept of 500. The equation can be graphed on the coordinate plane to obtain the solution shown in the image.",
        "gt_answers": "y = \\frac { 2 0 0 5 } { 4 0 0 7 }\n",
        "image_path": "./data/HME100K/test_images/test_1872.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the exponential function is y = a \\* 2^x.\n\nIn LaTeX format, this can be written as follows:\n\n$y = a \\cdot 2^x$\n\nThe base of the exponential function is 2, and the exponent is x. This means that for every unit increase in x, the value of y increases by a factor of 2. The constant a is used to scale the output of the function.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{e}^{-3} = \\frac{1}{5!} \\cdot \\frac{1}{2!} \\cdot \\frac{3}{4!}$$",
        "gt_answers": "E F = 3 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1874.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the number of moles of an unknown substance is unknown. The mass of the substance is 3.00 kg and the volume is 3.00 liters. The number of moles of the substance is calculated by dividing the mass by the molar mass of the substance.\n\nThe molar mass of the substance is not given, so the number of moles cannot be determined.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I don't see any image in the provided text. Please provide the image so I can answer your questions.",
        "gt_answers": "x ^ { 2 } + x ( x + 1 ) = 2 ( x + 1 ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1876.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in the image using LaTeX format, we need to use the \\sum operator and the \\* symbol to represent multiplication.\n\nWe can represent the expression as follows:\n\n\\begin{align\\*}\n\\sum\\_{i=1}^{n} x\\_i \\* y\\_i &= \\sum\\_{i=1}^{n} (x\\_i + 2) \\* (y\\_i - 3) \\\n&= \\sum\\_{i=1}^{n} x\\_i \\* y\\_i + \\sum\\_{i=1}^{n",
        "gt_answers": "\\frac { 3 } { 5 } \\times 3 = \\frac { 9 } { 5 } = 9 = 5\n",
        "image_path": "./data/HME100K/test_images/test_1877.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n$latex r = \\frac{d^2}{dx^2} + \\frac{1}{x} - \\frac{2\\pi^2}{x^2}$\n\nThis is a differential equation, which can be solved using numerical methods or analytical techniques.",
        "gt_answers": "\\angle D O E = 2 8 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1878.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{3xy+x^2y^2-4xy}{2y^2+2xy}$.",
        "gt_answers": "\\sqrt { y } = 2\n",
        "image_path": "./data/HME100K/test_images/test_1879.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{48}{(x+2)^2}$$\n\nNote: This answer assumes that the variable 'x' is used in the formula.",
        "gt_answers": "S _ { 2 } = 4 = 2 ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1880.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{1}{2}(5x^2 + 2x - 3) = \\frac{1}{2}(5(3x^2 + 2x) - 3) = \\frac{1}{2}(15x^2 + 10x - 3) = \\frac{1}{2}(15(3x + 2)x - 3) = \\frac{1}{2}(15(3 + 2)x^2 - 3) = \\frac{1}{",
        "gt_answers": "y = \\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_1881.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:\n\n$$\\text{Loss} = \\sqrt{\\left(\\frac{1}{3}\\right) + \\left(\\frac{1}{4}\\right)^2} + \\frac{1}{2}\\sqrt{\\left(\\frac{1}{5}\\right) + \\left(\\frac{1}{8}\\right)^2} + \\left(\\frac{1}{6}\\right) + \\frac{1}{2}\\sqrt{\\left(\\frac{1}{7}\\right) + \\left(\\frac{1}{9}\\right)^",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n$$\\text{Image content}=\\frac{1}{2}\\text{Image size}+\\frac{1}{4}\\text{Number of people}$$\n\nIn the formula, the image size is represented by $\"Image size\"$, the number of people in the image is represented by $\"Number of people\"$, and the image content is represented by $\"Image content\"$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \\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} + \\",
        "gt_answers": "\\frac { 1 } { 2 } \\times ( A D + B C )\n",
        "image_path": "./data/HME100K/test_images/test_1884.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2(x^2 + 3x - 5) = 2x^3 + 3x^2 - 5x.\n\nHere's how to derive the formula from the image:\n\n1. First, we need to identify the variable x.\n2. Next, we need to identify the coefficients and constants in the equation. In this case, the coefficients are 2, 3, and -5, and the constant is 2.\n3. Finally, we can write the equation in standard form by using the formula for",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written as:\n\n\\begin{align}\nx = \\frac{1}{2} \\times 2 + \\frac{1}{3} \\times 3 = \\frac{5}{6} \\times 6 = \\frac{5}{3} \\times 3 \\\n\\end{align}\n\nwhere x is equal to the sum of the two fractions.",
        "gt_answers": "\\frac { 8 } { 1 4 } \\textcircled { > } \\frac { 9 } { 2 1 }\n",
        "image_path": "./data/HME100K/test_images/test_1886.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we need to identify the variables and their values in the formula. The formula is given by:\n\n$$x^2+y^2=r^2$$\n\nThe variables in the formula are x, y, and r. The values of these variables can be determined by inspection of the image. The value of x is the distance from the center of the circle to the point where the chord intersects the circle. The value of y is the distance from the center of the circle to the point where the chord intersects the circle.",
        "gt_answers": "c = 2 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1887.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression can be written as:",
        "gt_answers": "y = - \\frac { 1 } { 4 } x ^ { 2 } + 2 x - 3\n",
        "image_path": "./data/HME100K/test_images/test_1889.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$$a^4 + b^4 = (a^2 + b^2)^2$$This is a quadratic equation, which can be solved using the quadratic formula:$$x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$$In this case, a = 1, b = 2, and c = 0, so the solution is:$$x = \\frac{-2 \\pm \\sqrt{4 - 4}}{2 \\* 1} = \\frac{-2 \\pm \\sqrt{0}}{2 \\*",
        "gt_answers": "( a - 4 ) ( a + 3 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_1890.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written in LaTeX format is:\n\n$$ \\text{F}=\\frac{\\text{m}\\cdot\\text{g}}{\\text{s}^2}$$",
        "gt_answers": "y = - \\frac { 1 } { 4 } x ^ { 2 } + 2 x - 3\n",
        "image_path": "./data/HME100K/test_images/test_1892.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222ba^2dx + \u222bb^3dy = (\u222bb^2dy)/2 + (\u222ba^2dx)/3 - (\u222b(a^2b)dy)/3",
        "gt_answers": "\\frac { 8 b + 9 a ^ { 2 } - 1 0 a } { 1 2 a ^ { 2 } b }\n",
        "image_path": "./data/HME100K/test_images/test_1893.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:$$\\frac{1}{3}-\\frac{1}{5}+\\frac{1}{7}=\\frac{1}{3}(3-\\frac{1}{5}+\\frac{1}{7})=\\frac{1}{3}(3-1-\\frac{1}{5}+\\frac{1}{7})=0$$This formula is used to calculate the area of a triangle with sides of length 3, 5, and 7 units.",
        "gt_answers": "q \\in ( \\frac { 1 - \\sqrt { 5 } } { 2 } , \\frac { 1 + \\sqrt { 5 } } { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_1894.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression written in LaTeX format. The expression is as follows:\n\n\\begin{aligned}\nx^2 + y^2 = r^2\n\\end{aligned}\n\nThis is a formula for the distance between two points in a two-dimensional space. The left-hand side of the equation is the square of the sum of the squares of the x and y coordinates of the two points. The right-hand side is the square of the distance between the two points, which is represented by the variable r.",
        "gt_answers": "x _ { 3 } = - 2 + 2 \\sqrt { 2 } , x _ { 4 } = - 2 - 2 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1895.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is not provided. Please provide the image for me to write out the expression of the formula.",
        "gt_answers": "\\frac { 2 0 8 0 } { x y } = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_1896.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\ntan(45\u00b0)=4/5cos^4(45\u00b0)-1/5cos^3(45\u00b0)+3/5cos^2(45\u00b0)-1/5cos(45\u00b0)+1/5.\n\nIn LaTeX format, this can be written as:\n\ntan(45\u00b0)=$\\frac{4}{5}\\cos^4(45\u00b0)$-$$\\frac{1}{5}\\cos^3(45\u00b0)$+$\\frac{3}{5}\\cos^",
        "gt_answers": "\\tan B = \\frac { A D } { B D } = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1897.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n$$x^2 + 3x - 4 = 0$$\n\nwhere x is the variable representing the position of the ball on the line. The equation can be solved by completing the square method:\n\n$$x^2 + 3x^2 = 9$$\n$$x^2 - 3x^2 = 5$$\n$$x^2 - 3x = 5 + 9 - 3x$$\n$$x^2 - 3x = 14$$\n$$x^2 - 3x =",
        "gt_answers": "a = 8\n",
        "image_path": "./data/HME100K/test_images/test_1898.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by the following LaTeX format:\n\n$$\\frac{10+4\\sqrt{2}}{3}$$\n\nThe equation is a quotient of two polynomials, with the numerator being 10 + 4\u221a2 and the denominator being 3.",
        "gt_answers": "x _ { 2 } = \\frac { 2 } { 3 } - \\frac { \\sqrt { 1 0 } } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1899.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by:\n\n<latex math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mi>x</mi><mo>=</mo><mi>3</mi></mrow><annotation encoding=\"application/x-tex\">y = 3</annotation></semantics></latex>\n\nThis equation states that x is equal to 3.",
        "gt_answers": "x ^ { 2 } + y ^ { 2 } - 4 x + 3 - y ^ { 2 } - 2 x + 2 = 0\n",
        "image_path": "./data/HME100K/test_images/test_1900.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula for the given image using LaTeX format, we can write:\n\n$$\\text{Image Content}$$\n\nThis formula represents the image content. The formula uses the Unicode character U+26999 (\u2764\ufe0f), which represents a red heart symbol, to represent the image content.",
        "gt_answers": "\\cdot - \\frac { 1 } { 2 } y - ( - 2 1 ) = y \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1901.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image using LaTeX format:\n\n$$ \\text{Image Content} = \\text{number of pixels} \\times \\text{resolution} $$\n\nThis formula calculates the resolution of an image based on the number of pixels in the image and its resolution. The resolution of an image is the number of pixels per inch (PPI) of the image. The more pixels an image has, the higher its resolution will be, and the higher the image's quality will be.",
        "gt_answers": "5 0 m ^ { 2 } = ( 5 0 0 0 ) d m ^ { 2 } 8 0 0 0 0 c m ^ { 2 } = ( 8 ) m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1902.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$x^2 + 3x + 1 = 0$$\n\nThis is a quadratic equation with roots $\\frac{1\\pm\\sqrt{5}}{2}$. The solution to this equation is $x = -\\frac{1\\pm\\sqrt{5}}{2}$.",
        "gt_answers": "\\frac { 8 } { 5 } x _ { 4 } = 2 4 .\n",
        "image_path": "./data/HME100K/test_images/test_1903.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{C}=\\frac{mg}{v^2}$$where C is the centripetal acceleration, m is the mass of the object, g is the acceleration due to gravity, and v is the velocity of the object.",
        "gt_answers": "\\angle A E B = 4 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1904.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{a + b}{c - d}$.",
        "gt_answers": "d = \\sqrt { 1 + k ^ { 2 } } \\cdot \\vert x _ { 1 } - x _ { 2 } \\vert\n",
        "image_path": "./data/HME100K/test_images/test_1907.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{align}\n    \\text{The area of the circle with radius $r$ is given by} \\\n    A = \\pi r^2\n\\end{align}\n```",
        "gt_answers": "y = \\frac { m } { x }\n",
        "image_path": "./data/HME100K/test_images/test_1908.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n$\\\\frac{x}{2} + \\frac{y}{2}$",
        "gt_answers": "x = - \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1909.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is as follows:$$\\frac{2x+4}{x-2}=\\frac{8x+16}{x-4}=\\frac{4x+8}{x-4}=\\frac{4x+8}{x-4}=4$$This is a quadratic equation in the form of $ax^2+bx+c=0$ with $a=2$, $b=4$, and $c=16$. It has two real roots, which can be found by completing the square, as shown above.",
        "gt_answers": "x ^ { 2 } - 2 x + x ^ { 2 } + 4 x + 4 = 8\n",
        "image_path": "./data/HME100K/test_images/test_1910.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression for the formula in the image using LaTeX format.\n\nThe formula in the image is: 1 + 2 = 3\n\nIn LaTeX format, the formula would be written as: $ 1 + 2 = 3 $\n\nThe equation is a simple arithmetic expression that states that the sum of 1 and 2 is equal to 3. This is a basic arithmetic principle that holds true no matter what context you are working in.",
        "gt_answers": "\\therefore y = \\frac { 1 } { 4 } x\n",
        "image_path": "./data/HME100K/test_images/test_1911.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is:$$x+5=y+6$$In this equation, x and y are the variables representing the number of pencils in the two rows. The left side of the equation represents the number of pencils in the first row, while the right side represents the number of pencils in the second row. The equation is true when x is equal to y.",
        "gt_answers": "x = \\frac { 1 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1912.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a LaTeX expression of the formula in the image:\n\n\\begin{center}\n\\frac{1}{3}\n\\end{center}\n\nNote that the fraction line is used to denote division, and the line break between the numerator and denominator is not required as LaTeX automatically adds a line break after a multiplication or division operator.",
        "gt_answers": "O N / / M C , O N = M C\n",
        "image_path": "./data/HME100K/test_images/test_1913.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a length of 20 units and a width of 5 units can be expressed as:\n\nA = l \u00d7 w\n\nwhere l is the length of the rectangle and w is the width of the rectangle. In this case, l = 20 and w = 5, so the area of the rectangle is:\n\nA = 20 \u00d7 5 = 100 units\u00b2\n\nTherefore, the area of the rectangle is 100 units\u00b2.",
        "gt_answers": "x = - \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1914.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 2x + 5y = 40.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This image shows the equation for the area of a triangle. The formula for the area of a triangle is A = (bh) / 2, where b is the base and h is the height. To find the area of this triangle, we can substitute the given values into the formula: A = (8 / 2) \\* 6 / 2 = 8 \\* 3 = 24. Therefore, the area of the triangle is 24 square units.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\text{P} = \\text{R} \\times \\text{a} \\times \\text{n} \\times \\text{t}$$\n\nwhere $\\text{P}$ is the product of $\\text{R}$, $\\text{a}$, $\\text{n}$, and $\\text{t}$; $\\text{R}$ is the radius of the circle; $\\text{a}$ is the area of the circle; $\\text{n}$ is the number of equal parts into which the circle is divided; and $\\text{t}$ is the time taken",
        "gt_answers": "A E = \\frac { 2 7 6 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1917.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is m / m, which represents the slope of a line or a function. The slope is the rate of change of the function with respect to the independent variable x. The unit of measurement for the slope is a ratio or fraction.\n\nIn LaTeX format, the equation would be written as:\n\n$$\\frac{m}{m}$$\n\nwhere m is the slope and m is the measure of the slope.",
        "gt_answers": "m \\geq - \\frac { 5 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1920.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the expression in LaTeX format:\n\n$$\\frac{10}{15} \\times \\frac{40}{50} = \\frac{20}{50}$$\n\nThe expression represents the result of multiplying the ratio of 10 to 15 by the ratio of 40 to 50. The result is then expressed as a ratio of 20 to 50.",
        "gt_answers": "( 1 1 - 9 ) \\div 1 1 = \\frac { 2 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_1921.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n&#x2211;x&#x2212;&#x2211;1&#x2212;1&#x2212;&#x2211;3&#x2212;x&#x2212;1&#x2212;&#x2211;1&#x2212;1\" role=\"presentation\">f(x)=\u2211\u221en=1\u221eanxn\u22121f(x)=\u2211n=1\u221e\u221ean",
        "gt_answers": "+ 2 z - 2 0 y + 5 z = 9 1\n",
        "image_path": "./data/HME100K/test_images/test_1923.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{w}{4}+\\frac{x^2}{9}+\\frac{y^2}{9}+\\frac{z^2}{9}=0$$This formula is a quadratic equation in three variables, with a constant term of 0.",
        "gt_answers": "W _ { 1 } = - ( x - \\frac { 7 } { 2 } ) ^ { 2 } + \\frac { 2 4 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1924.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I cannot generate LaTeX equations from the image provided as it is not a mathematical expression. If you can provide a mathematical expression or equation, I would be happy to write it out in LaTeX for you.",
        "gt_answers": "\\tan \\angle A P D = \\tan \\angle A C E = \\frac { A E } { C E } = \\frac { 5 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1926.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is: $\\frac{4x^2+4x-5}{2x+2}$.\n\nTo derive this formula, we can use the following steps:\n\n1. Simplify the expression inside the parentheses: $\\frac{4x^2+4x}{2x+2}$\n2. Multiply the numerator and denominator by 2: $\\frac{8x^2+8x}{4x+4}$\n3. Combine the terms in the numerator: $\\frac{4x(x+2)+4(x+2",
        "gt_answers": "I _ { 2 } = \\frac { 1 } { 3 } I ^ { \\prime } - \\frac { B L ^ { 2 } w } { 8 r }\n",
        "image_path": "./data/HME100K/test_images/test_1927.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression for the sum of two numbers. The expression is written as follows:$$5+4=9$$This expression represents the result of adding the numbers 5 and 4, which equals 9.\n\nThe sum of two numbers can be represented using the mathematical symbol `+` and can be written as:$$a+b$$where `a` and `b` are the two numbers being added. The expression can be read as \"the sum of a and b is equal to c\".",
        "gt_answers": "\\frac { 1 6 } { 3 } \\times 0 . 4 = \\frac { 3 2 } { 1 5 } B\n",
        "image_path": "./data/HME100K/test_images/test_1928.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I am unable to see the image as it is not provided. Can you please provide the image so I can assist you?",
        "gt_answers": "2 N a O H + H _ { 2 } S O _ { 4 } = N a _ { 2 } S O _ { 4 } + 2 H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_1929.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the expression for the formula in the image using LaTeX format:\n\n$$\\frac{2x^2+3x-5}{x+1}=\\frac{2x^2+3x-5}{x+1}=\\frac{2(x+1)^2+3(x+1)-5}{x+1}=2(x+1)^2+3(x+1)-5$$\nThis formula is a quadratic equation in one variable, x. The left-hand side of the equation is the numerator of the fraction, which represents the equation of a parab",
        "gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1930.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{x^2 + y^2}{x^2 - y^2}$$This can be derived by completing the square on the right-hand side of the equation. The formula can be used to calculate the distance between two points in a two-dimensional plane.",
        "gt_answers": "f ^ { \\prime } ( x ) = - \\frac { 1 } { x ^ { 2 } } - 1 + \\frac { a } { x }\n",
        "image_path": "./data/HME100K/test_images/test_1931.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression for the formula of a circle. The equation is given by the formula r = 3, where r is the radius of the circle and 3 is the radius of the circle. The equation can be represented using the LaTeX format as follows:\n\nr = 3.r = 3.r = 3r = 3\n\nwhere rr is the radius of the circle.",
        "gt_answers": "x _ { 1 } = - \\frac { 7 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_1933.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{4\\left(6x^2 + 9x - 3\\right) - \\frac{28}{3}\\left(4x - 2\\right)}{\\frac{9}{2}\\left(x + 2\\right) - \\frac{1}{2}} $$",
        "gt_answers": "\\vert \\frac { b ^ { 2 } } { 2 k } \\vert = 4\n",
        "image_path": "./data/HME100K/test_images/test_1934.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n$$\\text{ImageContent}\\_\\text{Content} = \\text{ImageContent}\\_\\text{Value}$$\n\nThis is a mathematical equation that shows that the value of an image is equal to the image itself.",
        "gt_answers": "1 0 = 1 . 2 k g\n",
        "image_path": "./data/HME100K/test_images/test_1935.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot display images in this text-based format. Please provide the formula in 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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: $\\frac{1}{4}(\\frac{3}{2}) - \\frac{1}{4}(\\frac{1}{2})$",
        "gt_answers": "\\frac { 5 0 + 5 1 } { 2 } = 5 0 . 5\n",
        "image_path": "./data/HME100K/test_images/test_1939.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the provided image does not contain any mathematical expression or formula. It appears to be an image of a person's hand with some text written on it. To write out the expression of a formula using LaTeX format, you need to provide a mathematical expression in the form of an equation or formula.",
        "gt_answers": "2 x ^ { 2 } + x - ( 2 x - 1 ) ^ { 2 } = - 1 3\n",
        "image_path": "./data/HME100K/test_images/test_1940.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: x^2 + 3x + 1 = 0.",
        "gt_answers": "x + \\frac { 8 } { x } = 6\n",
        "image_path": "./data/HME100K/test_images/test_1941.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 16x2+8y4-6x-10y2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a diagram with four overlapping circles, where each circle is labeled with a number from 1 to 4. The diagram is drawn with a hand-drawn style, with the numbers written in a bold, cursive font. The circles are colored in different shades of blue, with the number 1 in light blue, number 2 in medium blue, number 3 in dark blue, and number 4 in navy blue. The circles are slightly overlapped, with the number 2 partially covering the number 3 and the number 4 partially covering the number 1. The diagram",
        "gt_answers": "x = - \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_1943.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$f(x) = \\frac{1}{4} \\cdot x^2 + \\frac{5}{8} \\cdot x - \\frac{7}{12} \\cdot x^3$$This is a cubic polynomial function with constant term $c=-\\frac{7}{12}$.",
        "gt_answers": "4 . 5 \\frac { V ^ { 2 } } { r . }\n",
        "image_path": "./data/HME100K/test_images/test_1944.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, you would first need to create a mathematical expression for the formula using LaTeX syntax. This could be done by creating a new equation using the \\ equation command, which creates an equation with the specified parameters.\n\nFor example, to write out the formula in the image using LaTeX format, you could use the following LaTeX code:\n\n$ 60 \\times 6 + 5 = 365$\n\nThis would produce the equation 60 \\* 6 + 5 = 365, which is equivalent to the formula",
        "gt_answers": "\\angle A B E = 9 0 ^ { \\circ } - 6 0 ^ { \\circ } = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1945.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\begin{aligned} \\text{Image content} &= \\frac{1}{2}(a+b) + \\frac{1}{2}(c+d) \\\n&= \\frac{1}{2}(a+b) + \\frac{1}{2}(c+2d) \\\n&= \\frac{1}{2}a + \\frac{1}{2}b + \\frac{1}{2}c + \\frac{1}{2}d \\\n&= \\frac{1}{2}(a+b)",
        "gt_answers": "2 \\div 1 6 = \\frac { 2 } { 1 6 }\n",
        "image_path": "./data/HME100K/test_images/test_1946.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the volume of a cylinder can be written as:V = pi \\* r^2 \\* hwhere r is the radius of the cylinder and h is its height.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows:\n\n$$\\text{Area of the circle} = \\frac{1}{2} \\cdot r^2$$\n\nwhere r is the radius of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$$5x^4+14x^3+20x^2+27x+34$$This is a polynomial equation of degree 4, with the leading coefficient 5, and the constant term 34.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is: $\\frac{1}{2} \\cdot 2 + \\frac{1}{3} \\cdot 3 + \\frac{1}{4} \\cdot 4 = \\frac{5}{4}$\n\nThis is obtained by adding the fractions with the same denominator, $\\frac{1}{4}$, and simplifying the expression. The numerators are $\\frac{1}{2}$, $\\frac{1}{3}$, and $\\frac{1}{4}$, respectively.",
        "gt_answers": "2 \\frac { 3 } { 2 } = \\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_1951.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a mathematical expression for calculating the average rate of change of a quantity over a given period of time. The formula is written as follows:\n\n$\\frac{\\Delta Q}{\\Delta t}$\n\nwhere $\\Delta Q$ is the change in the quantity being measured over the given time period, and $\\Delta t$ is the duration of that period. This formula can be used to calculate the average rate of change of any quantity that varies over time, such as the price of a stock, the level of a pollutant in the air, or the amount of water in a river.\n##",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\na + b = c\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: y = 2x + 3.\n\nTo write out the expression of the formula in LaTeX format, you can use the following code:\n\n$$y = 2x + 3$$\nThis will give you the equation in LaTeX format, with the variable x in italics and the constant 3 in normal text.",
        "gt_answers": "a \\times b \\times c = a \\times ( b \\times c )\n",
        "image_path": "./data/HME100K/test_images/test_1954.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} & \\text{The image shows the formula } \\frac{a^2 + b^2}{a^2 - b^2} \\text{, where } a = 2 \\text{ and } b = 2 \\text{.}\\end{aligned}$$\n\nIs there anything else you need help with?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\begin{aligned}\n\nE &= hc/\u03bb \\\\\nE &= hc/\u03bb \\\\\nE &= hc/\u03bb\n\\end{aligned}$$where $E$ is the energy of the photon, $h$ is Planck's constant, $c$ is the speed of light, $\\lambda$ is the wavelength of the photon.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a perimeter of 9 cm is:\n\nA = lw\n\nwhere l is the length and w is the width. Plugging in the values given in the problem, we have:\n\nA = 9 \u00d7 4\nA = 36 cm\u00b2\n\nTherefore, the area of the rectangle is 36 cm\u00b2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression in the image:\n\n\\begin{center}\n\\(m\\_vy + \\frac{vy^2}{2m} = \\frac{1}{2}mv^2\\)\n\\end{center}\n\nThis is the equation of motion for an object moving under the influence of both a constant gravitational force and a constant acceleration. The left-hand side of the equation represents the net force acting on the object, which is the sum of the gravitational force and the acceleration. The right-hand side of the equation represents the net kinetic energy of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the expression of the formula in LaTeX format:\n\n\\begin{align}\ny &= 2x^2 - 5x + 2\\\n\\end{align}\n\nwhere x is the independent variable and y is the dependent variable. The equation is a quadratic equation of degree 2, which means that the highest power of x in the equation is 2. The constant term is 2, which is the coefficient of the x^2 term, and the linear term is -5x, which is the coefficient of the x term. The second linear term is 2, which",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ a + b + c = d $$\n\nwhere $a, b, c,$ and $d$ are positive integers.",
        "gt_answers": "A D = 3 + 6 - t = 9 - t\n",
        "image_path": "./data/HME100K/test_images/test_1962.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned}5-2+4&=3\\end{aligned}$$",
        "gt_answers": "3 \\div 3 = 1 2 4 \\div 4 = 6\n",
        "image_path": "./data/HME100K/test_images/test_1963.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} \\text{bx} = \\frac{1}{2}\\left(\\text{x}+\\text{y}\\right) \\quad & \\Rightarrow \\quad \\text{x}+\\text{y}=\\text{2bx} \\quad & \\Rightarrow \\quad \\text{x}=\\frac{1}{2}\\left(\\text{2bx}+\\text{y}\\right) \\quad & \\Rightarrow \\quad \\text{x}=\\frac{1}{2}\\left(\\text{y}+2bx",
        "gt_answers": "1 3 + x = ( 4 7 + x ) \\times \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1964.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $\\sqrt{2x^2 + 3}$. This formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, $x$ is the length of one side of the triangle, and $2x^2$ is the length of the hypotenuse. The term $3$ represents the length of the other side of the triangle. By substituting $x$ for the variable $x$, we",
        "gt_answers": "+ \\frac { x + 2 } { x - 2 } = \\frac { 8 } { ( x + 2 ) ( x - 2 ) }\n",
        "image_path": "./data/HME100K/test_images/test_1965.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression:\n\n$$\\text{s} = \\frac{100 \\times 0.5}{100 + 50} = \\frac{50}{150} = \\frac{1}{3}$$",
        "gt_answers": "( x - 2 y ) ( x - y ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_1967.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 5x^2 + 9x - 3. This is because the equation for a parabolic shape with a vertex at the origin is given by y = ax^2 + bx + c, where a, b, and c are constants. The x-coordinate of the vertex is given by x = -b/2a, and the y-coordinate is given by y = c/2a. In this case, a = 5, b = 9, and c = -3, so the equation becomes 5x^",
        "gt_answers": "1 2 - 8 = 4\n",
        "image_path": "./data/HME100K/test_images/test_1968.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$$ \\frac{100}{25} = \\frac{4}{1} $$\n\nwhich simplifies to:\n\n$$ \\frac{100}{25} = 4 $$",
        "gt_answers": "\\frac { 3 \\pi } { 2 } + 2 k \\pi ]\n",
        "image_path": "./data/HME100K/test_images/test_1970.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is the sum of the numerator and denominator of the fraction. The numerator is 1, and the denominator is 4. The sum of these is 5, which is written as 5 in the image.\n\n5(4)+1=51+1=62+1=62+1=62+1=62+1=62+1=62+1=62+1=62+1=62+1=62+1=62+1=62+1=62+1=6",
        "gt_answers": "\\frac { 3 7 \\pm \\sqrt { 6 9 3 . } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1971.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{5 - 3}{7 - 5} = \\frac{2}{2} = 1$$\n\nThis is a simple algebraic expression that evaluates to 1. The expression uses the division operation to find the quotient of 5 - 3 divided by 7 - 5, which equals 2. The fraction is then simplified to 1.",
        "gt_answers": "\\frac { 1 } { 5 } + \\frac { 2 } { 5 } - \\frac { 3 } { 5 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_1972.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{aligned}\n\\text{Let } x \\text{ be the set of all real numbers.} \\\\\n\\text{Let } A \\text{ be the set of all even integers greater than 4.} \\\\\n\\text{Let } B \\text{ be the set of all odd integers greater than 3.} \\\\\n\\text{Let } C = A \\cup B. \\\\\n\\text{Let } D = \\text{the set of all integers greater than 5.} \\\\\n\\text{Let } E = D - C. \\\\\n\\text{Let",
        "gt_answers": "\\vert - 1 - x \\vert = 3 \\vert x \\vert - 7\n",
        "image_path": "./data/HME100K/test_images/test_1973.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is x2 - 6x + 11.\n\nTo derive the formula, we can use the method of substitution. Let u = x2 and v = x. Then the equation becomes:\n\nu - 6v + 11 = 0\n\nMultiplying both sides by u, we get:\n\nu2 - 6uv + 11u = 0\n\nExpanding the product, we get:\n\nu2 - 6v2 + 11u = 0\n\nSimplifying the equation, we get:",
        "gt_answers": "x - \\frac { x + 9 } { 4 } = a\n",
        "image_path": "./data/HME100K/test_images/test_1976.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\text{Image Content} = \\frac{500\\times400}{100\\times100}$$",
        "gt_answers": "5 0 \\times 4 0 - 4 0 \\times 4 0 = ( 4 0 + 6 0 ) \\times\n",
        "image_path": "./data/HME100K/test_images/test_1977.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{equation} \\frac{dV}{dt} = \\frac{dW}{dt} + P \\end{equation}\n\nIn this formula, V is the volume of the gas in the cylinder, W is the work done on the gas, P is the pressure of the gas, and dt is the infinitesimal time interval.\n\nNote that this formula assumes that the gas is an ideal gas, which means that it behaves perfectly and has no internal structure. This assumption is necessary for the formula to",
        "gt_answers": "C O _ { 2 } + H _ { 2 } O = H _ { 2 } C O _ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1978.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:x2 + xy + y2 = xy2 + xy + y2x2 + y2 = xy2 + xy + y2x2 + y2 = xy2 + xy + y2x2 + y2 = xy2 + xy + y2x2 + y2 = xy2 + xy + y2x2 + y2 = xy2 + xy + y2x2 + y2 = xy2 + xy + y2x2 + y2 = xy2 + xy +",
        "gt_answers": "\\frac { k x _ { 1 } - 1 } { x _ { 1 } } + \\frac { k x _ { 2 } - 1 } { x _ { 2 } } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1979.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a mathematical expression for calculating the area of a rectangle with a given length and width. The formula is written as:\n\n$$ A = L \\times W $$\n\nwhere $A$ is the area of the rectangle, $L$ is the length, and $W$ is the width. This formula is a basic principle of geometry and can be used to calculate the area of any rectangle, regardless of its size or shape.",
        "gt_answers": "\\angle A B D = \\angle B A O = 1 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_1980.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is given by:\n\n<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><msub><mi>x</mi><mi>n</mi></msub><mo>=</mo><msup><mi>a</mi><mi>r</mi></msup></mrow><annotation encoding=\"application/x-tex\">\\frac{1}{a^{2}+b^{2}}</annotation></semantics></math>\n\nwhere xn is the",
        "gt_answers": "x k m / h\n",
        "image_path": "./data/HME100K/test_images/test_1981.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is x + 3y - 6z = 9. This is a linear equation with three variables, x, y, and z. The equation is written in the form of x + 3y - 6z = 9, which means that the value of the equation is 9 when the values of x, y, and z are equal to 1, 2, and 3, respectively.",
        "gt_answers": "\\frac { x } { x + 1 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1982.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as follows:\n\n$$\\text{Number of apples} = \\frac{10}{5}\\cdot \\frac{4}{5} \\cdot 3 = \\frac{20}{5}\\cdot 4 = \\boxed{4}$$",
        "gt_answers": "m \\% = \\frac { 0 . 4 g } { 1 g } \\times 1 0 0 \\% = 4 0 \\%\n",
        "image_path": "./data/HME100K/test_images/test_1983.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\nx - (1)y = x - y \\* (1)\n\nwhere x and y are variables and (1) represents the constant value of 1.",
        "gt_answers": "x = \\frac { a - 2 } { ( a + 2 ) ( a - 2 ) }\n",
        "image_path": "./data/HME100K/test_images/test_1986.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$ \\begin{aligned} \\text{Image Content} \\end{aligned} $$\n\nNote that this is a placeholder for the actual image content, which is not shown in the provided text.",
        "gt_answers": "x ^ { 2 } = \\frac { 3 } { a + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_1987.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $ 5 \\times 2 + 12 = 17 $.",
        "gt_answers": "( 5 + 1 ) \\times 2 = 1 2 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_1989.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX representation of the expression in the image:\n\n$$\\frac{1}{2}\\left(\\frac{2}{3}+\\frac{1}{4}\\right)=\\frac{1}{4}$$\n\nExplanation:\n\n* The expression in the image is $\\frac{1}{2}\\left(\\frac{2}{3}+\\frac{1}{4}\\right)$\n* This can be rewritten as $\\frac{1}{2}\\left(\\frac{2}{3}+\\frac{1}{4}\\right)=\\frac{1}{4}$ using the distributive property of multiplication over addition",
        "gt_answers": "y = \\frac { x } { k }\n",
        "image_path": "./data/HME100K/test_images/test_1990.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image is:\n\n&#x220A;40&#x22C5;5&#x220A;6&#x22C5;8&#x220A;2&#x22C5;2\" role=\"presentation\" style=\"position: relative;\">40\u00b15\u00d76\u00b18\u00d72\u00b1240\u00b0C40\u00b15\u00d76\u00b18\u00d72\u00b12\\frac{40\\pm 5}{6\\pm 8}\\frac{2\\pm 2}{40",
        "gt_answers": "4 0 5 \\div 5 0 = 8 \\cdots 5\n",
        "image_path": "./data/HME100K/test_images/test_1992.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$\\frac{m}{t} = \\frac{1}{2}\\left(\\frac{1}{t} - \\frac{2}{t^2}\\right) - \\frac{1}{4}\\left(\\frac{1}{t} - \\frac{3}{t^2}\\right)$$\n\nwhere $m$ is the mass of the object and $t$ is the time it takes for the object to fall from rest to the ground.\n\nThe formula can be derived from the equations of motion for an object falling under the influence of gravity. The",
        "gt_answers": "\\rho _ { A } = \\frac { m _ { A } } { V _ { A } } = \\frac { 4 k y } { 2 \\times 1 0 ^ { - 7 } m ^ { 3 } } = 2 \\times 1 0 ^ { 3 } k g / m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1993.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{equation}\nx = \\frac{1}{2} \\times 2 + \\frac{1}{4} \\times 4 = \\frac{5}{2}\n\\end{equation}\n\nThis formula multiplies the sum of $\\frac{1}{2}$ and $\\frac{1}{4}$ with $\\frac{1}{2}$ to get $\\frac{5}{2}$.",
        "gt_answers": "y = - 8 0 \\times \\frac { 3 0 0 } { 1 7 } + 2 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_1995.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:$$\\sqrt{(x + y)^2 + 2xy} = x + y + 2xy$$This formula gives the sum of the squares of x and y, and their product.",
        "gt_answers": "y _ { 2 } = \\frac { 1 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_1996.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nThe equation represents a line with a slope of 0.5 and y-intercept of 4.5.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear. Please provide the image for me to determine the formula.",
        "gt_answers": "x = - \\frac { 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_1998.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is A = l x w, where l is the length and w is the width. In this case, the length is 4 cm and the width is 2 cm. So the area of the rectangle is 4 cm x 2 cm = 8 cm\u00b2.\n\nHere's the LaTeX code for the formula:\n\n\\begin{center}\nA = l x w \\\\\n4 cm & 2 cm \\\\\n8 cm$^2$\n\\end{center}",
        "gt_answers": "\\frac { x ^ { 2 } } { 3 } + y ^ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_1999.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the ratio of the area of the circle to the square.\n\nUsing LaTeX format, the formula can be written as:\n\n\\frac{\u03c0r^2}{4}\n\nwhere r is the radius of the circle.",
        "gt_answers": "K _ { A P } + K _ { B P } = 0\n",
        "image_path": "./data/HME100K/test_images/test_2000.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\na + b = 5\n\\end{align\\*}\n\nHere, 'a' and 'b' are variables, and the equation states that their sum is equal to 5.",
        "gt_answers": "x = \\frac { 7 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2001.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:$$y = x^2 + 2x - 3$$This is a quadratic equation in the form of a quadratic equation with constant term 3 and leading coefficient 2. The x-intercepts are given by the formula x = -b / 2a, which corresponds to the points (0, -3) and (2, 0) in this case.",
        "gt_answers": "\\angle 1 6 0 ^ { \\circ } \\angle 2 6 0 ^ { \\circ } \\angle 3 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2002.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for finding the distance between two points (x1, y1) and (x2, y2) is:",
        "gt_answers": "\\frac { C M } { M A } = \\frac { M N } { A B }\n",
        "image_path": "./data/HME100K/test_images/test_2003.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{k} = \\frac{3}{2} \\cdot \\frac{2}{4} \\cdot \\frac{4}{3} \\cdot \\frac{3}{4} = \\frac{1}{4} $$\nThis formula is a geometric sequence with a common ratio of $\\frac{2}{3}$. The formula gives the fifth term in the sequence.",
        "gt_answers": "k ^ { 2 } - 4 - k ^ { 2 } - k - 6 = 0\n",
        "image_path": "./data/HME100K/test_images/test_2004.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\nThe image shows a graph with two functions f(x) = 3x2 and g(x) = 2x - 1 overlaid on a common x-axis. The graph is symmetric about the origin, with both functions decreasing as x increases and both approaching zero at x = 2.",
        "gt_answers": "\\angle A O D = 3 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2005.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not written in LaTeX format. However, it can be written as follows:\n\n5 + 3x4 + 6x5 + 8x6 + 9x7 = 35x7 + 20x8 + 15x9 + 10x10 + 15x11 + 5x12 + 5x13 + 5x14 + 3x15 + 3x16 + 2x17 + 3x18 + 3x19 + 3x",
        "gt_answers": "1 5 . 7 \\div 3 . 1 4 = 5 ( d m )\n",
        "image_path": "./data/HME100K/test_images/test_2006.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$ 2x^2 + 4x - 5 = 0 $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image. Please provide the image so I can assist you.\n\nIf the image is of a function, the formula for the function is:\n\nf(x) = x^2 + 2x + 1",
        "gt_answers": "\\frac { x + 2 } { 3 } - 2 ( x - 1 ) = - 4\n",
        "image_path": "./data/HME100K/test_images/test_2009.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the image you provided:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->, line width=1.5pt] (0,0) -- (4,0) node[right] at (2,0) {$\\alpha$};\n\\draw[->, line width=1.5pt] (0,0) -- (0,4) node[above] at (0,2) {$x$};\n\\draw[->, line width=1.5pt] (4,0) -- (4,4",
        "gt_answers": "( 4 x + 3 ) : 3 = ( 1 0 x - 2 ) :\n",
        "image_path": "./data/HME100K/test_images/test_2012.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image given is:\n\n![Image Content](https://i.imgur.com/e8l7vXP.png)",
        "gt_answers": "\\frac { B C } { M D } = \\frac { C N } { B N }\n",
        "image_path": "./data/HME100K/test_images/test_2013.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nx4 + 3x3 + 5x2 + 5x + 12\n\nWhere, x is the variable representing the input values for the formula, and the coefficients 1, 3, 5, 3, and 12 represent the contribution of each input value to the output.",
        "gt_answers": "\\vert x - 1 \\vert = 3\n",
        "image_path": "./data/HME100K/test_images/test_2014.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:$$\\sqrt{649}\\sqrt{5}+\\sqrt{729}\\sqrt{5}=9\\sqrt{5}+\\frac{1}{2}\\sqrt{729}\\sqrt{5}$$",
        "gt_answers": "( 8 - 2 m m - 1 )\n",
        "image_path": "./data/HME100K/test_images/test_2015.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n<LaTeX>\n$$\\begin{aligned}\n\\text{number of triangles} &= 6 \\\n\\text{number of circles} &= 8 \\\n\\text{number of squares} &= 4 \\\n\\text{total number of shapes} &= 6 + 8 + 4 = 18\n\\end{aligned}$$\n<LaTeX>\n\nwhere each shape is represented by the letter \"T\" for triangles, \"C\" for circles, and \"S\" for squares. The formula",
        "gt_answers": "( 1 + 5 0 \\% ) \\cdot 8 0 \\% x - x = 8\n",
        "image_path": "./data/HME100K/test_images/test_2016.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression in the image using LaTeX format is:\n\n\\begin{center}\na = \\frac{1}{2} \\\\\nb = \\frac{3}{4} \\\\\nc = \\frac{1}{4}\n\\end{center}\n\nThe values for a, b, and c can be calculated by dividing the fractions on the right side of the equation by the fractions on the left side. For example, to calculate a, we would divide 1/2 by 3/4, which gives us 1/4. We can then use this value to",
        "gt_answers": "A l _ { 2 } O _ { 3 } + 2 N a O H = 2 N a A l O _ { 2 } + H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_2017.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a function of x and y, given by: y = x + 2xy - 3x3.",
        "gt_answers": "\\overrightarrow { D S } = ( \\frac { \\sqrt { 2 } } { 2 } a\n",
        "image_path": "./data/HME100K/test_images/test_2018.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula:\n\n$$\\begin{aligned} 8 &+ 4\\left(x + \\frac{1}{2}\\right) + 3 \\\\ & = \\left(8 + 4x + 3\\right) + \\left(4 + \\frac{1}{2}\\right) \\\\ & = 8 + 4x + 3 + 4 + \\frac{1}{2} \\\\ & = 8 + 4x + \\frac{9}{2} \\end{aligned}$$\n\nThe expression is simply the sum",
        "gt_answers": "\\Delta O A P 6 = \\frac { 8 \\times 3 } { 2 } = 1 6\n",
        "image_path": "./data/HME100K/test_images/test_2019.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ x = \\frac{a+b}{c-d}$$where $a$, $b$, $c$, and $d$ are constants.",
        "gt_answers": "v = a ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2020.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by A = l \u00d7 w, where l is the length and w is the width. Using LaTeX format, we can write this as $\\text{A} = \\text{l} \\times \\text{w}$.",
        "gt_answers": "\\cos \\frac { \\alpha } { 2 } < 0\n",
        "image_path": "./data/HME100K/test_images/test_2021.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{1}{1+x^2}=\\sqrt{\\frac{1}{1+x^2}}$$\n\nThis is a formula for the square root of 1 plus x squared, which is the hypotenuse of a right triangle with legs of length 1 and x.",
        "gt_answers": "\\because \\angle E A B = \\angle E A F + \\angle F A B = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2022.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x + 10y + 5z = 30, where x, y, and z are variables.",
        "gt_answers": "\\sqrt { 1 + k ^ { 2 } } \\vert k + \\frac { 2 } { k ^ { 2 } } \\vert = \\frac { 3 \\sqrt { 1 + k ^ { 2 } } } { k ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_2023.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\begin{aligned} 4x^2 + 9x - 3 &= 0 \\\n\\frac{4x^2 + 9x - 3}{0} &= 1 \\\nx = \\frac{-3 \\pm \\sqrt{12}}{2} \\\nx &= \\frac{-3 + \\sqrt{12}}{2} \\\nx &= \\frac{-3 - \\sqrt{12}}{2} \\\n\\end{aligned}$$\n\nThe solutions to the equation are:\n\n$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n![Image Content](https://upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Pythagoras-theorem-for-right-triangle-with-square-on-hypotenuse.svg/1200px-Pythagoras-theorem-for-right-triangle-with-square-on-hypotenuse.svg.png)\n\nThe image shows the Pythagorean theorem in a right triangle with a square on the hypotenuse.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 3x^2 + 2x - 5 $$\n\nwhere x is a variable. This formula represents a parabola with a vertex at the origin and a minimum value of -2.",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2026.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression for the formula in the image using LaTeX format:\n\n$$\\text{ImageContent} = \\frac{2 \\times \\text{magnitude of the image}}{3 \\times \\text{height of the image}} \\times \\frac{1}{\\text{width of the image}}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: $\\frac{1}{2}(x + 3) - \\frac{1}{4}(y - 2)$.",
        "gt_answers": "x _ { 1 } = 1 - \\frac { 1 } { 2 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2029.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{equation}\n\\text{number of apples in the basket} = \\frac{10 - 2}{5}\n\\end{equation}\n\nThe expression is obtained by finding the number of apples in the basket, which is 10, and subtracting the number of apples that have been taken out of the basket, which is 2. The result is then divided by 5 to obtain the number of apples remaining in the basket.",
        "gt_answers": "\\frac { 3 } { 4 } \\times \\frac { 4 } { 5 } = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2030.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{equation}\na + b = c\n\\end{equation}\n\\end{center}\n\nThis equation states that the sum of `a' and `b' is equal to `c'.",
        "gt_answers": "\\frac { c } { a + b } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_2031.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not clear. Can you please provide more information or context about the formula?",
        "gt_answers": "x ^ { 2 } = \\frac { a ^ { 2 } } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_2032.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 1. (2x + 5) \\* 7 - 4 + 3 = 16x + 3 + 7 - 4 = 20x + 3 + 3 = 23x + 3.",
        "gt_answers": "( 1 7 ) + ( 5 0 ) = ( 6 7\n",
        "image_path": "./data/HME100K/test_images/test_2033.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$ \\frac{t+10}{t-5} $$\n\nwhere t is a variable representing time in seconds.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as: A = \u03c0r^2, where r is the radius of the circle.\n\nUsing LaTeX format, the formula can be written as:\n\n$$ A = \\pi r^2 $$\n\nwhere r is the radius of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the following equation: A = bh, where b is the width and h is the height.",
        "gt_answers": "a + 1 6 a - 3 6 = 9\n",
        "image_path": "./data/HME100K/test_images/test_2037.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as:$$\\frac{x^2}{4}+\\frac{y^2}{9}+\\frac{z^2}{16}=\\frac{500}{12}\\$$This is a quadratic equation in three variables, with the constant term 500/12 on the right side. The coefficients of the variables are 0.5 for x, 0.5 for y, and 0.25 for z.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a linear regression equation in the form of y = b0 + b1x, where b0 is the intercept and b1 is the slope. The equation is represented by the equation y = 3x - 2.",
        "gt_answers": "x = \\frac { 1 9 - 3 y } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2039.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:$$\\frac{1}{2}\\times\\frac{3}{4}\\times\\frac{5}{6}\\times\\frac{7}{8}\\times\\frac{9}{10}\\times\\frac{11}{12}\\times\\frac{13}{14}\\times\\frac{15}{16}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: 3 \\* ( 5 - 3 ) \\* ( 8 + 5 ) - 3 \\* ( 2 + 6 ) \\* ( 2 - 1 ) + 3 \\* ( 5 + 2 ) \\* ( 6 - 3 ) + 2 \\* ( 4 + 3 ) \\* ( 4 - 1 ) + 1 \\* ( 3 + 2 ) \\* ( 3 - 1 ) + 3 \\* ( 4 + 1 ) \\* (",
        "gt_answers": "t = - \\frac { 9 ( 1 - \\sqrt { 3 } ) } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2041.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the formula for the boiling point of a substance. The boiling point is the temperature at which a substance changes from a liquid to a gas. The formula for the boiling point of a substance is given by the equation:boiling point = (Vapor pressure + liquid pressure) / (density of the liquid - density of the vapor)boiling point = (Pv + Pl) / (\u03c1l - \u03c1v)\\boiling\\_{point} = \\left(\\frac{P\\_{v}+P\\_{l}}{\u03c1\\_{l}-\\rho",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression on the image:\n\n$$\\frac{120 - 86}{16 + 10} = \\frac{34}{26}$$\n\nIs there anything else I can help with?",
        "gt_answers": "\\frac { P ^ { 2 } } { 4 } + P ^ { 2 } = - \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2043.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the image you provided:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[black,thick] (0,0) -- (1,0) node[midway,right] {$x$};\n\\draw[black,thick] (0,0) -- (0,1) node[midway,above] {$y$};\n\\draw[black,thick] (1,0) -- (1,1) node[midway,above] {$y=x$};\n\\draw[black,thick] (0,1",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{10\\times 5 + 4\\times 3 + 1\\times 2 - 3\\times 1 + 2\\times 4 + 3\\times 6 + 1\\times 5}{10 + 4 + 1 + 3 + 2 + 4 + 3 + 5} = \\frac{55}{47} \\approx 1.17$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle is given by:\n\nA = l \\* w,\n\nwhere l is the length and w is the width of the rectangle.\n\nThe area of the rectangle in the given image is 15 cm^2.",
        "gt_answers": "x = 6 \\div \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2047.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$ E = mc^2 $$\n\nwhere $E$ is the energy of the object, $m$ is the mass of the object, and $c$ is the speed of light in a vacuum.",
        "gt_answers": "- 5 \\leq x + y + z \\leq 5\n",
        "image_path": "./data/HME100K/test_images/test_2048.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: $\\frac{\\frac{20}{50}}{\\frac{30}{60}}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\sqrt {36 - x^2}$.\n\nThis formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Using this theorem, we can write the formula for the area of a right triangle as$\\sqrt {base \\* height}$.\n\nIn the image, the length of the hypotenuse is 12, so the formula becomes$\\sqrt {",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format of the expression:\n\n\\begin{equation}\n5x^2 + 6x - 1 = 0\n\\end{equation}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{4x}{3}$",
        "gt_answers": "\\frac { 1 } { 5 } \\times \\frac { 5 } { 8 } = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2053.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{a}{b}=\\frac{b}{a}$.\n\nIn the image, the formula is written as: $\\frac{6}{x}=\\frac{x}{6}$. This means that the ratio of $6$ to $x$ is equal to the ratio of $x$ to $6$. In other words, $\\frac{6}{x}$ and $\\frac{x}{6}$ represent the same value.",
        "gt_answers": "x = \\frac { 6 } { 7 } \\div \\frac { 2 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_2054.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a blackboard with some equations written on it. The first equation is 4(x + 5) - 9 = 3x - 5, which can be rewritten as 4x + 5 - 9 = 3x - 5. The second equation is x2 + 6x - 12 = 0, which can be rewritten as x2 + 6x - 12 = 0. The third equation is y = mx + b, which is the equation of a line in the form y = mx + b. The fourth equation",
        "gt_answers": "C H = \\frac { 2 \\sqrt { 5 } } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2055.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by:\n\n$$\\frac{4x^2+4x-3}{2x-1}=\\frac{4(x+1)^2+1}{2(x+1)-3}=(x+1)^2-3$$\n\nAlternatively, we can write the expression as:\n\n$$\\frac{4x^2+4x-3}{2x-1}=\\frac{2(x+1)^2+2(x+1)-3}{2(x+1)-3}=(x+1)^2-3",
        "gt_answers": "x = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2057.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by $A = \\pi r^2$, where $A$ is the area and $r$ is the radius of the circle. In this case, the radius is 3 cm and the area is 9 cm^2.\n\nThe area formula for a circle with radius $r$ is given by $A = \\pi r^2$. Therefore, the area of the circle is $9 = \\pi (3)^2$. Solving for $3^2$, we get $3^2 = 9$. Therefore, $3 = 3$.##",
        "gt_answers": "x _ { 2 } = \\frac { 1 - \\sqrt { 5 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2058.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \\frac{1}{1 + x^2} \\cdot \\frac{1}{1 + x} = 1 - x^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we need to identify the variables and their respective values.\n\nFrom the given image, we can observe that the given formula is used to calculate the volume of a cone with a radius of 3.5 cm and a height of 22 cm. The formula uses the volume of a cone formula V = (1/3)\u03c0r^2h.\n\nUsing this formula, we can write out the expression for the volume of the cone as follows:\n\nV = (1/3)\u03c0r^2h\n= (1",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format. Can you please provide the LaTeX format for the formula?",
        "gt_answers": "y \\frac { - e ^ { x } } { x } ( x \\neq 0 )\n",
        "image_path": "./data/HME100K/test_images/test_2061.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula with a fraction in the denominator and a number in the numerator. The formula is expressed as follows: ( 1/3)\\* 2 + 5 = 4.5\\*2 + 5 = 8.5.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as:\n\n$$\\frac{x+y+z}{2}$$\n\nwhere x, y, and z are the lengths of the sides of the image.",
        "gt_answers": "x = 2 _ { 4 } - \\frac { 2 0 } { 3 k - 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2063.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression in the image:\n\n\\begin{align\\*}\n\\text{ImageContent} &= \\frac{1}{2} \\cdot \\left(\\frac{1}{3}\\right) \\cdot \\left(\\frac{2}{5}\\right) \\cdot \\left(\\frac{4}{7}\\right) \\cdot \\left(\\frac{5}{9}\\right) \\cdot \\left(\\frac{6}{11}\\right) \\cdot \\left(\\frac{7}{13}\\right) \\cdot \\left(\\frac{8}{1",
        "gt_answers": "x _ { 1 } = - 2 + 2 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2064.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format of the expression in the image:\n\n$$\\frac{5(a + b)}{(a - 3)(b - 2)} = \\frac{5(a + b)}{(a - 3)(b - 2)}$$\n\nIs there anything else I can help you with?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{equation}\n\\frac{a^{2}+b^{2}}{c^{2}}\n\\end{equation}\n\\end{center}\n\nHere, `a`, `b`, and `c` are variables, and the expression calculates the ratio of the sum of `a` squared and `b` squared to `c` squared.",
        "gt_answers": "x = \\frac { 4 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_2067.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write the expression of the formula in the image using LaTeX format. Here is the expression:\n\n\\begin{center}\n\\begin{aligned}\n\\frac{d^2x}{dt^2} &= \\frac{1}{m}\\frac{dx}{dt}\\frac{d^2x}{dt^2} - \\frac{1}{m^2}\\frac{d^2x}{dt^2} + \\frac{1}{m}\\frac{dx}{dt}\\frac{d^2x}{dt^2} - \\frac{1}{m",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "4x^2+8x+5",
        "gt_answers": "x = \\frac { 4 \\pi } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_2069.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for adding two numbers. The first number is 5 and the second number is 4. The formula for adding two numbers is: 5 + 4 = 9.",
        "gt_answers": "\\frac { 2 + x } { 2 } > \\frac { 2 x - 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2070.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\nsin(5\u03c0/6)\n\nThis formula can be written in LaTeX format as:\n\nsin(5\u03c0/6)\n\nThe image is of a mathematical expression that represents the ratio of the length of a line to its width. The formula is sin(angle), where angle is the angle whose sine is being calculated. The value of angle is given in the image as 5\u03c0/6, which is an acute angle of approximately 85.71 degrees.",
        "gt_answers": "\\sin a = - \\frac { 4 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2071.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for a point on the unit circle with polar coordinates (r,\u03b8) is given by r=cos\u03b8and\u03b8=sinr. Therefore, the equation is'r=cos\u03b8'.",
        "gt_answers": "x = \\frac { 1 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2072.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula for the area of a triangle with sides of length 3 and 4 can be written as:\n\nA = (1/2) \\* (3^2 + 4^2)\n\nThis formula uses the Heron's formula to find the area of a triangle by taking the sum of the squares of its sides. The constant 1/2 is used to simplify the formula and make it easier to calculate.",
        "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": "MiniGPT4"
    },
    {
        "question": "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 - 4.",
        "gt_answers": "4 \\times 6 \\times 2 = 4 8 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_2074.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:3m=0m.",
        "gt_answers": "3 m = 3 0 d m\n",
        "image_path": "./data/HME100K/test_images/test_2075.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is the integral of a function f(x) with respect to x. It is represented as a sum of infinitesimal quantities. The expression is given by:\n\n\u222bf(x) dx\n\nwhere f(x) is the integrand and dx is an infinitesimal quantity of integration.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image you have provided is a mathematical expression. It appears to be an equation that represents the sum of two fractions. The equation is given as: y = 3x + 4x + 5x + 6x. The equation represents the sum of the four fractions, with each fraction being added to the sum. The equation is written in LaTeX format as: y = \\frac{3}{1} + \\frac{4}{1} + \\frac{5}{1} + \\frac{6}{1}. This is a mathematical expression that represents the sum of four fractions.",
        "gt_answers": "y _ { 4 } = - \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2078.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\nm= 3x+2y\n\nwhere m is the number of people in a classroom, x is the number of girls in the classroom, and y is the number of boys in the classroom.",
        "gt_answers": "m = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2079.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression in the image:\n\n\\begin{center}\n\\frac{1}{\\sqrt{x^2+y^2}}\n\\end{center}\nThis formula represents the distance between two points in a two-dimensional space. The numerator is the difference between the squares of the x and y coordinates, while the denominator is the square root of that sum.",
        "gt_answers": "y _ { 2 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_2080.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{align\\*}\ny &= x^2 + 2x - 1\\\n&= (x + 1)(x + 1)\\\n&= x^2 + x + 1\\\n&= x^2 + 1\\\n\\end{align\\*}\n\nTherefore, the equation of the line passing through the given point is y = x^2 + 1.",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2081.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{3}{4} x^2 + \\frac{1}{2} x + \\frac{1}{4}$\n\nThe formula in the image is a quadratic equation, which has the form $ax^2+bx+c$. The coefficients $a$, $b$, and $c$ are determined by the given values of $x$ and $y$, which are 3 and 5, respectively. The solutions of the equation are the values of $x$ that satisfy the equation.\n\nTo find the solutions, we set",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image can be written as:\n\n$$\\begin{aligned} & (2x^2 + 4x - 3) \\cdot (\\frac{1}{2} - x) \\cdot (x + 3) \\cdot (x - 1) = \\frac{1}{4}x^4 - \\frac{1}{2}x^3 + \\frac{1}{2}x^2 - 3x + 3 \\end{aligned}$$\n\nThe image represents a polynomial function of degree 4, where the variable x is raised to the power of",
        "gt_answers": "C a ( O H ) _ { 2 } + C O _ { 2 } = C a C O _ { 3 } \\downarrow + H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_2087.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is given by: $\\frac{a}{b}=\\frac{x^2+y^2}{2a}+\\frac{y}{2b}$.\n\nHere, $x$ and $y$ are the coordinates of the point on the curve and $a$ and $b$ are the semi-major and semi-minor axes of the ellipse, respectively. The equation of the ellipse is given by $\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1$.",
        "gt_answers": "x = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2088.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\mathrm{K\\_2 \\: O\\_2 + \\mathrm{CH\\_4 \\rightarrow CO\\_2 + 2H\\_2}}$$ This is a chemical equation representing the combustion reaction of methane gas in oxygen, with the products being carbon dioxide and water vapor.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=1.5]\n\\draw[black] (0,0) -- (3,0) node[midway, below] {$x$};\n\\draw[black] (0,0) -- (0,3) node[midway, left] {$y$};\n\\draw[black] (3,0) -- (3,3) node[midway, right] {$z$};\n\\draw[black] (0,3) -- (3,3) node",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 5x + 6x + 8x - 4x - 4x + 12x + 5x - 4x - 12x + 8x + 6x - 5x - 4x + 12x + 5x - 4x - 8x - 4x + 6x - 5x - 4x + 8x + 6x - 4x + 5x - 4x + 12x + 5x",
        "gt_answers": "6 \\div \\frac { 1 } { 9 } = 5 4\n",
        "image_path": "./data/HME100K/test_images/test_2091.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is not provided. Can you provide the image so I can write the expression in LaTeX format?",
        "gt_answers": "\\overrightarrow { C B } = ( 0 , 4 , 0 )\n",
        "image_path": "./data/HME100K/test_images/test_2092.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n$\\frac{1}{x^2 + 2x + 1} = \\frac{1}{x(x + 1) + 1}$\n```\nThe left side of the equation is the derivative of the function $f(x) = \\frac{1}{x^2 + 2x + 1}$. The right side of the equation is the derivative of the function $g(x) = \\frac{1}{x(x + 1) + 1}$.\n\nThe two expressions are equivalent because they represent the same derivative. The difference in the forms of",
        "gt_answers": "\\angle 1 = \\angle B A D\n",
        "image_path": "./data/HME100K/test_images/test_2093.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is (x + 3)2 + (y - 4)2 = 9.\n\nTo derive this formula, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.\n\nUsing this theorem, we can find the length of each side of the triangle in the image:\n\n* The length of the hypotenuse is (x + 3)2 = (x",
        "gt_answers": "a _ { 2 } = \\frac { 3 - \\sqrt { 1 3 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2094.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x=4sin(y)+3cos(y).\n\nThe LaTeX code for this expression is:\n\n$$x = 4\\sin(y) + 3\\cos(y)$$",
        "gt_answers": "A D = O G = \\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_2095.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{n}{2n+1}$$\n\nwhere $n$ is a nonnegative integer.",
        "gt_answers": "C H _ { 2 } = C H L O O H\n",
        "image_path": "./data/HME100K/test_images/test_2096.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{5}{3}$.",
        "gt_answers": "S _ { \\Delta C D O } = \\frac { 3 } { 8 } \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2097.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{1}{\\sqrt{x^2 + 3x - 5}}$.",
        "gt_answers": "x = \\frac { 1 } { 4 } \\times 3\n",
        "image_path": "./data/HME100K/test_images/test_2098.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you would use the following code:\n\n\\begin{center}\n$10 \\times 2 = 20$\n\\end{center}\n\nThis code creates an equation that is displayed as 10 multiplied by 2 equals 20.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a right triangle with legs of length a and b is given by:\n\nA = 12 bhsin\u03b8,cos\u03b82\\frac{A}{b} = \\frac{1}{2}bh\\sin\\theta\\cos\\theta^2A=2bhsin\u03b8cos\u03b82\u200bwhere b is the base of the triangle, h is the height, and \u03b8 is the angle between the hypotenuse and one of the legs. The area of the triangle is given by the formula above.",
        "gt_answers": "x _ { 1 } = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2100.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not provided. Please provide an image so I can write out the expression using LaTeX format.",
        "gt_answers": "3 0 : 2 0 = 6 : 4\n",
        "image_path": "./data/HME100K/test_images/test_2101.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{R} = \\frac{\\text{V} - \\text{V}_0}{\\text{I} + \\frac{\\text{V}\\_0}{\\text{R}}}$$",
        "gt_answers": "\\therefore \\frac { S _ { \\Delta A E F } } { S _ { \\Delta A B C } } = ( \\frac { A E } { A B } ) ^ { 2 } = \\frac { A E \\cdot A F } { A B \\cdot A C }\n",
        "image_path": "./data/HME100K/test_images/test_2102.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is:\n\n$$x^2+y^2=r^2$$\n\nwhere $x$ and $y$ are the coordinates of any point on the ellipse and $r$ is the radius of the ellipse. This formula is known as the standard form of an ellipse equation.",
        "gt_answers": "( 1 - P ) ^ { 4 } = \\frac { 1 } { 8 1 } \\therefore P = \\frac { 1 } { 3 } \\therefore P = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2103.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image using LaTeX format is: $\\frac{1}{3}+\\frac{1}{4}+\\frac{2}{5}+\\frac{1}{6}=\\frac{29}{30}$",
        "gt_answers": "2 - 2 a = 4 - 2 a = 2\n",
        "image_path": "./data/HME100K/test_images/test_2104.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$a = \\frac{e-b}{c-d}$\n\\end{center}\n\nThis formula represents a linear equation, where `a`, `b`, `c`, and `d` are constants. The variable `x` is not explicitly present in the formula, but it can be represented as the unknown value that satisfies the equation.",
        "gt_answers": "A E \\cdot C D = A D \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_2105.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{ImageContent}$$\n\nwhere $\\text{ImageContent}$ is the image itself.",
        "gt_answers": "b + 1 = 0\n",
        "image_path": "./data/HME100K/test_images/test_2106.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{equation}\nE = mc^2\n\\end{equation}\n\nHere, $E$ represents the energy of the object, $m$ represents its mass, and $c$ represents the speed of light in a vacuum. The equation states that the energy of an object is equal to its mass multiplied by the speed of light squared.",
        "gt_answers": "4 0 0 \\times 1 0 0 \\times \\frac { 1 } { 1 0 0 0 0 0 } = 4 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_2107.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the expression of the formula in the image using LaTeX format:\n\n$$\\frac{x^2 + 3x - 5}{x - 1} = \\frac{x^2 + 3x - 5}{x - 1} + 1$$",
        "gt_answers": "x + 1 = \\sqrt [ 3 ] { 2 7 }\n",
        "image_path": "./data/HME100K/test_images/test_2108.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not provided. Please provide the formula in LaTeX format for me to write out.\n\nPlease write in English language.",
        "gt_answers": "F e _ { 2 } O _ { 3 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_2109.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:\n\n$$ \\text{Sin}(\\text{a}) = \\frac{\\text{opposite}}{\\text{hypotenuse}} $$\n\nwhere 'a' is the angle whose sine is to be found and 'opposite' and 'hypotenuse' are the lengths of the triangle's other two sides, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the triangle can be written as:A=12bh3\\frac{A}{bh^3}A=bh3\\frac{A}{bh^3}A=3bh1\u200bwhere `b` is the base of the triangle and `h` is the height. The formula for the area of a triangle is `A=bh3`.",
        "gt_answers": "3 . 1 4 \\times 1 = 3 . 1 4 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_2111.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by A = l \\* w, where l is the length and w is the width. Using the values given in the image, we can calculate the area of the rectangle as follows:\n\nA = 4 \\* 3 = 12 cm\u00b2\n\nTherefore, the area of the rectangle is 12 cm\u00b2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image is not provided. Can you please provide the image so that I can assist you with the LaTeX expression?",
        "gt_answers": "0 - \\frac { ( 1 + x ) ^ { 2 } } { 9 } = - \\frac { 1 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_2114.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{5}{3} + \\frac{6}{3} = \\frac{5 + 6}{3} = 11$$",
        "gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2115.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is: A = l \\* w. To find the area of the rectangle in the image, we can use this formula: A = 3 \\* 4 = 12.",
        "gt_answers": "\\frac { 1 0 6 } { 5 0 } = \\frac { 1 0 . 6 g } { x }\n",
        "image_path": "./data/HME100K/test_images/test_2116.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the expression in the image is:\n\n![Image of a graph showing the formula for the expression given in the previous question](https://i.imgur.com/7vZR8Lh.png)\n\nThis equation represents the exponential function y = ab^x. The base a is raised to the power of x, and the constant b is used as the exponent. This equation models the growth of a population or any other system that follows exponential growth.",
        "gt_answers": "A ( - 2 , 0 ) , B ( 0 , 2 )\n",
        "image_path": "./data/HME100K/test_images/test_2118.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 1 kg / 2 kg = 0.5 kg/2 kg.",
        "gt_answers": "k _ { 3 } = \\frac { k _ { 1 } } { k _ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_2119.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\frac{1}{2} \\cdot \\left(\\frac{x}{4} + \\frac{x}{5}\\right) = \\frac{1}{4} + \\frac{1}{5}$$\n\nThis formula can be read as: one-half times the sum of x divided by four and x divided by five is equal to four-fifteenths plus five-fifteenths.",
        "gt_answers": "\\angle B A C = 5 0 ^ { \\circ } + 3 0 ^ { \\circ } = 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2120.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\nP(A,B,C) = P(A,B)\u222aP(B,C)\u222aP(A,C)\u222aP(A,B,C)\n\nwhere P(A,B,C) is the joint probability density function of random variables A, B, and C, and P(A,B)\u222aP(B,C)\u222aP(A,C)\u222aP(A,B,C) is the union of the probability densities of the individual random variables.\n\nThe equation expresses that the joint probability",
        "gt_answers": "\\cos ^ { 2 } \\alpha = \\frac { 1 } { 1 + \\tan ^ { 2 } \\alpha } = \\frac { 1 6 } { 2 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2122.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX format of the formula in the image:\n\n$$\\text{Imaginary part of } \\left( \\frac{a+bi}{c+di} \\right) = \\frac{a-bi}{c-di}$$\n\nwhere $a, b, c, d$ are real numbers.",
        "gt_answers": "B Q = \\frac { 8 } { 2 + x }\n",
        "image_path": "./data/HME100K/test_images/test_2124.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by: $\\frac{1}{x^2+4x+5}$. This can be derived by expanding the expression for the quadratic function $y=ax^2+bx+c$ and substituting the given values for a, b, and c. The resulting expression simplifies to $\\frac{1}{x^2+4x+5}$.",
        "gt_answers": "x _ { 2 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2125.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX formula for the expression in the image:\n\n$$\\text{r} = \\frac{\\text{v}}{\\text{t}}$$\n\nIn this formula, r is the rate of change of the quantity being measured, v is the change in the quantity being measured, and t is the time taken to make that change.",
        "gt_answers": "C O S A = \\frac { 5 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_2126.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the expression in the image:\n\n\\begin{center}\n$x^2 + 3x + 1 = 0$\n\\end{center}\nThis is the quadratic equation in standard form with a leading coefficient of 1 and the constant term 1. It has two roots, one of which is positive and the other is negative.",
        "gt_answers": "\\frac { 9 } { 6 } x = \\frac { 7 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2127.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:$$\\text{0.5}\\left( \\frac{4}{3} \\right)\\left(\\frac{2}{1}\\right) + \\frac{1}{2}\\left(\\frac{5}{3}\\right) - \\frac{3}{5}\\left(\\frac{2}{1}\\right) = \\frac{11}{15}$$This equation represents the average of the three numbers shown in the image.",
        "gt_answers": "0 . 2 5 \\times 3 . 4 = 0 . 7 6 . 0 0 1 . 5 \\times 1 1 . 2 4 = 1 8 . 0 4\n",
        "image_path": "./data/HME100K/test_images/test_2128.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Could you please provide the image so that I can write out the formula?",
        "gt_answers": "3 . 1 4 \\times ( 6 \\div 2 ) ^ { 2 } \\times 1 0 + 3 . 1 4 \\times ( 6 \\div 2 ) ^ { 2 } \\times 4 \\times \\frac { 1 } { 3 } 3 2 0 . 2 8 ( c m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_2129.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\left(\\frac{x-1}{3}\\right)^2 + \\left(\\frac{x-1}{3}\\right)\\left(\\frac{2}{x-1}\\right) = \\left(\\frac{x-1}{3}\\right)^2 + \\left(\\frac{2}{x-1}\\right) $$\n\nThe image shows an algebraic expression that is evaluated at the point x = 1. The expression is a quadratic function in x with a minimum value of 2 at x = 1.\n##",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the line represented in the image can be written as: y = 2x + 6. This is a linear equation with a slope of 2 and an intercept of 6.\n\nTo derive this equation from the image, we can draw a line through the two points (2, 4) and (4, 6). This line has a slope of 2 and an intercept of 6, which is the same as the equation for the line represented in the image.\n\nIt is important to note that this equation is only an approximation of the line represented in the image. The actual equation",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{2n}{n+4}$\n\nThe image is a fraction expression for the sum of 2 numbers divided by the sum of 4 numbers. The numerator is 2n, which represents the sum of the two numbers, and the denominator is n+4, which represents the sum of 4 numbers.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the formula: $ \\text { A } = l \\times w$, where l is the length and w is the width. The area of the rectangle in the image is given by the formula: $ \\text { A } = 3 \\times 4 = 12$ square units.",
        "gt_answers": "x = \\alpha - \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2133.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: x^2 + 2x + 1 = 0.\n\nTo solve the equation, we can use the quadratic formula: x = (-b +/- sqrt(b^2 - 4ac))/(2a).\n\nPlugging in the values for a, b, and c, we get:\nx = (-(-2 +/- sqrt((-2)^2 - 4(1)(1)))/(2(1)))\nx = (-2 +/- sqrt(4 - 4)/)/(2\\*1)\nx =",
        "gt_answers": "x = 2 + \\frac { 2 } { 3 } y\n",
        "image_path": "./data/HME100K/test_images/test_2134.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is 2x2 - 4x + 1. The equation is a linear equation because it has only one variable, x. The equation has a constant term of 1 and a linear term of -4x. The variable x represents the input or independent variable in the equation. The equation can be used to determine the value of x when the constant term and linear term are known. For example, if the constant term is 4 and the linear term is -2, the equation can be used to determine the value of x when 2x2 = 4x - 1.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we need to identify the variables and operators involved in the equation.\n\nThe formula given in the image is:\n\n$$ \\frac{x^2 + 4x + 5}{x^2 - 6x + 8} $$\n\nThe variables in this formula are x and the constants 4, 5, and 8. The operator used is division.\n\nUsing LaTeX format, we can write the formula as follows:\n\n$$ \\frac{x^2 + 4x + 5}{x^2",
        "gt_answers": "y _ { 1 } - y _ { 2 } = x _ { 1 } ^ { 2 } - x _ { 2 } ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2137.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is given below:\n\n$$\\text{G} = \\frac{1}{4}\\left(\\frac{x^2 + y^2}{2} + \\frac{z^2}{3}\\right)$$",
        "gt_answers": "\\frac { I } { I _ { 2 } } = 2\n",
        "image_path": "./data/HME100K/test_images/test_2138.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2} + \\frac{1}{4} - \\frac{1}{8} + \\frac{1}{16} - \\frac{1}{32} + \\frac{1}{64} - \\frac{1}{128}$",
        "gt_answers": "( b + 2 ) \\neq 0\n",
        "image_path": "./data/HME100K/test_images/test_2141.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n(1 + (a + b)c)d = (1 + (ad + bc)b)c",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the expression in the image:\n\n\\begin{center}\n\\begin{equation}\n2(x^2 + 4x - 8) - 5(x - 2) = 0\n\\end{equation}\n\\end{center}\n\nThis equation represents a quadratic function in the form of $ax^2 + bx + c = 0$, where $a = 2$, $b = -4$, and $c = -8$. The quadratic formula can be used to find the roots of this equation:\n\n\\begin{center",
        "gt_answers": "x = 2 \\times 4 . 8 \\div ( 2 . 4 + 3 . 6 )\n",
        "image_path": "./data/HME100K/test_images/test_2143.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 3x + 2y = 7xy.\n\nThis is a linear equation, as it only contains the variables x and y, and no other mathematical operations or constants. The solution to this equation involves finding the values of x and y that make the equation true.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick] (0,0) -- (2,2) -- (4,0) -- cycle;\n\\draw[thick, dashed] (0,0) -- (2,0) -- (4,2) -- cycle;\n\\draw[thick] (2,0) -- (2,2);\n\\draw[thick] (2,2) -- (4,2);\n\\node[above] at (2,2) {$\\alpha",
        "gt_answers": "5 x = 5 \\times 6 = 3 0\n",
        "image_path": "./data/HME100K/test_images/test_2148.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}x^2+y^2=r^2\\end{aligned}$$\n\nIn this formula, x and y are the coordinates of the point on the circle, and r is the radius of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{5}{4}$.\n\nThe expression can be written as: $\\frac{a}{b}$, where $a$ is the numerator (5) and $b$ is the denominator (4).\n\nThe image shows the fraction $\\frac{5}{4}$, which is a simple fraction representing the ratio of 5 to 4. This means that for every 4 parts, there are 5 parts.",
        "gt_answers": "\\frac { 5 } { 8 } x = \\frac { 1 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2151.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by the following LaTeX formula:\n\n$$ \\frac{x^2}{a^2+x^2} $$\nwhere $x$ is a variable and $a$ is a constant. This expression represents the probability density function of a normal distribution with mean $a$ and variance $a^2$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\u222b \u222b \u222b \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "\\pm \\sqrt { m ^ { 2 } - 4 m } = - 2 + 2 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2153.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression in the image:$$x + 2y = 6$$This formula represents a line in the xy plane with a slope of 2 and a y-intercept of 6. The equation is in the standard form of a linear equation, where the coefficient of x is 1 and the coefficient of y is 2. This means that for every unit increase in x, the value of y increases by 2 units.",
        "gt_answers": "\\frac { x - ( - b ) } { 2 } < 1 2\n",
        "image_path": "./data/HME100K/test_images/test_2154.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe given formula in the image can be expressed in LaTeX as follows:\n\n$$\\text{m} = \\frac{\\text{a}}{\\text{b}} \\times \\left(1 - \\frac{\\text{c}}{\\text{d}}\\right)$$\n\nwhere $\\text{a}$ and $\\text{b}$ are the lengths of the sides of the rectangle, and $\\text{c}$ and $\\text{d}$ are the widths of the rectangle. The expression can be read as `m equals a divided by b, times the difference of c divided by d, with the value of",
        "gt_answers": "1 1 4 m + 6 n = 4 9\n",
        "image_path": "./data/HME100K/test_images/test_2155.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{align\\*}\nx &= \\frac{1}{4}\\left(3t^2 + 9\\right) \\\ny &= \\frac{1}{4}\\left(t^2 - 3t + 9\\right) \\\nz &= \\frac{1}{4}\\left(t^2 + 9\\right)\n\\end{align\\*}\n\nwhere t is the time in seconds.",
        "gt_answers": "\\vert - \\frac { \\sqrt { 2 } } { 3 } \\vert = \\frac { \\sqrt { 2 } } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2156.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression:\n\n$$\\frac{5+6}{7-3}=\\frac{5+6}{4}=\\frac{9}{1}=9$$",
        "gt_answers": "1 . 5 \\times 0 . 5 = 0 . 7 5 m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2157.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by the formula:\n\nw = sqrt(2E/m)",
        "gt_answers": "P = \\frac { w } { t }\n",
        "image_path": "./data/HME100K/test_images/test_2158.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I'm not able to see the image you provided. Can you please provide a different image that I can see and use to write out the formula in LaTeX format?",
        "gt_answers": "a b = 1 4 2 8\n",
        "image_path": "./data/HME100K/test_images/test_2159.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear enough to determine its expression. Please provide a clearer image for a better understanding.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n\\begin{center}\n\\begin{equation}\ny = \\frac{1}{2}(x - 9) + 3\n\\end{equation}\n\\end{center}\n\nThe formula is a quadratic equation in the form of y = ax^2 + bx + c, where a = 1/2, b = -9, and c = 3. The solution to the equation is x = -3, which gives y = -3/2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression in the image:\n\n$$\\frac{x^2 + 3x - 5}{x + 2}$$\n\nThis is the expression for the quadratic function f(x) = x^2 + 3x - 5/x + 2. The denominator is the sum of the polynomial x + 2, which is the constant term in the function.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\nf(x) = \\frac{1}{2}(a^2 + b^2) - \\sqrt{ab}\n\\end{align\\*}",
        "gt_answers": "A E = \\frac { 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2165.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\nwhere a and b are constants.",
        "gt_answers": "\\angle D B E = 3 0 ^ { \\circ } .\n",
        "image_path": "./data/HME100K/test_images/test_2166.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$$5\\times 5 - 4 = 20 - 4 = 16$$This expression represents the area of the square with sides of 5 units.",
        "gt_answers": "\\square = 4 5\n",
        "image_path": "./data/HME100K/test_images/test_2167.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format of the expression:\n\n\\begin{align\\*}\n2 + 3 &= 5 \\\n\\end{align\\*}",
        "gt_answers": "z = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2168.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$100 \\times \\left(\\frac{1000}{2000}\\right) + 100 = \\frac{10000}{20000}$$\n\nThis formula is used to calculate the value of the image, which shows two circles with different diameters and a square that is the same size as the smaller circle. The first term of the formula, 100 \\* (1000/2000), represents the area of the smaller circle. The second term, 10",
        "gt_answers": "A O = O C = \\frac { 1 } { 2 } A C\n",
        "image_path": "./data/HME100K/test_images/test_2169.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by the following equation:\n\n$$\\text{Im}\\_{2} = \\frac{V\\_{2}}{V\\_{1}} \\times \\sqrt{\\frac{R\\_{2}}{R\\_{1}}}$$\n\nwhere $\\text{Im}\\_{2}$ is the imaginary part of the complex number $z\\_{2}$, $V\\_{2}$ is the voltage of the upper plate of the capacitor in the image, $V\\_{1}$ is the voltage of the lower plate of the capacitor in the image",
        "gt_answers": "b ^ { 2 } - 4 a c = ( 4 + k )\n",
        "image_path": "./data/HME100K/test_images/test_2170.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $ E = mc^2 $.\n\nHere's a breakdown of the formula:\n\nE = energy\nm = mass\nc = speed of light in a vacuum\n^2 = squared\nSo the formula states that energy (E) is equal to mass (m) multiplied by the speed of light (c) squared. This is a fundamental equation in physics that describes the relationship between energy and mass.",
        "gt_answers": "O D = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2172.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{5 + 3}{4 - 1}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with width w and height h is:\n\nA = w \\* h",
        "gt_answers": "3 1 4 \\div 7 8 . 5 = 4 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_2175.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n\\begin{align\\*}\nx &= \\frac{1}{2}\\left(\\frac{a}{b} + \\frac{b}{a}\\right) \\\n&= \\frac{1}{2}\\left(\\frac{5}{7} + \\frac{7}{5}\\right) \\\n&= \\frac{1}{2}(5 + 7) \\\n&= \\frac{1}{2}(12) \\\n&= \\frac{6}{4} \\\n&= 1.5\n\\end{align\\",
        "gt_answers": "\\sqrt { 2 } < k < \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2176.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{P - \\omega}{T}$ where $\\frac{P}{T}$ represents the pressure drop across the diffuser, $\\omega$ represents the frequency of the incoming flow, and $T$ represents the transit time of the fluid through the diffuser.",
        "gt_answers": "t = 0\n",
        "image_path": "./data/HME100K/test_images/test_2177.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by\n\n$$\\text{G}(x) = \\frac{1}{2}\\left(\\frac{x}{10} + 2\\right)^2$$",
        "gt_answers": "A D + D O = A O , D O = x\n",
        "image_path": "./data/HME100K/test_images/test_2178.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for this image is given by: $\\frac{a}{b}$ where $a$ and $b$ are the numbers in the image.",
        "gt_answers": "x _ { 3 } = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2179.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by:\n\nA = \u03c0r^2\n\nwhere \u03c0 is the mathematical constant approximately equal to 3.14, and r is the radius of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can follow these steps:\n\n1. Identify the variables in the formula: t, x, and y.\n2. Write out the formula using LaTeX format, including the variables:\nb) $\\frac{x}{y+5}=\\frac{a}{x-3}$\n3. Evaluate the formula for the given values of x and y:\nx=2, y=7\n4. Write out the solution set in interval notation:\n{x | x = 2 (or 3) and y =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not provided. Please provide the formula for me to write it out using LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is 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+",
        "gt_answers": "y _ { 3 } = - \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2183.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\begin{align\\*} 2x + 5 &= 7 \\\n\\end{align\\*} $$\nThis equation is an example of a simple algebraic expression that represents the equation of a line in the Cartesian coordinate system. The variable x is represented by the letter x, while the constant 5 and 7 are represented by the numbers 5 and 7, respectively. The operator '+' represents addition, and the equals sign '=' represents equality.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{x + 3y - 5}{x - y + 2} $$\n\nThe image shows the formula for the arithmetic mean of two numbers. The numerator is the sum of the two numbers, and the denominator is their difference. The fraction bar separates the numerator and denominator, and the exponents indicate the power of each variable in the numerator and denominator. In this case, both the numerator and denominator have a power of 1, which means that each variable contributes equally to the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is given by:\n\n$$A = \\frac{1}{2}bh$$\n\nwhere `b` is the base of the triangle and `h` is the height. To find the area of the triangle in the image, we first need to determine the base and height.\n\nThe base of the triangle can be found by measuring the length of the side of the triangle opposite the angle that measures 90 degrees. This is given by the length of the line segment that connects the two points where the curved line intersects the top and bottom edges of",
        "gt_answers": "\\frac { 8 n } { 8 } = n\n",
        "image_path": "./data/HME100K/test_images/test_2186.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $\\frac{1}{2}a^2 + \\frac{1}{4}b^2 = \\frac{1}{2}c^2$.",
        "gt_answers": "A B ^ { 2 } = B C ^ { 2 } + C A ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2188.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $400\\ 3 - \\frac{2}{3}\\left(\\frac{50}{2}\\right) = \\frac{400\\ 3 - 50\\ 2 + 75}{3} = 300\\ 3$",
        "gt_answers": "\\frac { 4 0 } { 1 0 0 } = \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2189.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is not provided. Please provide the equation so I can write it in LaTeX format.",
        "gt_answers": "\\angle A E B = \\angle 1\n",
        "image_path": "./data/HME100K/test_images/test_2190.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\textstyle\\prod_{i=1}^{n}(\\textstyle a\\_i + b\\_i) = \\textstyle\\prod_{i=1}^{n}a\\_i + \\prod_{i=1}^{n}b\\_i$",
        "gt_answers": "9 = \\frac { 9 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_2191.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is written in LaTeX format as follows:\n\n$$\\text{T}=\\frac{E}{a}+\\frac{V}{b}$$\n\nwhere T is the total time, E is the elapsed time, a is the average speed, and V is the distance to be covered. The formula represents the time it takes to travel a certain distance at a certain average speed.",
        "gt_answers": "x \\leq 4 \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_2192.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{(a + b)^2 + (b - a)^2}{2ab} $$\n\nwhere a and b are the lengths of the sides of the rectangle in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\text{b} = \\frac{x + 5y - 3z}{x - y + 3z - 6} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is\n\n\\begin{align\\*}\n\\text{Image Content} = \\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16}\n\\end{align\\*}\n\nwhere each term represents the proportion of the image that is shown in that part. The sum of the four terms is equal to 1, which means that the entire image is shown.",
        "gt_answers": "( 2 x + 3 ) ^ { 2 } - ( 3 x + 3 ) = 4 0\n",
        "image_path": "./data/HME100K/test_images/test_2195.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the equation 1/4x2 + 3/4x - 2 is:1/4x2 + 3/4x - 2 = (1/4)(x2) + (3/4)(x) - 2. In LaTeX format, this equation can be written as:1/4x2 + 3/4x - 2 = (1/4)x^2 + (3/4)x - 2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{500 + 300}{150 + 100} = \\frac{800 + 400}{250 + 150} = \\frac{1,300 + 500}{350 + 200} = \\frac{1,800 + 600}{450 + 300} = \\frac{2,400 + 700}{500 + 3",
        "gt_answers": "\\frac { 1 0 0 } { x } - 1 = \\frac { 1 3 5 } { 2 5 - x }\n",
        "image_path": "./data/HME100K/test_images/test_2197.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{\\frac{1}{2}\\left(\\frac{3}{4}\\right) + \\frac{1}{2}\\left(\\frac{1}{3}\\right) + \\frac{1}{2}\\left(\\frac{1}{4}\\right)}{\\frac{1}{2}\\left(\\frac{2}{3}\\right) + \\frac{1}{2}\\left(\\frac{1}{2}\\right) + \\frac{1}{2}\\left(\\frac{1}{3}\\right)}$\n\nNote that this expression is a",
        "gt_answers": "\\Delta A O B \\cong \\Delta C O D ( A S A )\n",
        "image_path": "./data/HME100K/test_images/test_2198.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\frac{5}{2}$$x = \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is as follows:\n\n$$\\text{ImageContent} = \\frac{100}{320}\\left(\\frac{200}{640}\\right)\\left(\\frac{300}{960}\\right)\\left(\\frac{400}{1280}\\right) - \\frac{250}{640}$$\n\nThis formula calculates the value of $\\text{ImageContent}$ based on the values of $x$, $y$, $z$, and $w$, which are given in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$\\text{Volume} = \\frac{l}{2}\\left(\\sqrt{r^2 + h^2} + r\\right)$$\n\nwhere $l$ is the length of the liquid column, $r$ is the radius of the base of the cone and $h$ is the height of the cone.",
        "gt_answers": "2 5 2 \\div 2 + 5 6 = 1 8 2\n",
        "image_path": "./data/HME100K/test_images/test_2201.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{r} = \\frac{\\text{a} \\times \\text{b}}{\\text{c} + \\text{d}}$$\n\nwhere $\\text{a}$, $\\text{b}$, $\\text{c}$, and $\\text{d}$ are the values of the variables in the formula.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a mathematical expression in LaTeX format for the formula of a rational expression:$$\\frac{3}{4} - \\frac{1}{2}$$The expression can be simplified as follows:$$\\frac{3}{4} - \\frac{1}{2} = \\frac{3 - 1}{4 + 2} = \\frac{2}{6} = \\frac{1}{3}$$Therefore, the simplified expression is $\\frac{1}{3}$.",
        "gt_answers": "- \\frac { b } { 2 a } = \\frac { 2 } { - 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2203.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a diagram showing the multiplication of two numbers. It is labeled \"n x m\" and has two boxes with numbers 3 and 5 in them, indicating the multiplication of 3 and 5. The answer is 15.\n\nThe LaTeX code for this diagram would be:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw (0,0) -- (2,0) node[right] {n};\n\\draw (2,0) -- (4,0) node[right] {m};\n\\draw (4,0) -- (",
        "gt_answers": "2 8 1 - 2 2 3 = 5 8 ( g )\n",
        "image_path": "./data/HME100K/test_images/test_2204.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is $\\frac{x+y+z}{x+y-z}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align}x + 4y &= 10 \\ \\ \\Rightarrow \\ \\ x &= 10 - 4y \\end{align}\n\nThis equation can be solved for y by isolating y on one side of the equation:\n\n\\begin{align}y &= (10 - x) / 4 \\ \\ \\Rightarrow \\ \\ y &= (10 - 5) / 4 \\ \\ \\Rightarrow \\ \\ y &= 1 / 4 \\end{align}\n\nThus,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 4(x^2 + 2x - 2) - 4(x^2 - 4x + 4) = 4x^2 - 16x + 12.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{100\\times100}{50}=\\frac{10000}{50}=\\2000$$\n\nThis formula is using the multiplication method to solve for the area of the rectangle. The width is 100 cm and the length is 100 cm. The height is 50 cm. The area of the rectangle can be found by multiplying the width and length and then dividing by the height: A = l \u00d7 w/h. In this case, the area is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as:\n\n$$\\begin{aligned} x + 2y &= 10 \\\n3x + 4y &= 18 \\\nx - y &= 6 \\\n\\end{aligned}$$\n\nThe solution is x = 2 and y = 4.",
        "gt_answers": "x - 1 = \\pm 2\n",
        "image_path": "./data/HME100K/test_images/test_2209.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $ $\\frac{\\left(x - 2\\right)^2 + 3x - 1}{x + 1}$.",
        "gt_answers": "x = - \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2210.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as:\n\n$$ y = 10\\left(\\frac{x}{2}\\right)^2 + 25 $$\n\nThis is a quadratic equation with the variable x and a constant term of 25. The parabola has a vertex at $(0,25)$ and passes through the point $(1,25)$.",
        "gt_answers": "y = a ( x - h + 2 ) ^ { 2 } + k\n",
        "image_path": "./data/HME100K/test_images/test_2211.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not visible. Please provide the image to determine the equation.",
        "gt_answers": "x _ { 4 } = - \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2212.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:$$\\text{Gravitational force on an object at distance $r$ from the center of the earth is given by}$$$$F\\_g = \\frac{G \\* m\\_1 \\* m\\_2}{r^2}$$where $G$ is the gravitational constant, $m\\_1$ and $m\\_2$ are the masses of the two objects, and $r$ is the distance between them.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle is given by:\n\nA = \u03c0r^2,\n\nwhere A is the area of the circle, r is the radius of the circle, and \u03c0 is the mathematical constant pi, approximately equal to 3.14159. To find the area of the circle in the image, we can use the formula above with the given values of r and \u03c0.\n\nFirst, we need to find the radius of the circle. The radius of a circle is equal to half of its diameter, which is given by the length of the hypotenuse of",
        "gt_answers": "9 - \\frac { m } { 9 } =\n",
        "image_path": "./data/HME100K/test_images/test_2214.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the given expression:$\\frac{a+b}{2a}=\\frac{a+b}{2b}$The expression is an identity, which means that it is true no matter what values a and b have. This is because the numerator and denominator are equivalent expressions, so they cancel each other out.",
        "gt_answers": "y _ { 2 } = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2215.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I can't see the image. Can you please provide it so I can help you?",
        "gt_answers": "M < - \\frac { 9 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2217.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle can be expressed using LaTeX as:\n\n$$ A = \\frac{1}{2}bh $$\n\nwhere $A$ is the area of the triangle, $b$ is the base length, and $h$ is the height of the triangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is not clear. Please provide the image so that I can write out the formula in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{x^2+y^2}{x+y}=\\frac{r^2+s^2}{r+s}$$\n\nwhere $x$ and $y$ are the coordinates of point $A$, $r$ and $s$ are the coordinates of point $B$, and $r+s$ and $x+y$ are the distance from point $A$ to the line $y=x$.",
        "gt_answers": "\\frac { 1 } { 3 } = \\frac { 3 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_2222.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a complex number that cannot be expressed in LaTeX format. It appears to be the result of a calculation involving a logarithmic function.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is given by the following LaTeX expression: $\\frac{1}{4}\\left( \\frac{1}{2}\\right)^2 - \\frac{1}{2}\\left( \\frac{1}{3}\\right)^2 + \\frac{1}{3}\\left( \\frac{1}{4}\\right)^2 + \\frac{1}{4}\\left( \\frac{1}{5}\\right)^2$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression on the image:\n\n\\begin{center} a = \\frac{x^2 + 4x + 20}{x - 5} \\end{center}\n\nTo derive this formula, we can substitute the given values into the given equation:\n\n\\begin{center} f(x) = x^2 + 4x + 20 \\end{center}\n\n\\begin{center} g(x) = x - 5 \\end{center}\n\nThen, we can use the Quotient Rule",
        "gt_answers": "A E = A F + E F = 4 0 +\n",
        "image_path": "./data/HME100K/test_images/test_2226.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n$$ \\frac{1}{1+\\frac{1}{2}} $$\n\nThis is a simple arithmetic expression that can be evaluated by hand or with a calculator. It represents the reciprocal of the sum of 1 and 1/2, which is 1/1+1/2. The expression is equivalent to writing out the division of 1 by 1+1/2.",
        "gt_answers": "( x + y ) ^ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_2228.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not visible as it is an image. However, assuming the image represents a mathematical expression, it can be written as follows using LaTeX format:\n\n\\begin{align\\*}\nI = \\frac{1}{2}m\\dot{v}^2 + \\frac{1}{2}m\\dot{v}\\ddot{v} - \\frac{1}{2}m\\dot{v}\\dot{v} - \\frac{1}{2}m\\dddot{v}^2 + V\n\\end{align\\*}\n\nwhere $I$ represents",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the formula in the image:\n\n$$\\begin{aligned}\n\\text{Image Content} & = \\frac{\\text{A}}{\\text{B}\\cdot\\text{C}} \\\\\n    & = \\frac{\\text{Image Content of A}}{\\text{Image Content of B}\\cdot\\text{Image Content of C}}\n\\end{aligned}$$\n\nNote that this formula assumes that the image content of A, B, and C are independent of each other. If that's not the case, you may need to modify the formula accordingly.",
        "gt_answers": "a = 2 \\sqrt { 2 } o r a \\geq 4\n",
        "image_path": "./data/HME100K/test_images/test_2230.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the given formula:\n\n$$ \\frac{1}{x} $$\n\nThis formula represents the reciprocal of the variable x.",
        "gt_answers": "( a + b ) \\times c = a \\times c + b \\times c\n",
        "image_path": "./data/HME100K/test_images/test_2232.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{equation}\nP\\_casing = \\frac{1}{3} \\sum\\_{i=1}^{n} \\frac{1}{2i-1}\n\\end{equation}\n\\end{center}\n\nwhere $n$ is the number of terms in the sum.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$\\begin{aligned}\nE &= mc^2 \\\\\n&= \\frac{1}{2}mv^2 \\\\\n&= \\frac{1}{2}m\\left(\\frac{v}{c}\\right)^2 \\\\\n&= m\\left(\\frac{v}{c}\\right)^2\n\\end{aligned}$$\n\nHere, we start with the formula for energy, which is $E = mc^2$. We can rearrange this formula using the distributive",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation of a quadratic function, which is a polynomial of degree 2. The equation is y = x^2 + 4x - 5. The function passes through the point (0, 5) and has a vertex at (1, 2).",
        "gt_answers": "x = \\frac { 1 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2235.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{x^2 - 4x + 5}{x - 2}$. This can be rewritten as $\\frac{(x - 2)(x + 3)}{x - 2}$. The denominator is $(x - 2)$, and the numerator is $(x + 3)$. When the numerator is divided by the denominator, the result is $\\frac{x + 3}{x - 2}$. This is the same as $\\frac{x + 3}{x - 2}$, which is the formula for the",
        "gt_answers": "x = 3 \\times \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2236.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{\\sqrt{2}\\left(1+\\frac{1}{2}\\right)\\left(1-\\frac{1}{2}\\right)}=\\frac{1}{\\sqrt{2}\\left(1+\\frac{1}{2}\\right)\\left(1-\\frac{1}{2}\\right)}=\\frac{1}{\\sqrt{2}\\left(\\frac{1}{2}+\\frac{1}{2}\\right)\\left(\\frac{1}{2}-\\frac{1}{2}\\right)}=\\frac{1}{\\sqrt{2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: $\\frac{3x+2}{x^2+4x-5}$. This is obtained by dividing the numerator of the given expression by the denominator, which is $(3x+2)$.\n\nNote that the given expression has a variable on the numerator, so it cannot be evaluated without knowing the value of $x$. However, if we assume $x=4$, then the expression becomes $\\frac{9+2}{16+8-5}=\\frac{11}{21}=\\frac{5}{11}$.\n\nSo, the value",
        "gt_answers": "x = 3 \\cdot \\frac { 7 } { 3 } - 4 = 3\n",
        "image_path": "./data/HME100K/test_images/test_2238.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not clear as it is written in a non-mathematical format. It appears to be a symbol with a red line through it, but it is not clear what the symbol represents or what the red line means. Therefore, I cannot provide an expression for this image in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length L and width W is A = LW. The formula for the area of a triangle with base b and height h is A = (1/2)bh. The formula for the area of a trapezoid with base b1 and height h1, and base b2 and height h2 is A = (b1h1 + b2h2)/2. The formula for the area of a parabolic segment with vertex at the origin and height h is A = (1/2)h^2.\n\nThe area of the image is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The equation is $\\frac{2x}{x^2+10x+10}$.\n\nHere is the LaTeX format for the equation:\n\n$$\\frac{2x}{x^2+10x+10}$$\n\nThe equation represents a quadratic function with a leading coefficient of 2 and a constant term of 10. The parabola opens upwards and has its vertex at the origin.",
        "gt_answers": "e = \\frac { - 5 + 1 1 } { 4 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2241.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as: 2x + 2y - 4 = 0. This is a linear equation in two variables with a constant term of -4. The solution to this equation is x = -2 and y = 1.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->] (0,0) -- (3,0) node[below right] {$ x$};\n\\draw[->] (0,0) -- (0,1) node[above right] {$ y$};\n\\filldraw (1,0) circle[radius=2pt];\n\\filldraw (2,0) circle[radius=2pt];\n\\filldraw (3,0) circle[radius=2pt];\n\\node[",
        "gt_answers": "y = \\frac { 3 1 } { 2 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2243.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\text{V}=\\frac{\\text{100}}{\\sqrt{\\text{3}}}$$\n\nThis formula gives the volume of a cube with side length 100cm. The volume is calculated by dividing the side length by the square root of 3.",
        "gt_answers": "n \u3001 H ^ { \\prime } = 0\n",
        "image_path": "./data/HME100K/test_images/test_2244.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{x}^{2}+3\\text{x}+1=0$$\n\nThis formula is a quadratic equation of degree 2 with three roots, which are the solutions to the equation. To solve this equation, we can use the quadratic formula:\n\n$$\\text{x}=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}$$\n\nwhere a, b, and c are the coefficients of the quadratic equation:\n\n$$a=1,\\quad b=3,\\quad c=1$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression of the formula in the image using LaTeX format:\n\n$$\\frac{x^2 + 4x + 4}{x^2 - 4x + 4} = \\frac{x^2 + 4x + 4}{x^2 - 4x - 4}$$\n\nThe expression simplifies to $\\frac{x+2}{x-2}$, which is a difference of squares and therefore always positive.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\begin{align\\*} \\frac{1}{x}+\\frac{1}{y}+\\frac{1}{z} &= \\frac{3}{x}+\\frac{3}{y}+\\frac{3}{z} \\\\\\\n&= \\frac{3(x+y+z)}{xy+yz+zx} \\\\\\\n&= \\frac{3xyz}{xy+yz+zx} \\\\\\\n&= \\frac{3xyz}{x(y+z)+(x+y)z+xz} \\\\\\\n&=",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we need to consider the following steps:\n\n1. Define the variables:\nLet x be the variable representing the width of the rectangle and y be the variable representing the height of the rectangle.\n2. Write the formula using LaTeX:\nThe formula for the area of a rectangle is A = l x w, where l is the length and w is the width. Using LaTeX, we can write this as:\nA = l \\* w\n3. Apply the formula to the image:\nUsing the values given in the image, we",
        "gt_answers": "\\frac { x } { 1 6 } = \\frac { 4 x + 5 } { 8 } + 2\n",
        "image_path": "./data/HME100K/test_images/test_2248.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2x + 5y = 10. This is a linear equation with two variables, x and y, and a constant value of 10. The solution to this equation is the point at which the equation is satisfied, which is (2, 5).",
        "gt_answers": "\\frac { 1 } { x - y } = V\n",
        "image_path": "./data/HME100K/test_images/test_2249.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as follows in LaTeX format:\n\n\\begin{equation}\n 2 \\cdot 2 + 3 = 11\n\\end{equation}\n\nwhere $\\cdot$ denotes multiplication and the expression on the right-hand side represents the addition of 2 and 3.",
        "gt_answers": "x = 0\n",
        "image_path": "./data/HME100K/test_images/test_2252.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear. Please provide a clear and legible image for me to write out the formula in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Im}(\\text{C})$$\n\nwhere $\\text{C}$ is the capacitance of the capacitor in the circuit.",
        "gt_answers": "O B = B D = O C = C D\n",
        "image_path": "./data/HME100K/test_images/test_2254.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not visible, as it is written in red ink on a white surface.",
        "gt_answers": "C G - B F = B L\n",
        "image_path": "./data/HME100K/test_images/test_2257.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "V = \\pi \\times ( R ^ { 2 } - r ^ { 2 } ) \\times h\n",
        "image_path": "./data/HME100K/test_images/test_2258.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is: $\\frac{1}{x^2 + 2x + 1}$. This is a quadratic equation with a vertex at the origin. The x-coordinate of the vertex is -b/2a, where a and b are the coefficients of the quadratic equation. The y-coordinate of the vertex is -b/2a. The equation has two real roots, which can be found by solving for the values of x that satisfy the equation. The solution is x = -b/2a, which satisfies the equation $\\frac{1}{x^2 + 2x + 1",
        "gt_answers": "y _ { 4 } = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2260.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: y = x + 4.",
        "gt_answers": "y _ { 2 } = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2261.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX format for the expression in the image:\n\n$$\\frac{1}{x^2+4x+4}=\\frac{1}{2}\\left(\\frac{1}{2}+\\frac{1}{4}\\right)$$\n\nAlternatively, you can write it as:\n\n$$\\frac{1}{x^2+4x+4}=\\frac{1}{2}(2+\\frac{1}{4})$$\n\nThis formula is derived from completing the square method, which involves adding and subtracting the square of half of the coefficient of x^2",
        "gt_answers": "\\angle 1 + \\angle C A F = \\angle 2 + \\angle C A F\n",
        "image_path": "./data/HME100K/test_images/test_2262.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\begin{aligned} 2x + 3y &= 11 \\quad \\Rightarrow \\quad x + y &= 5 \\quad \\Rightarrow \\quad x &= 5 - y \\end{aligned}$$\n\nThe first equation is obtained by adding 2 times the first variable x to 3 times the second variable y and then equalling it to 11.\n\nThe second equation is obtained by adding x and y and then equalling it to 5.\n\nThe third equation is obtained by subtracting y from 5-",
        "gt_answers": "1 \\div 1 2 = \\frac { 1 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2264.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows:\n\n\\begin{equation}\\text{d}x^2 + \\text{d}y^2 = \\text{d}z^2 \\text{ or } x^2 + y^2 = z^2 \\end{equation}\n\nThis is a basic equation in calculus known as the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The equation",
        "gt_answers": "O H \\bot C D\n",
        "image_path": "./data/HME100K/test_images/test_2268.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a single phase AC circuit is given by:",
        "gt_answers": "E _ { k } = e U _ { c } = h v - W _ { 0 }\n",
        "image_path": "./data/HME100K/test_images/test_2269.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX code for the expression in the image:\n\n\\begin{align\\*}\n\\frac{1}{2}(x^2 + y^2) = \\frac{1}{4}x^2 + \\frac{1}{4}y^2\n\\end{align\\*}\n\nIn this equation, x and y are variables, and the expression on the right-hand side is the same as the expression on the left-hand side after simplifying the fraction.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\begin{align\\*}\ny & = x^4 - 4x^3 + 6x^2 - 4x + 1\n\\end{align\\*}\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the given image is: $\\frac{1}{2}x^2 + \\frac{1}{4}x - \\frac{1}{4}$",
        "gt_answers": "x = \\pm \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2276.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the given formula:\n\n\\begin{aligned}\n\\frac{x+4y-6}{x-2y+3} &= \\frac{a+2b-3}{a-b+2}\\\n\\end{aligned}\n\nIn this formula, $x$ and $y$ are variables, and $a$ and $b$ are constants. The denominator is a polynomial of degree 2, which means it has two variables, $x$ and $y$. The numerator is a polynomial of degree 1, which means it has one",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the formula in the image:\n\n$$\\frac{n}{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}{40",
        "gt_answers": "n ^ { 2 } + n = n \\times ( n + 1 )\n",
        "image_path": "./data/HME100K/test_images/test_2278.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n\\begin{equation}\nx^2+y^2=r^2\n\\end{equation}\n\nwhere $x$ and $y$ are the coordinates of the point $(x,y)$ on the unit circle, and $r$ is the radius of the circle.",
        "gt_answers": "x > \\frac { 1 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2279.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX code for the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw (0, 0) -- (2, 2) -- (0, 4) -- cycle;\n\\draw (2, 2) -- (0, 2) -- (2, 0) -- cycle;\n\\filldraw (0, 2) circle (2pt) node[above right] {$ f(x) $};\n\\filldraw (2, 2) circle (2pt) node[above right] {$ e $",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in the image using LaTeX format, you can follow these steps:\n\n1. Select the image using the LaTeX \\includegraphics command:\n\n\\includegraphics[width=0.5\\textwidth]{image.png}\n\n2. Include the LaTeX math library by adding the following line before the image:\n\n\\usepackage{amsmath}\n\n3. Write the formula using LaTeX math syntax:\n\nThe formula for the area of a rectangle is given by $A = l \\times w$, where $l$ is the length and $w$ is the width. The area",
        "gt_answers": "x _ { 3 } = - \\frac { 8 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2282.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2 + 2 = 4.\n\nThis is a simple arithmetic expression that adds two numbers together to get a result of 4. It can be written in LaTeX format as:$$2+2=4$$\n\nThe formula is written in chalk on a blackboard, and the numbers are written in white. The equals sign is represented by the mathematical symbol \"=\".",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is the formula for the volume of a cone, which is V = (1/3)\u03c0r^2h, where r is the radius of the base and h is the height of the cone.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you would need to write the equation as: x^2 + 3x + 5 = 0. This equation represents the quadratic equation in the image, which has three roots: x = -3, x = -2, and x = -1.",
        "gt_answers": "\\frac { 2 \\times 3 } { 5 } = \\frac { 6 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2285.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for finding the slope of a line passing through two points can be expressed as follows:\n\n$$m = \\frac{x\\_2 - x\\_1}{y\\_2 - y\\_1}$$\n\nwhere $x\\_1$ and $y\\_1$ are the coordinates of the first point, $x\\_2$ and $y\\_2$ are the coordinates of the second point, and $m$ is the slope of the line passing through the two points.",
        "gt_answers": "- \\sqrt { 2 x - 3 } = x - 3\n",
        "image_path": "./data/HME100K/test_images/test_2286.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\sin(x) = \\frac{e^x - e^{-x}}{2} $$",
        "gt_answers": "y = \\sqrt { 8 9 - 8 x } ( 0 < x < w )\n",
        "image_path": "./data/HME100K/test_images/test_2287.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the expression of the formula for the area of a circle. The formula for the area of a circle is given by A = \u03c0r^2, where r is the radius of the circle. The area of a circle is equal to \u03c0 times the square of its radius.\n\nIn this image, the formula for the area of a circle is written in LaTeX format as A = \\pi r^2. The variable r is represented by the letter r in lowercase. The letter pi (\u03c0) is represented by the symbol \"\u03c0\" in LaTeX. The multiplication symbol \"^\" is used to represent",
        "gt_answers": "5 ^ { 2 } + ( 1 0 - t ) ^ { 2 } = 1 0 ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2289.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is not clear from the image provided. The image appears to be a scribble with no discernible mathematical expression.",
        "gt_answers": "\\angle 2 = A D = 2\n",
        "image_path": "./data/HME100K/test_images/test_2292.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is a complex number that represents the position of a point in 3-dimensional space. In LaTeX format, it can be written as:$$\\left[ \\begin{array}{lll} x & y & z \\end{array}\\right]$$where $x,y,z$ are the coordinates of the point in 3-dimensional space.\n\nNote that this formula is not a function, but rather a representation of a point in space. In LaTeX, it can be written as a matrix with three columns, each representing one of the coordinates.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n$$\\frac{d^2x}{dt^2} + \\frac{k}{m} \\frac{dx}{dt} - \\frac{m\\omega^2}{k} x = 0$$\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $$ 2x^2 + 2xy + y^2 = 4xy $$\n\nThe equation is a quadratic equation in the form of y = ax^2 + bx + c, where a = 1, b = 2x, and c = 2xy.\n\nTo solve the equation, we need to factor the left-hand side as (x + y)(x + y). Then, we can substitute the factors into the right-hand side of the equation to get:\n\n(x + y)(x + y) =",
        "gt_answers": "2 B = \\frac { 8 } { 6 } \\pi\n",
        "image_path": "./data/HME100K/test_images/test_2295.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a trapezium is given by:\n\nA = (1/2)bh \\* (n - 1)\n\nwhere n is the number of sides of the trapezium and bh is the height of the trapezium.\n\nTo find the area of the trapezium in the image, we can substitute the given values into the formula:\n\nA = (1/2) 36 \\* (4 - 1)\nA = (1/2) 36 \\* 3\nA = 48\n\nThere",
        "gt_answers": "\\angle _ { 1 } = 4 8 ^ { \\circ } ( g i v e n )\n",
        "image_path": "./data/HME100K/test_images/test_2296.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{area} = \\frac{1}{2}bh$$\n\nwhere $b$ is the base width of the trapezium and $h$ is the height.",
        "gt_answers": "g = - \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2297.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be: $latex h\\_p = \\frac{h\\_t^2 - \\left( \\frac{v\\_t^2}{r\\_t^2} \\right)^2}{2v\\_t^2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Number of integers in the set } S = \\left\\lbrace{3, 4, 5}\\right\\rbrace = \\frac{10 - 3}{2} = \\frac{7}{2} = 3.5$$\n\nAlternatively, the expression can be written as:\n\n$$\\text{Number of integers in the set } S = \\left\\lbrace{3, 4, 5}\\right\\rbrace = \\frac{S \\cap \\mathbb{",
        "gt_answers": "+ \\textcircled { 4 } : 4 x = 3\n",
        "image_path": "./data/HME100K/test_images/test_2300.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be $\\frac{8+3\\sqrt{x}+2\\sqrt{x}}{x}$.\n\nHere's a step-by-step guide on how to write out the expression in LaTeX format:\n\n1. The first step is to write out the formula as it appears in the image, using LaTeX notation for each mathematical operation.\n2. In the formula, we have $8+3\\sqrt{x}+2\\sqrt{x}$, which is the numerator of the fraction.\n3. We also have $x$, which is the",
        "gt_answers": "\\frac { 1 8 } { 9 0 } ( 1 8 )\n",
        "image_path": "./data/HME100K/test_images/test_2301.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b \u222b\u222b(x2+y2)dxdy=\u222b\u222b\u222b\u222b(x2+y2)dxdy\\int\\int\\int (x^2+y^2) dx dy = \\int\\int\\int (x^2+y^2) dx dy\u222b\u222b\u222b\u222b\u200b(x2+y2\u200b)dxdy\u200b=\u222b\u222b\u222b\u222b\u200b(x2+y2\u200b)dxdy\u200bThe expression is the indefinite integral of the function f(x,y)=x2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: f = ( ( ( ( ( x + y ) / 2 ) ) ) ^ 2 ) - ( ( ( ( ( x - y ) / 2 ) ) ) ^ 2 ).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed using LaTeX as follows:\n\nThe area of a circle with radius r is given by:\n\nA = \u03c0r\u00b2",
        "gt_answers": "x + y = 3 2 0 0\n",
        "image_path": "./data/HME100K/test_images/test_2304.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation shown in the image is the formula for the sum of two numbers.\n\nTo write it in LaTeX format, you can use the following code:\n\nx + y = xyzx+y=x2+y2where x and y are the two numbers being added together, and z is the sum of x and y.\n\nAlternatively, you can write it as:\n\nx + y = xyxy + yzx + y = x2 + y2where x and y are the two numbers being added together, and z is the sum of x and y.\n##",
        "gt_answers": "x = \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_2305.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is x^2 - 4x + 3.",
        "gt_answers": "x = \\frac { 1 4 } { 1 7 }\n",
        "image_path": "./data/HME100K/test_images/test_2306.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following code:\n\n$$\\begin{aligned} x^2 + 4x + 4 = 0 \\Rightarrow x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} \\end{aligned}$$\n\nwhere $a = 1$, $b = 4$, and $c = 4$. Plugging these values into the formula, we get:\n\n$$\\begin{aligned} \\left(\\frac{-4 \\pm \\sqrt{16 -",
        "gt_answers": "a = b = c = 3 ^ { \\frac { 1 } { 6 } }\n",
        "image_path": "./data/HME100K/test_images/test_2308.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent}$$\n\nIn this formula, the image content is represented by the letter \"x\" in the formula. The letter \"x\" is used to indicate the image content of the expression.",
        "gt_answers": "x - 2 = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2309.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear. Can you please provide more context or information about what the formula is for?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression for the formula in the image using LaTeX format:\n\n\\begin{center}\n$\\frac{b}{2a + b}$\n\\end{center}\n\nThe formula is a proportion with the numerator being `b` and the denominator being `2a + b`. The expression uses the `frac` command to display the fraction.",
        "gt_answers": "4 y ^ { 2 } + 9 + 1 2 y + y ^ { 2 } = 9\n",
        "image_path": "./data/HME100K/test_images/test_2313.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written in LaTeX format is:\n\n$$ 0. 1 + 2 = 3 $$\n\nNote: The formula has been written with the LaTeX command '$$' to indicate that it is a mathematical expression.",
        "gt_answers": "\\angle O H M = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2314.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression written in LaTeX format:\n\n$$\\frac{3\\times 5 - 4}{9} = \\frac{15 - 4}{9} = \\frac{11}{9} = 1$$\n\nThis expression represents the following mathematical statement:\n\n$$\\frac{3\\times 5 - 4}{9} = \\frac{15 - 4}{9} = \\frac{11}{9} = 1$$\n\nWhich is equal to 1.",
        "gt_answers": "2 : 9 = \\frac { 1 } { 3 } : x\n",
        "image_path": "./data/HME100K/test_images/test_2315.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image:\n\n$$\\frac{1}{2}(a + b) - \\frac{1}{2}(c + d)$$\n\nThis formula calculates the difference between the sum of two numbers and the sum of two other numbers. The variables $a$ and $b$ represent the first two numbers, and $c$ and $d$ represent the second two numbers. The fraction $\\frac{1}{2}$ is used to simplify the expression.",
        "gt_answers": "\\frac { 4 } { 3 } x = 2 0\n",
        "image_path": "./data/HME100K/test_images/test_2316.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $\\frac{a+b}{2c}$.\n\nHere, $\\frac{a+b}{2c}$ is the formula for the area of a triangle, where a is the base, b is the height, and c is the hypotenuse. The formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the base and height.\n\nTherefore, the formula for the area of the triangle in the image is $\\frac{(3",
        "gt_answers": "a : b = \\frac { 3 } { \\sqrt { 5 } }\n",
        "image_path": "./data/HME100K/test_images/test_2317.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as:x^2 + y^2 = 4xy. This is a quadratic equation in the form of ax^2 + bx + c, where a = 1, b = y^2, and c = xy.",
        "gt_answers": "x = \\frac { 6 } { 5 } \\div 3\n",
        "image_path": "./data/HME100K/test_images/test_2318.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format of the formula for the given image:\n\n$$\\begin{aligned}250\\sin^{-1}\\left(\\frac{2300-\\frac{3400}{4000}}{2100+\\frac{4000}{4500}}\\right)&=250\\sin^{-1}\\left(\\frac{2300-\\frac{3400}{4000}}{2100+\\frac{4000}{4500}}\\right)\\end{aligned}$$\n\nThe image shows the",
        "gt_answers": "1 6 8 0 \\div 3 = 5 6 0 2 8 0 0 \\div 5 = 5 6 0 3 9 2 0 \\div 7 = 5 6 0\n",
        "image_path": "./data/HME100K/test_images/test_2319.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not provided. Please provide the image so that I can help you.",
        "gt_answers": "= - \\frac { 1 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2320.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the equation given in the image is:\n\n$$ \\frac{x+7}{x-5} = 11 $$",
        "gt_answers": "\\frac { 1 4 2 } { 7 . 1 g } = \\frac { 1 1 7 } { y }\n",
        "image_path": "./data/HME100K/test_images/test_2321.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 3x + 4y + 5z = 21 $$\n\nwhere x, y, and z are variables representing the numbers in the image.",
        "gt_answers": "1 0 0 x = 4 0 0 - 9 0 = 9 0 + 1 0 0 \\times 3 . 1\n",
        "image_path": "./data/HME100K/test_images/test_2322.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize, but the image is not clear enough to read the expression. Can you provide a clearer image?",
        "gt_answers": "2 H _ { 2 } O _ { 2 } \\xlongequal { M n O _ { 2 } } 2 H _ { 2 } O + O _ { 2 } \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_2323.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:\n\n$$\\frac{100\\text{ kg} + 150\\text{ kg}}{2}$$\n\nThis is an expression that describes the weight of the person in the image, who is holding a box of vegetables. The total weight of the person and the box of vegetables is calculated by adding the weights of the person (100 kg) and the box of vegetables (150 kg) and then dividing by 2.",
        "gt_answers": "\\vert b + 1 \\vert = \\vert \\frac { b } { 2 } - 1 \\vert \\times 3\n",
        "image_path": "./data/HME100K/test_images/test_2324.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$50\\times\\left(\\frac{100}{2}\\right) + \\left(\\frac{100}{3}\\right) \\times 20$$",
        "gt_answers": "5 9 0 + 6 0 = 6 5 0\n",
        "image_path": "./data/HME100K/test_images/test_2325.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 3x + 5y = 18 $$",
        "gt_answers": "\\sin \\alpha = - \\frac { 4 } { 5 } < 0\n",
        "image_path": "./data/HME100K/test_images/test_2326.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2}(3x^2 + 5x - 2)$.",
        "gt_answers": "5 1 2 \\div 8 5 = 6 \\cdots 2 5 1 2 \\div 8 9 = 5 \\cdots 6 7\n",
        "image_path": "./data/HME100K/test_images/test_2327.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is given by:\n\n![](https://latex.org/img/png/2dc/bc/22/12/bc2212.png)\n\n![](https://latex.org/img/png/2dc/bc/22/12/bc2212.png)\n\nWhere $\\text{x}$ is the number of people in the room, $\\text{y}$ is the number of people who like the color red, and $\\text{z}$ is the number of people who like the color green.",
        "gt_answers": "\\angle D B C + \\angle E C B = \\frac { 1 } { 2 } \\times 1 2 0 ^ { \\circ } = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2328.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n$x = \\frac{1}{2}(4y + 3z)$",
        "gt_answers": "x = \\frac { 1 } { 2 } : \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2329.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b(\u222b(2x + 5)dx + 3x\u00b2)dy = \u222b(\u222b(2x + 5)dx)dy + 3/2\u222b(x\u00b2)dy\n\n\u222b(\u222b(2x + 5)dx + 3x\u00b2)dy = \u222b(\u222b(2x + 5)dx)dy + 3/2\u222b(x\u00b2)dy + C\n\n\u222b(\u222b(2x + 5)dx + 3x\u00b2)dy = \u222b(",
        "gt_answers": "O E \\bot O F\n",
        "image_path": "./data/HME100K/test_images/test_2330.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by:\n\nx = (b / a) \\* (y - c)\n\nwhere,\nb = length of the hypotenuse of the right angled triangle\na = length of the hypotenuse of the isosceles triangle\nc = length of the hypotenuse of the right angled triangle.",
        "gt_answers": "\\therefore \\frac { D F } { C D } = \\frac { 1 } { 3 } \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_2332.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a rectangle with length 2 and width 3 can be written as: 2 \\* 3 = 6 sqft.\n\nThis expression uses the multiplication operator (\\*) to multiply the length and width of the rectangle to find its area. The result is 6 sqft.",
        "gt_answers": "- 2 < a < 0 \\therefore M = 4 a + 2 ( a + 2 ) + 2\n",
        "image_path": "./data/HME100K/test_images/test_2333.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = l x w\n\nwhere l is the length and w is the width.\n\nFor the rectangle with the dimensions 2x3, the area is:\n\nA = 2 x 3\n= 6\n\nTherefore, the area of the rectangle is 6 square units.",
        "gt_answers": "x - y = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_2334.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$ \\frac{x^2+y^2}{x^2-y^2} $$",
        "gt_answers": "f ^ { \\prime } ( x ) = 2 a + \\frac { b } { x ^ { 2 } } + \\frac { 1 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_2335.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 3 + 2 \\* 3 - 5 = 6.",
        "gt_answers": "( O B + \\overrightarrow { O C } ) ( \\overrightarrow { O C } - \\overrightarrow { O B } ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_2336.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression for the formula in the image using LaTeX format:\n\n\\begin{align} \\frac{d^2x}{dt^2} + \\omega^2 x &= \\frac{k m}{m + C} \\frac{dx}{dt} + \\omega x \\tag{1} \\end{align}\n\nwhere $\\omega$ is the angular frequency of the system, $k$ is the spring constant, $m$ is the mass of the object, and $C$ is the damping coefficient.\n\nIn this equation, the first term on the",
        "gt_answers": "B . ( 1 ) F e + H _ { 2 } S O _ { 4 } = F e S O _ { 4 } + H _ { 2 } \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_2337.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{f(x) = \\frac{x^2 - 4x - 5}{x - 2}}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{n!}{n^n}$\n\nHere, the variable n represents the number of terms in the sequence, which starts at 1 and ends at n. The exclamation mark represents the factorial of n. The superscript n represents n raised to the power of n. The fraction bar represents the ratio of the number of terms in the sequence to the total number of terms. The power of n in the denominator is equal to the number of terms in the sequence.\n\nThe result of the formula is the total number of terms",
        "gt_answers": "[ k \\pi - \\frac { 3 } { 8 } \\pi\n",
        "image_path": "./data/HME100K/test_images/test_2339.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 3x^2 + 4y^2 = 33.",
        "gt_answers": "\\sqrt { x + a } = \\sqrt { 2 x - 4 } - 1\n",
        "image_path": "./data/HME100K/test_images/test_2340.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the rectangle with a length of 5 inches and a width of 4 inches is:",
        "gt_answers": "6 x + 8 \\square\n",
        "image_path": "./data/HME100K/test_images/test_2341.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = l \\* w\n\nwhere l is the length and w is the width.",
        "gt_answers": "t = L\n",
        "image_path": "./data/HME100K/test_images/test_2342.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n\\frac{x + 2}{x - 5} &= \\frac{a + 2b}{a - 5c}\\\n&= \\frac{a + 2b}{a - 5c} \\\n&= \\frac{a + 2b}{a^2 - 5ab + 5b^2} \\\n&= \\frac{a + 2b}{a^2 - 5b^2 + 2ab} \\\n&= \\frac{a +",
        "gt_answers": "( \\frac { 9 } { 2 } \\leq t \\leq \\frac { 1 3 } { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_2344.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression for the derivative of the function f(x) = x^4. The derivative is given by: df/dx = 4x^3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $$ \\frac{1234567890}{12} = \\frac{1234567890\\*2}{12\\*2} = \\frac{246913580}{24} = 10, 375 $$ This formula is used to calculate the sum of the first 10 positive integers, which is 55.",
        "gt_answers": "S _ { \\Delta } A O F = \\frac { 1 } { 2 } A D . F G = 1 2\n",
        "image_path": "./data/HME100K/test_images/test_2346.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ (a + b) \\times (c + d) = ac + ad + bc + bd $$\n\nThis formula is known as the distributive property, which states that the product of two numbers can be calculated by multiplying each of the numbers together.\n\nYou can verify this by substituting values into the formula, such as a = 3, b = 4, c = 5, and d = 6. Then, you can simplify the expression by combining like terms:\n\n$$ (3 + 4) \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not written in LaTeX format. It appears to be a mathematical equation, but it is not clear what it represents.\n\nHowever, if you provide the equation in LaTeX format, I can help you with any questions you have.",
        "gt_answers": "- \\pi < - B < - \\frac { 1 } { 2 } \\pi\n",
        "image_path": "./data/HME100K/test_images/test_2348.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by the equation:\n\n![mathematical expression](https://latex.codecogs.com/svg.image?%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{caloric content } = \\frac{\\text{metabolic rate } \\times \\text{ time }}{\\text{body weight }}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is: $\\frac{3x+2y-5}{x+y-3}=\\frac{2x-y+5}{x+y-3}$",
        "gt_answers": "x - 2 y + 8 = 0\n",
        "image_path": "./data/HME100K/test_images/test_2351.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the formula in the image:\n\n$$\\frac{5 - 2}{3 - 1} = \\frac{3}{2}$$\n\nIn words, this formula says that the fraction of 5 over 2 is equal to the fraction of 3 over 2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a line with a slope of 2 and y-intercept of 5 is given by the equation y = 2x + 5. This formula can be represented in LaTeX format as follows:\n\n$y = 2x + 5$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$\\text{Volume of the cone } = \\frac{1}{3} \\cdot \\pi \\cdot r^2$$ where $r$ is the radius of the base of the cone.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given as:\n\nx^2 + 2x + 1 = 0\n\nSolving for x:\n\nx = - b / 2a\n\nwhere a and b are the coefficients of the equation. In this case, a = 1 and b = 2, so:\n\nx = - 2 / 2\n\nx = - 1\n\nTherefore, the solution to the equation is x = - 1.",
        "gt_answers": "x = 1\n",
        "image_path": "./data/HME100K/test_images/test_2355.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, the expression for the formula in the image is:$$\\frac{a}{b} = \\frac{c}{d}$$This equation is derived from the fact that the ratio of two numbers is equal to the ratio of the sum of those numbers to the product of the two numbers. In this case, the numerator is $\\frac{a}{b}$, and the denominator is $\\frac{c}{d}$. The result is a ratio of the two numbers, which can be simplified to the expression given above.",
        "gt_answers": "b = \\frac { m - 4 } { 3 } < 0\n",
        "image_path": "./data/HME100K/test_images/test_2356.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To display the formula for the expression in the image using LaTeX format, you can use the following LaTeX code:\n\n$$\\frac{1}{2} + \\frac{3}{4} + \\frac{5}{6}$$\n\nThis formula calculates the average of the numbers 1, 3, and 5. The fraction bars are used to indicate the division of each number by the total number of parts, which is 6 in this case.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the equation for the image, we first need to identify the shape of the graph. The graph appears to be a parabola with its vertex at the origin. We can find the equation of this parabola by using the formula for a parabola with vertex at the origin:\n\ny = ax^2 + bx + c\n\nWe can then use this equation to find the equation of the line that passes through the two points of the graph. The two points are (0, 0) and (1, 1). Substituting these values into the equation gives us:",
        "gt_answers": "b = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2358.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ x = \\frac{a}{b} $$\n\nwhere $a$ and $b$ are the values in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$$ \\left( \\frac{20}{x} \\right) - \\left( \\frac{10}{x+5} \\right) = 20 - 10 \\left( \\frac{x+5}{x} \\right) = 10 $$\n\nwhere $x$ is any real number.",
        "gt_answers": "\\cdot \\sin A \\sin B = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2360.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$$5\\times 3 - 2$$$The variable $x$ is equal to $5$. The variable $y$ is equal to $3$. The variable $z$ is equal to $-2$. The formula is $-5x + 3y - 2z$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as follows:\n\n$$\\begin{align\\*}\nx + 3y &= 10 \\\n3x + y &= 10 \\\n\\end{align\\*}$$\n\nThe image shows two equations that represent the same line in a coordinate plane. The two equations are different forms of the same equation, one in slope intercept form and the other in standard form. The solutions of the two equations are the same.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is f(x) = x^3 - 3x^2 + 2x + 1. This is a polynomial function of degree 3, which can be written as f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n$$\\text{F} = \\text{m} \\times \\text{a}$$\n\nwhere $\\text{F}$ is the force, $\\text{m}$ is the mass of the object, and $\\text{a}$ is the acceleration of the object.",
        "gt_answers": "y ^ { 2 } + y = 1 y ^ { 2 } - y = 1\n",
        "image_path": "./data/HME100K/test_images/test_2366.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><msub><mi>a</mi><mi>n</mi></msub><mo stretchy=\"false\">=</mo><msub><mi>d</mi><mi>f</mi></msub><mo stretchy=\"false\">-</mo><mi>l</mi></mrow><annotation encoding=\"application/x-tex\">\\frac{1}{3}</annotation></",
        "gt_answers": "a _ { n } = a _ { 1 } + ( n - 1 ) d\n",
        "image_path": "./data/HME100K/test_images/test_2367.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $\\frac{5x^2 + 8x + 4}{3x^2 + 2x + 1}$.\n\nTo derive the equation, we first identify the polynomial in the numerator and denominator, which are both quadratic polynomials. The coefficients of the numerator and denominator are given by:\n\n$$\\begin{aligned}5x^2 + 8x + 4 &= 5(x^2 + 2x + 4) \\,\\ \\text{and} \\ \\ 3x^2 + 2x +",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is: f(x) = 4x + 30. This can be derived by looking at the pattern of the numbers in the image. The first number in the sequence is 58, which can be represented as 58 = 50 + 8. The second number is 80, which can be represented as 80 = 50 + 30. The third number is 120, which can be represented as 120 = 100 + 20. By continuing this pattern, we can see that the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is: x^2 + (2x)(3y) + 4y^2.",
        "gt_answers": "x _ { 2 } = \\frac { 1 + \\sqrt { 1 0 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2373.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 1.5 cm is given by A = pi \\* r^2, where pi is the mathematical constant approximately equal to 3.14159. Using this formula, the area of the circle in the image is A = 3.14159 \\* 1.5^2 = 12.2089 cm^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\nsin(x)=cos(x)sin(y)cos(y)sin(z)cos(z)cos(x)sin(z)sin(x)cos(y)cos(x)sin(y)cos(x)cos(y)sin(z)sin(y)cos(z)sin(z)sin(x)cos(z)cos(y)sin(x)cos(y)sin(z)sin(y)cos(z)cos(y)sin(x)cos(y)sin(z",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 2x + 3y = 10 \\times 10^5 \\ m $$\n\nwhere x and y are variables representing the number of apples and pears, respectively.",
        "gt_answers": "2 0 0 \\times 4 . 5 = 9 0 0 ( k m )\n",
        "image_path": "./data/HME100K/test_images/test_2376.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\nThis is a LaTeX expression for the given image:\n\n$$\\frac{2^{s-1}}{2^s} = \\frac{1}{2}\\left(1-\\frac{1}{2}\\right) = \\frac{1}{4}$$\n\nTherefore, the expression for the given image is $\\frac{2^{s-1}}{2^s} = \\frac{1}{4}$.\n```\n\nThis is the LaTeX format of the given expression:\n\n$$\\frac{2^{s-1}}{2^s} = \\frac{1}{2",
        "gt_answers": "S = ( 4 5 2 . 1 6 ) m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2377.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:",
        "gt_answers": "x 0 . 1 m = 9 8 0 p a\n",
        "image_path": "./data/HME100K/test_images/test_2379.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression for the formula in the image using LaTeX format.\n\nGiven the image: <Img>ImageContent</Img>, we can express the equation as:\n\nx4 + x3 + 2x2 + x + 3 = 0\n\nTo express this equation in LaTeX format, we can use the following code:\n\n$$ x^4 + x^3 + 2x^2 + x + 3 = 0 $$\n\nThe $x$ symbol represents the independent variable, and the coefficients in front of each term represent the power of $x",
        "gt_answers": "x _ { 1 } = 2 , x _ { 2 } = - 2\n",
        "image_path": "./data/HME100K/test_images/test_2381.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{equation}\n3x^2 + 2y^2 = 10\n\\end{equation}",
        "gt_answers": "y = 1 3 \\times \\frac { 9 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2382.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$ \\frac{3\\times 5 + 2}{6} = \\frac{15 + 2}{6} = 5 $$",
        "gt_answers": "V _ { p A B C } = \\frac { 3 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2383.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![Img](https://i.imgur.com/qRlUJNm.png)\n\nwhere $latex T = 180\\degree C$ and $latex x = 10\\degree C$ and $latex y = 12\\degree C$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Please provide the image so I can assist you.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\nx = (3 - (5/2)) / (2 - (1/2))\n\nThis is the equation for the midpoint of the line segment connecting the points (1, 3) and (4, 5).",
        "gt_answers": "M _ { x } = \\frac { 2 \\sqrt { 3 } } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_2386.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression for the area of a circle. The formula for the area of a circle is A = (3.1416 x r^2) / 4, where r is the radius of the circle. Using this formula, the area of the circle in the image would be approximately 3.1416 x (16 - 4) = 14.3556.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{5x^2 + 3x - 24}{x + 4}$. This is a polynomial equation of degree 2 with a leading coefficient of 5 and a constant term of - 24.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is:\n\n$$ 2x^2 + 2y^2 = 25 $$\n\nwhere x and y are the Cartesian coordinates of the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the velocity of an object moving along a circular path can be expressed as follows:v=r\u03c9where r is the radius of the circular path and \u03c9 is the angular velocity of the object. The angular velocity can be expressed in terms of the angular acceleration \u03b1\u03c9=r\u03b1where \u03b1 is the angular acceleration of the object. The velocity can be found by substituting the values of r and \u03b1 into the equation:v=r\u03c9=r\u03b1v=\u03b1rwhere v is the velocity, r is the radius, and \u03b1 is the angular acceleration.\n\nNote: This is a text-based",
        "gt_answers": "V = \\frac { s m } { b } ( k m / h )\n",
        "image_path": "./data/HME100K/test_images/test_2390.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the derivative of a function f(x) with respect to x. It is written as: d/dx f(x).",
        "gt_answers": "P _ { M = } \\frac { 1 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2392.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as:\n\n$$\\frac{x^2 - 5x + 6}{x - 2} = \\frac{x^2 - 7x + 12}{x - 4}$$\n\nExpanding the denominator:\n\n$$\\frac{x^2 - 7x + 12}{x - 4} = \\frac{(x - 4)(x + 2) - 7x + 12}{x - 4} = (x - 4)(x + 2) - 7x +",
        "gt_answers": "( y - x + z ) x = 5\n",
        "image_path": "./data/HME100K/test_images/test_2393.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{x+5}{3x^2}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\n2x^2 + 3x - 5 = 0\n\\end{align\\*}\n\nNote that the $x$ variable is used twice in the equation, so it is necessary to use the `\\text` command to distinguish between the two instances of $x$. Also, the equals sign is represented using the `\\=` symbol in LaTeX.",
        "gt_answers": "4 = 3 \\frac { 2 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2396.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 3x^2 - 10x + 5.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n\\begin{equation} m = 2n + 2 \\end{equation}\n\nThis equation represents a quadratic equation in the variable `m`, with the constant term `2n + 2`.",
        "gt_answers": "\\vert m \\vert - 2 = 1\n",
        "image_path": "./data/HME100K/test_images/test_2398.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: f(x) = 1/ (9 - x)4/5 + 3/ (7 - 2x)2/5 - 1/ (11 - x)4/5.",
        "gt_answers": "8 + 1 = 9 4 + 7 = 1 1\n",
        "image_path": "./data/HME100K/test_images/test_2399.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not visible as it is written in Japanese characters.\n\nIf you provide the image, I can assist you in writing out the formula in LaTeX format.",
        "gt_answers": "D C = t , E C = \\frac { 4 } { 3 } t\n",
        "image_path": "./data/HME100K/test_images/test_2400.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is x^2 + x - 5 = 0.",
        "gt_answers": "y _ { 1 } = 6 , y _ { 2 } = - 3\n",
        "image_path": "./data/HME100K/test_images/test_2401.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{100+75}{25}$.\n\nThe formula is: $\\frac{b+a}{c}$, where a=100, b=75, and c=25. The numerator is the sum of a and b, and the denominator is c. The formula represents the average of a and b when their sum is divided by c.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$\\text{0.5}^{2}\\times\\text{20}\\times\\text{3} = \\text{15}$\n\nwhere $\\text{0.5}$ is the radius of the circle and $\\text{20}$ and $\\text{3}$ are the number of degrees in a circle and the number of petals on a flower, respectively.",
        "gt_answers": ". 2 + 0 . 6 = 0 . 8 m\n",
        "image_path": "./data/HME100K/test_images/test_2405.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$ 5x + 6y = 26 $$\n\nTo solve the equation, we can isolate x by subtracting 6y from both sides:\n\n$$ 5x = 26 - 6y $$\n\nThen we can solve for x by dividing both sides by 5:\n\n$$ x = (26 - 6y) / 5 $$\n\nSubstituting the given values, we get:\n\n$$ x = (13 - 6y) / 5 $$\n\nSo the",
        "gt_answers": "\\frac { 4 } { 5 } \\times \\frac { 3 } { 2 } \\times = \\frac { 1 2 } { 5 } \\times\n",
        "image_path": "./data/HME100K/test_images/test_2406.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: y = 3x2 + 5x - 7. The equation can be written in LaTeX format as: $y = 3x^2 + 5x - 7$.",
        "gt_answers": "\\frac { 1 } { \\sqrt { 3 + 1 } } = \\frac { \\sqrt { 3 } - 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2408.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{1}{4}\\times\\frac{2}{5} + \\frac{5}{6} = \\frac{5}{12}$$This is a simple arithmetic expression that can be evaluated by substituting the values of the variables and following the rules of arithmetic.",
        "gt_answers": "x = \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_2409.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical formula written in LaTeX format. The formula is a sum of two terms, one of which is an algebraic expression involving the variables x, y, and z, and the other is a constant value of 20. The formula is evaluated using the values x = 4, y = 5, and z = 6, and the result is 45.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:<img>x^2+2x-3</img>.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$ E = mc^2 $\n\nwhere E is the energy of the object, m is its mass, and c is the speed of light in a vacuum. This formula is derived from the equation of special relativity, which describes the relationship between space and time. It states that the energy of an object is equal to its mass times the square of the speed of light.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}\nx = \\frac{a^2 + b^2}{2ab}\ny = \\frac{a^2 - b^2}{2ab}\n\\end{aligned}$$\n\nwhere $a$ and $b$ are the lengths of the two sides of the right triangle in the image.",
        "gt_answers": "\\frac { E G } { D C } = \\frac { A E } { A C } = \\frac { 3 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2413.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$N = \\frac{t}{v}$$\n\nwhere $N$ is the number of people on the bus, $t$ is the time it takes for all people to get off the bus, and $v$ is the velocity at which the people get off the bus.",
        "gt_answers": "\\lambda = V . T\n",
        "image_path": "./data/HME100K/test_images/test_2414.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format of the expression for the formula in the image:\n\n$$\\text{A}=\\frac{1}{2}\\left(\\frac{\\text{B}}{\\text{C}}+\\frac{\\text{C}}{\\text{D}}\\right)$$\n\nwhere A, B, C, and D are the variables given in the image.",
        "gt_answers": "x _ { 2 } = - \\frac { 5 - \\sqrt { 5 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2415.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is: $ \\frac{b}{a} = \\frac{x}{y} $ in LaTeX format.\n\nwhere $a$ and $b$ are positive integers, and $x$ and $y$ are nonnegative integers.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not clear as the text is not visible.\n\nIf you can provide the equation and the image, I can help you write it out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as follows:\n\nx + 5 = y\n\nwhere x and y are variables.",
        "gt_answers": "y = \\pm \\frac { 2 \\sqrt { 7 } } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_2418.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given below using LaTeX format:\n\n&#x3B4;x+4&#x2212;4x&#x3B4;4&#x2212;2x2&#x3B4;x&#x2212;2\" role=\"presentation\" style=\"position: relative;\">3y4x+4\u22124x3y4x+4\u22122x2y3y4\u22122x\u22122y3y2x\u22122y3y2x\u22122\" class=\"inline-graphic inline",
        "gt_answers": "3 \\sqrt { - 6 4 } = - 4\n",
        "image_path": "./data/HME100K/test_images/test_2419.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression of the formula in the image:\n\n$$a + 2n = 4$$\n\nThis formula is a simple arithmetic expression that can be used to solve problems involving the addition of natural numbers. The variable $n$ represents any natural number, and the constant $a$ represents any integer value. The expression states that the sum of $a$ and $2n$ is equal to $4$.",
        "gt_answers": "A C = 2 A N = 2 \\sqrt { A O _ { 1 } ^ { 2 } - O _ { 1 } N ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_2420.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as:\n\nA = \u03c0r^2,\n\nwhere A is the area, r is the radius of the circle, and \u03c0 is the mathematical constant approximately equal to 3.14.\n\nThe area of a circle with a radius of 5 is given by:\n\nA = \u03c0r^2\nA = \u03c0(5)^2\nA = 25\u03c0\n\nSo the area of the circle is 25\u03c0 square units.",
        "gt_answers": "x ^ { 2 } - 6 x = x ^ { 2 } - 7 x + 1 0\n",
        "image_path": "./data/HME100K/test_images/test_2421.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 100 + \\frac{90}{x} $$\n\nwhere x is the variable.",
        "gt_answers": "A O = O C = O E = 3 .\n",
        "image_path": "./data/HME100K/test_images/test_2422.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format expression of the formula in the image:\n\n$$\\frac{P}{Q}$$\n\nwhere $P$ and $Q$ are the two numbers on either side of the division symbol.",
        "gt_answers": "D F + C F = E F + A F . A E = 0\n",
        "image_path": "./data/HME100K/test_images/test_2423.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for a circle with center (h, k) and radius r is:x^2 + y^2 = r^2. This equation represents the equation of a circle with center (h, k) and radius r.",
        "gt_answers": "x _ { 1 } = - 2 , x _ { 2 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_2424.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 3x^2 + 2x - 5 $$",
        "gt_answers": "( 1 0 \\times 6 + 1 0 \\times 5 + 6 \\times 5 ) \\times 2 = 2 8 0 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_2425.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$$\\text{Volume of revolution of a circular cylinder with radius } r = \\frac{1}{2}\\text{ and height } h = \\frac{1}{4}\\text{ is } V = \\frac{1}{3} \\pi r^2 h$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n1 + \u221a2 = \u221a3",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{x+y}{2}=\\sqrt{x^2+y^2}$. This is a quadratic equation that represents a parabolic relationship between the variables x and y. The formula can be used to find the midpoint between two points in a two-dimensional coordinate system.\n\nIn LaTeX format, the equation can be written as: $\\frac{x+y}{2}=\\sqrt{x^2+y^2}$\n\nThis is a simple formula that shows the relationship between two variables. The x and y represent the coordinates of the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is not provided. Please provide the formula for the image to be written out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2}\\cdot 3 + \\frac{5}{6} \\cdot 4 = \\frac{3}{4} + \\frac{15}{12} = \\frac{18}{12} = \\frac{15}{12}$.",
        "gt_answers": "x = \\frac { 5 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_2430.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To calculate the mass of a substance, we can use the formula for density:\n\nmass = density x volume\n\nwhere mass is the mass of the substance and density is the mass per unit volume. The volume is given by the formula:\n\nvolume = length x width x height\n\nwhere length, width, and height are the dimensions of the substance. To find the mass of the substance, we substitute the values of the volume and density into the formula:\n\nmass = density x volume\nmass = (density) x (length x width x height)\nmass = (density",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}x^2 + \\frac{1}{4}x^4 + \\frac{1}{8}x^6$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20=20\\*10=200$\n\nThis is a sum of consecutive integers from 1 to 20. The result is 200.",
        "gt_answers": "\\angle B A D = \\angle E A G = 9\n",
        "image_path": "./data/HME100K/test_images/test_2435.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a representation of the exponential function y = x^3. In LaTeX format, it would be written as:\n\n$$y = x^3$$\n\nwhere $x$ is the independent variable and $y$ is the dependent variable. The equation states that the value of $y$ is equal to the value of $x$ cubed.",
        "gt_answers": "1 + 4 y + 4 y ^ { 2 } + y ^ { 2 } = 1 3\n",
        "image_path": "./data/HME100K/test_images/test_2436.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not provided, so it is not possible to write it out in LaTeX format.",
        "gt_answers": "\\frac { c d } { m } = 0\n",
        "image_path": "./data/HME100K/test_images/test_2437.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\n&#x2212;&#x2211;&#x2202;&#x2202;E=mc2\" role=\"presentation\" style=\"position: relative;\">\u2212E=mc2\u2212E=mc2 E = mc2 \\ E = m c^2 \n\nwhere E is the energy, m is the mass, and c is the speed of light in a vacuum. This equation states that the energy of an object is equal to its mass times the speed of light squared.",
        "gt_answers": "x ( a - 1 ) = 6 t _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2438.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\n    f(x) &= \\frac{1}{3x^2 + 1} \\left( 2x^3 + 6x^2 + 8x + 4 \\right) \\\n    &= \\frac{2x^3 + 6x^2 + 8x + 4}{3x^2 + 1} \\\n    &= \\frac{2x^3 + 6x^2 + 8x + 4}{3x^2} \\",
        "gt_answers": "O E ^ { 2 } = D O \\cdot D\n",
        "image_path": "./data/HME100K/test_images/test_2439.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\n150sin&#x226;150&#x226;150sin&#x226;x+150cos&#x226;150&#x226;150cos&#x226;x=130cos&#x226;150&#x226;150sin&#x226;x+150cos&#x226;150&#x226;150cos&#",
        "gt_answers": "1 3 0 k g = 0 . 1 3 t\n",
        "image_path": "./data/HME100K/test_images/test_2442.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n$$ \\text{Image content} = \\text{some text} $$\n\nIn LaTeX, the expression is written in math mode using the dollar sign ($) to indicate the start and end of the equation, and the equals sign (=) to indicate the equality of the expression. The text that appears in the image is written in regular text mode using the letters and spaces as they appear in the image.\n\nThe expression is read as \"the image content is equal to some text\".",
        "gt_answers": "( x ^ { 2 } - 4 ) ( x ^ { 2 } + 1 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_2443.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = l \u00d7 w\n\nwhere l is the length and w is the width. In the image, the length is represented by the number 4 and the width is represented by the number 3. Therefore, the area of the rectangle is:\n\nA = 4 \u00d7 3 = 12 cm2\n\nIn LaTeX format, the formula would be written as:\n\n$ A = l \u00d7 w = 4 \\times 3 = 12 \\mathrm{cm}^2 $",
        "gt_answers": "k = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2444.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: 2 + 2 = 4.\n\nThis is a simple arithmetic equation that states that two plus two equals four. It can be written in LaTeX format as:\n\n$$ 2 + 2 = 4 $$\nThis equation is true no matter what context you are using it in, whether it is in mathematics, science, or everyday life.",
        "gt_answers": "\\angle A B D + \\angle E B C = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2445.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{equation}\nf(x) = \\frac{1}{2}\\left(\\frac{x}{10}\\right)^2 + \\frac{1}{3}\\left(\\frac{x}{15}\\right)^3 + \\frac{1}{4}\\left(\\frac{x}{20}\\right)^4 + \\frac{1}{5}\\left(\\frac{x}{30}\\right)^5 + \\frac{1}{6}\\left(\\frac{x}{50}\\",
        "gt_answers": "T = \\frac { 1 } { 3 0 } s\n",
        "image_path": "./data/HME100K/test_images/test_2446.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be expressed as: $\\frac{a}{b}=\\frac{c}{d}$.",
        "gt_answers": "\\frac { 2 x + 1 } { 5 } \\leq \\frac { x + 1 } { 2 } \\textcircled { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2448.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{bh}{k}$$\nwhere $b$ is the area of the base of the rectangle, $h$ is the height of the rectangle, and $k$ is the perimeter of the rectangle.",
        "gt_answers": "x = \\frac { 9 } { 1 9 }\n",
        "image_path": "./data/HME100K/test_images/test_2449.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "3 0 1 . 4 4 + 5 0 . 2 4 \\times 2 = 4 0 1 9 2 d m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2450.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the given formula:$$\\frac{2x+5}{x-3}$$The formula is a simple algebraic expression that can be written using LaTeX. The expression involves the division of two polynomials, with the numerator being $2x+5$ and the denominator being $x-3$. The fraction line is used to indicate the division operation, with the numerator and denominator separated by a slash.\n\nIn LaTeX, the expression can be written using the following code:$$\\frac{2x+5}{x-3}$$The $2x$ and $x-",
        "gt_answers": "P \\cap \\theta = \\{ x \\vert \\frac { 3 } { 2 } \\leq x < 2 \\}\n",
        "image_path": "./data/HME100K/test_images/test_2452.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX format for the expression of the formula in the image:\n\n$$ f(x) = \\begin{cases} x^2 - 4, \\quad & x \\leq 2 \\\\ 0, \\quad & 2 < x \\leq 4 \\\\ 2x - 4, \\quad & x > 4 \\end{cases} $$\n\nThis formula defines the piecewise function f(x) that maps the interval [0,4] to the real numbers. The function has three pieces: a parabolic segment from x=0 to x=2,",
        "gt_answers": "F e _ { 2 } O _ { 3 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_2453.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is: $\\frac{3 + 4}{5 - 2}$. This is because the image shows the expression 3 + 4, which is added to 5 to obtain the denominator 5 - 2. The result is then simplified using the distributive property of addition, which states that a(b + c) = ab + ac.",
        "gt_answers": "\\frac { 1 } { y } - 3 y - 2 = 0\n",
        "image_path": "./data/HME100K/test_images/test_2455.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{y} = \\frac{5000 - 3500}{4000 - 2000} = \\frac{500}{1000} = 0.5$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 5 cm is A = \u03c0r^2, where r is the radius of the circle. Therefore, the area of the circle is A = \u03c0(5)^2 = 25\u03c0.",
        "gt_answers": "\\sqrt { 2 x + 1 } = x - 1\n",
        "image_path": "./data/HME100K/test_images/test_2457.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \\frac{x}{x+2} \\* \\frac{y}{y+5} = \\frac{2x}{x+2} \\* \\frac{5y}{y+5} = \\frac{2x}{x+2} \\* \\frac{5y}{y+5} = \\frac{2x}{x+2} \\* \\frac{5y}{y+5} = \\frac{2(x+5y)}{(x+2)(y+5)} = \\frac{7x+10",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by A = (r^2)\u03c0.\n\nIn LaTeX format, this can be written as:\n\n$$A = \\left(\\frac{r}{2}\\right)^2 \\pi$$",
        "gt_answers": "9 x - x = 1 2 x + 2 = 5 x + 5 - 1 7 x = 7 - 1\n",
        "image_path": "./data/HME100K/test_images/test_2460.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the dot product of two vectors. The dot product of two vectors, a and b, is defined as the sum of the products of their corresponding components:$$ a \\cdot b = a\\_1 b\\_1 + a\\_2 b\\_2 + \\dots + a\\_n b\\_n $$In LaTeX format, this equation can be written as:$$ a \\cdot b = \\sum\\_{i=1}^n a\\_i b\\_i $$This equation shows that the dot product of two vectors is equal to the sum of the products of their corresponding components.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align}\n\\frac{1}{2} \\cdot \\frac{1}{4} + \\frac{1}{4} \\cdot \\frac{1}{4} &= \\frac{1}{8} + \\frac{1}{8} \\notag \\\\\n&= \\frac{1}{4} \\notag \\\\\n&= \\frac{1}{4} \\cdot \\frac{1}{2} \\notag \\\\\n&= \\frac{1}{8} \\cdot \\frac{1}{2} \\",
        "gt_answers": "\\angle S _ { \\Delta } A O P = S _ { \\Delta } P X\n",
        "image_path": "./data/HME100K/test_images/test_2462.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can follow these steps:\n\n1. Determine the variables: In the formula, there are two variables, x and y.\n2. Write the formula: The formula is given by the equation: y = (2x + 1) / x.\n3. Use LaTeX format: The LaTeX format for the formula is given by:\ny = \\frac{(2x + 1)}{x}\n4. Substitute the variables: To substitute the variables, we can use the following:\ny = \\frac{(2",
        "gt_answers": "S _ { 5 } = 5 ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2463.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n\\begin{align}\n2\\sqrt{2x^2 + 2x + 1} - \\sqrt{x^2 + x + 1} = 2\\sqrt{x^2 + 2x + 1} - \\sqrt{x^2 + x + 1}\n\\end{align}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{3x^2+2y^2}{x^2+y^2}=\\sqrt{3}\\cdot\\frac{x^2+y^2}{x^2+y^2}=\\sqrt{3}\\cdot\\frac{x^2+y^2}{x^2+y^2}=\\sqrt{3}\\cdot\\frac{x^2+y^2}{x^2+y^2}=\\sqrt{3}\\cdot\\frac{x^2+y^2}{x^2+y",
        "gt_answers": "x = \\sqrt [ 3 ] { - 9 }\n",
        "image_path": "./data/HME100K/test_images/test_2465.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$ 10 + 3\\times 2 = 15 $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{center}\n$ \\frac{t^2}{4} - \\frac{9t}{2} + 3t - \\frac{3}{4}$\n\\end{center}\n\nThis is the formula for the area of a triangle with base $t$ and height $3$.",
        "gt_answers": "A E \\bot B C\n",
        "image_path": "./data/HME100K/test_images/test_2468.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, the formula in the image is given by:\n\n\\begin{equation}\nx = 3 \\cdot 2^y\n\\end{equation}\nwhere $x$ is the number obtained by raising $2$ to the power of $y$.",
        "gt_answers": "x = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2469.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\frac{1}{3} \\times 2 + \\frac{1}{4} \\times 2 = \\frac{1}{3} \\times 4 + \\frac{1}{4} \\times 2 = \\frac{7}{6} + \\frac{1}{4} = \\frac{13}{6} = \\boxed{2} $$\n\nThe formula for the area of a rectangle is given by:\n\n$$A = l \\times w$$\n\nwhere l is the length and w",
        "gt_answers": "( 3 y ) ^ { 2 } - 2 ( 3 y ) y + y ^ { 2 } = 4\n",
        "image_path": "./data/HME100K/test_images/test_2471.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\left(\\frac{a}{b}\\right)^2\\left(\\frac{c}{d}\\right)^2\\left(\\frac{e}{f}\\right)^2\\left(\\frac{g}{h}\\right)^2\\left(\\frac{i}{j}\\right)^2\\left(\\frac{k}{l}\\right)^2\\left(\\frac{m}{n}\\right)^2\\left(\\frac{p}{q}\\right)^2\\left(\\frac{r}{s}\\right)^2\\left(\\frac{t}{",
        "gt_answers": "1 - 2 m , x = - 3 m - 1\n",
        "image_path": "./data/HME100K/test_images/test_2472.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize, but it's difficult to provide an expression for the formula in the image without knowing what the formula represents. Can you please provide more information or context about the formula?",
        "gt_answers": "u = 3\n",
        "image_path": "./data/HME100K/test_images/test_2474.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is \\frac{2000}{300+1500}.",
        "gt_answers": "\\frac { 9 } { 1 6 } \\approx 0 . 5 0 6\n",
        "image_path": "./data/HME100K/test_images/test_2475.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$x = 4 - 3y$",
        "gt_answers": "x = \\frac { 9 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_2476.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as:\n\n$$\\text{d}x = \\frac{3}{2}x^2 + \\frac{1}{2}x - 5$$\n\nThe image shows the graph of the differential equation, which can be expressed in terms of the variable $x$ as:\n\n$$\\frac{d}{dx}x^n = nx^{n-1}$$\n\nThe derivative of $x^2$ is $2x$, of $x$ is $1$, and of $-5$ is $-5$. Substituting these",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{center} r = \\frac{GmM}{r^2} \\end{center}\n\nIn this formula, r is the radius of the sphere, G is the gravitational constant, m is the mass of the sphere, and M is the mass of the Earth. The formula gives the radius of the sphere's orbit around the Earth.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle with width w and height h is:\n\nA = w \\* h\n\nIn LaTeX format, this equation can be written as:\n\nA = w \\* h",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image with the number 400 in LaTeX format would be:\n\n$$ 400 = \\frac{500}{2} $$\n\nThe image shows a pair of fractions, with the numerator being 500 and the denominator being 2. This results in a fraction with a value of 400.",
        "gt_answers": "4 9 2 \\div 8 0 = 6 \\cdots 1 2\n",
        "image_path": "./data/HME100K/test_images/test_2481.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as follows:\n\n\\begin{align\\*}\n\\text{Number of hexagons in the second row} & = \\frac{3n + 3}{2} \\\n\\text{Number of hexagons in the third row} & = \\frac{3n - 1}{2} \\\n\\text{Number of hexagons in the fourth row} & = \\frac{3n - 3}{2}\n\\end{align\\*}\nwhere n is the number of hexagons in the first row.",
        "gt_answers": "S O _ { 3 } ^ { 2 } + C l _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2482.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a polynomial equation of degree 2.\n\nThe equation is: y = x^2 - 4x + 2\n\nThis equation can be derived by using the quadratic formula: y = ax^2 + bx + c, where a = 1, b = -4, and c = 2. Substituting these values into the formula, we get:\n\ny = 1x^2 - 4x + 2\n\nExpanding the parentheses, we get:\n\ny = x^2 - 4x + 2",
        "gt_answers": "( x - 2 > 0\n",
        "image_path": "./data/HME100K/test_images/test_2483.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by the equation:\n\nf(x) = 3x2 - 5x + 2\n\nThis is a quadratic function with vertex at the origin and a minimum value of -2 at x = 2.",
        "gt_answers": "x _ { 1 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2484.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{x}^2 + (2n - 1)^2 = 4n^2$$\n\nwhere $n$ is a non-negative integer. To see why this is true, we can expand the left-hand side of the equation:\n$$\\text{x}^2 + (2n - 1)^2 = (\\text{x} + (2n - 1))^2 = \\text{x}^2 + 4n^2 - 2\\text{x}(2n - 1",
        "gt_answers": "x = - \\frac { 6 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2485.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as:",
        "gt_answers": ": \\angle B D N + \\angle N + \\angle D B N = 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2486.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:$$\\begin{aligned} 3x^2+5x-10 &= 0 \\Rightarrow x^2+5x-10 = 0 \\Rightarrow x^2-5x+10 = 0 \\Rightarrow x(x-5) = 0 \\Rightarrow x = 0, 5 \\Rightarrow x = 0, 5\\end{aligned}$$This formula is a quadratic equation in one variable x, which can be solved by completing the square method or by using the quadratic formula.",
        "gt_answers": "h ( x ) \\leq 0\n",
        "image_path": "./data/HME100K/test_images/test_2490.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{\\text{sin}(x)}{\\text{cos}(x)}$$",
        "gt_answers": "S _ { \\Delta } D H O = S _ { \\Delta } A C D + S _ { \\Delta } A O C + S _ { \\Delta } C O H - S _ { \\Delta } A O D\n",
        "image_path": "./data/HME100K/test_images/test_2491.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{3}{4}+\\frac{5}{6}=\\frac{11}{12}$$\n\nThis is a simple arithmetic expression that can be evaluated using the rules of algebra. To evaluate the expression, we simply replace the variables with their corresponding values and perform the operations. In this case, we have two fractions that we need to add: $\\frac{3}{4}$ and $\\frac{5}{6}$. We can add these fractions by simply finding their sum, which is $\\frac{8}{12}$. Then,",
        "gt_answers": "1 2 \\div \\frac { 1 } { 3 } = 3 6 ( m )\n",
        "image_path": "./data/HME100K/test_images/test_2492.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{\\frac{3}{x}}{\\frac{4}{y}}$.",
        "gt_answers": "\\sqrt [ 3 ] { 6 \\frac { 6 } { 2 1 5 } } = 6 \\sqrt [ 3 ] { \\frac { 6 } { 2 1 5 } }\n",
        "image_path": "./data/HME100K/test_images/test_2494.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is as follows:$$\\frac{1}{2} \\times \\frac{2}{3} \\times \\frac{5}{6} = \\frac{5}{12}$$The image shows three fractions, each having a numerator and denominator. The numerator of the first fraction is 1, the denominator is 2, the numerator of the second fraction is 2, the denominator is 3, and the numerator of the third fraction is 5, the denominator is 6. By multiplying these fractions, we obtain the result $\\",
        "gt_answers": "t = \\frac { 1 2 } { 6 . 4 } = 1 . 8 8 ( s )\n",
        "image_path": "./data/HME100K/test_images/test_2495.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ \\frac{250 - 300}{400 + 300} = \\frac{50}{700} = \\frac{1}{14.2857} $$\n\nwhere the numerator is $-250$ and the denominator is $400 + 300$.",
        "gt_answers": "\\frac { O D } { D A } = \\frac { O F } { O C }\n",
        "image_path": "./data/HME100K/test_images/test_2497.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{center}\n$x = \\frac{a^2 + b^2}{a^2 - b^2}$\n\\end{center}\n\nwhere $a$ and $b$ are the lengths of the sides of the square.",
        "gt_answers": "S = \\frac { 1 } { 2 } a t ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2498.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{x+y}{2} $$",
        "gt_answers": "- \\vert - \\frac { 2 0 } { 7 } \\vert , - ( - \\frac { 3 } { 5 } ) , - 3 , 8 , 4 , 3\n",
        "image_path": "./data/HME100K/test_images/test_2499.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format. Here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->] (0,0) -- (2,0) node[right] {$ x$};\n\\draw[->] (0,0) -- (0,2) node[above] {$ y$};\n\\draw[->] (1,1) -- (3,1) node[right] {$ x$};\n\\draw[->] (1,1) --",
        "gt_answers": "\\frac { 5 2 + 3 8 + 1 6 } { 2 0 0 } = \\frac { x } { 1 0 0 }\n",
        "image_path": "./data/HME100K/test_images/test_2500.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$\\begin{aligned}x^2 + 2x + 1 &= x^2 + 2x \\qquad \\text{(substituting }x+1\\text{ for }x^2+x) \\\\&= (x+1)^2 - 2(x+1) + 1 \\qquad \\text{(expanding the right side)} \\\\&= (x+1)^2 - 2x - x + 1 \\qquad \\text{(combining like terms",
        "gt_answers": "x _ { 1 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_2501.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula can be written as:\n\n$$ \\frac{2}{x+2}+\\frac{5}{x-2}=\\frac{10}{x} $$",
        "gt_answers": "\\frac { 2 } { 5 } x = \\frac { 1 0 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2502.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the image you provided:\n\n$$3x+5=7$$\n\nThe equation is in standard form, with the variable $x$ on the left side of the equation and the constant value $7$ on the right side. The equation is balanced, with the number of variables on each side equal to the number of constants on each side.",
        "gt_answers": "x = \\frac { 3 2 3 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_2503.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:$$\\text{a}\\leq\\text{b}\\leq\\text{c}$$where $\\text{a}$ is the minimum value, $\\text{b}$ is the maximum value, and $\\text{c}$ is the mean value.",
        "gt_answers": "a _ { 1 } = \\frac { 3 + \\sqrt { 1 3 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2504.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}(2x + 3y) = 10$\n\nExplanation: The formula in the image is the equation of a line in slope-intercept form, with a slope of 3 and an intercept of 10. To write it in LaTeX format, we first need to enclose the equation in parentheses, then divide both sides by 2 to simplify the equation. The x and y variables are enclosed in parentheses, and the coefficients of x and y are multiplied by 2 and 3,",
        "gt_answers": "b = - \\frac { 2 0 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2506.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$\\frac{1}{1+x}$",
        "gt_answers": "x = 1 , y = 3 - \\sqrt { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_2507.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a base of 2 and a height of 5 is:\n\nA = base x height\nA = 2 x 5\nA = 10 square units\n\nTherefore, the area of the rectangle in the image is 10 square units.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, you can use the following LaTeX code:\n\n\\begin{align\\*}\n& 2x^2 + 4x - 12 \\\n&= (2x + 2)(x + 3) \\\n&= (2x + 3)(x + 2) \\\n&= (x + 1)(2x + 3)\n\\end{align\\*}\n\nThis equation can be read as, \"the sum of two numbers is the product of their sum and three.\"",
        "gt_answers": "\\frac { 4 } { B D } = \\frac { 8 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2509.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is pi + 1 = 4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX formula for the given image:\n\n$$\\begin{aligned}\n3x^2 + 2x - 5 &= 0 \\ \\Rightarrow x = \\frac{5 + \\sqrt{13}}{6} \\ \\ or \\ x = \\frac{5 - \\sqrt{13}}{6}\n\\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:$$\\text{ImageContent}$$where the red line represents the point of intersection between the two lines.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$\\frac{1000}{(1000 \\* \\frac{3500}{6000}) + 2000}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This image shows the formula for an unknown equation, represented by the symbol x. It also shows the equation's values, including the values of x and y. The equation is represented as x = (bas + b) / (cx + d).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{f(x) = \\frac{x^2}{4x + 10}}$$\n\nNote: The formula in the image is written in a different format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for calculating the area of a circle. The formula is given by the equation: A = \u03c0r^2, where A is the area of the circle and r is its radius. The radius is denoted by the letter 'r' in the formula. The result is written in the image as A = pi r^2.",
        "gt_answers": "x = \\frac { 9 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2519.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: f(x) = (a + bx) / (c + dx).\n\nHere's how to derive the formula:\n\n1. Start with the equation of a line given by the equation y = mx + b, where m is the slope and b is the y-intercept.\n2. Replace x with the expression (a + bx), which is the equation of a line that is parallel to the original line but has a different slope and y-intercept.\n3. Replace y with the expression c + dx, which is the equation of a",
        "gt_answers": "\\frac { 2 } { x } = \\frac { x } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2520.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is not provided. Please provide the image for me to write the expression.",
        "gt_answers": "( m - 1 ) ^ { 2 } = ( \\sqrt { 2 0 1 9 } + 1 ) - 1 ) ^ { 2 } = 2 0 1 9\n",
        "image_path": "./data/HME100K/test_images/test_2521.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not provided.",
        "gt_answers": "\\vert x + \\frac { 1 } { 2 } \\vert + \\vert x - \\frac { 3 } { 2 } \\vert \\leq 3\n",
        "image_path": "./data/HME100K/test_images/test_2523.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{2x+3}{x^2-9}$.\n\nTo derive this expression, we first simplify the expression inside the parentheses:\n\n$2x + 3 = 2(x + 3) = 2x + 3x + 3 = \\frac{2x}{1} + \\frac{3x}{1} = \\frac{2}{1}x + \\frac{3}{1}x = \\frac{2x + 3}{1}$\n\nNext, we factor the numerator and denominator:",
        "gt_answers": "P = \\frac { U _ { 1 } ^ { 2 } } { R _ { 1 } }\n",
        "image_path": "./data/HME100K/test_images/test_2526.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not shown. Could you please provide the equation?",
        "gt_answers": "\\angle B A E = \\frac { 1 } { 2 } \\angle B A C = 4 0\n",
        "image_path": "./data/HME100K/test_images/test_2527.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula written in LaTeX format. The formula is for calculating the area of a triangle.\n\nThe formula is:\n\n`A = (1/2) \\* (b1 + b2 + b3)`\n\nWhere b1, b2, and b3 are the lengths of the sides of the triangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given by the equation: $\\frac{x^3+y^3}{x^2+y^2}=\\frac{20}{13}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align}\na &= 5 \\cr\nb &= 4 \\cr\nc &= 6 \\cr\nd &= 8 \\cr\ne &= 9 \\cr\nf &= 10\n\\end{align}\n\nNote: This answer assumes that the formula is correctly written in the image.",
        "gt_answers": "a ^ { 2 } + a - 6 = 0\n",
        "image_path": "./data/HME100K/test_images/test_2531.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I don't see any image or expression of a formula in the message. Please provide the image and the formula to calculate the expression.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{1}{3}-\\frac{1}{4}=\\frac{1}{12}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX formula for the expression given in the image:\n\n$ 2x + 5 = 14 $\n\nTo solve this equation, we can use the following steps:\n\n1. Simplify the left-hand side of the equation by subtracting 2x from both sides.\n2. Multiply both sides by 5 to get 10x on one side and 7 on the other.\n3. Add 7 to both sides to get 10x = 14 + 7\n4. Sol",
        "gt_answers": "a _ { 9 } : 2 \\times 9 - 1 = 1 7\n",
        "image_path": "./data/HME100K/test_images/test_2537.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{x^3}{2} + 4x^2 - 12x + 8$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\text{l} = \\frac{1}{\\sqrt{2}}\\left(\\sqrt{3} + \\frac{2}{\\sqrt{5}}\\right) \\quad \\text{or} \\quad \\text{l} = \\sqrt{2}\\left(\\frac{3}{\\sqrt{5}} + \\frac{2}{\\sqrt{2}}\\right)$$\n\nwhere $\\text{l}$ is the length of the hypotenuse of the right-angled triangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the following: c2d2 2c2d2 2c2d2 2c2d2 2c2d2 c2d2 2c2d2 2c2d2 2c2d2 c2d2 2c2d2 2c2d2 2c2d2 2c2d2 c2d2 2c2d2 2c2d2 2c2d2 c2d2 2c2d2 2c2d2 2c",
        "gt_answers": "c > d\n",
        "image_path": "./data/HME100K/test_images/test_2540.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows:\n\n$$\\text{ImageContent} = \\text{UC}\\_\\text{f}$$\n\nwhere $\\text{UC}\\_\\text{f}$ represents the formula in the image.",
        "gt_answers": "u < f\n",
        "image_path": "./data/HME100K/test_images/test_2541.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written out in LaTeX format, as it is written in handwriting. However, it can be written out in LaTeX format as follows:\n\n$$\\text{bd } a\\_{loc}^{7} \\times \\text{bd } a\\_{loc}^{5} \\times \\text{bd } a\\_{loc}^{3} \\times \\text{bd } a\\_{loc}^{1} \\times \\text{bd } a\\_{loc}^{-1} \\times \\text{bd } a\\_{loc}^{-3} \\times \\text{bd } a\\",
        "gt_answers": "B D / / A C \\angle O A C = 7 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2543.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n2(1 - cos(x/2))cos(x/2) + 3sin(x/2)sin(x/2) = (1 - cos(x/2))(2cos(x/2) + 3sin(x/2)) = cos(x/2) - cos(x/2) + 3sin(x/2) = 1 - cos(x/2) + 3sin(x/2)",
        "gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2544.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$$E = mc^2$$\n\nwhere $E$ is the energy of the object, $m$ is its mass, and $c$ is the speed of light in a vacuum.",
        "gt_answers": "F = G = m g = 1 \\times 1 0 ^ { 3 } k g \\times 1 0 N / k g = 1 \\times 1 0 ^ { 4 } N\n",
        "image_path": "./data/HME100K/test_images/test_2545.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{1}{2}x^2 + \\frac{1}{4}x - \\frac{1}{8} $$\n\nThis is the formula for the parabolic function with the center at the origin and the vertices at the points (0, -1) and (2, 0).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle is given by:\n\nA = l \u00d7 wA = l \u00d7 wwhere l is the length of the rectangle and w is the width of the rectangle.\n\nIn the image, the length of the rectangle is 4 and the width is 6. Therefore, the area of the rectangle is 4 \u00d7 6 = 24 square units.\n\nThe sum of the perimeters of the two rectangles is given by:\n\nP1 + P2 = 2(4 + 5) + 2(6 + 8) = 2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align}\nx^4 + 3x^3 + 4x^2 + 5x + 6 &= 3x^4 + 3x^3 + 4x^2 + 5x + 6 \\\n&= (x + 3)(x + 2)(x + 1)(x + 4) \\\n&= x^4 + 3x^3 + 4x^2 + 5x + 6\n\\end{align}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is A = pi \\* r^2, where A is the area, pi is the mathematical constant approximately equal to 3.14, and r is the radius of the circle.\n\nIn the image, the radius of the circle is given by the equation r = 1. The area of the circle can be calculated as A = pi \\* r^2 = pi \\* 1^2 = pi.",
        "gt_answers": "y = \\pm 1\n",
        "image_path": "./data/HME100K/test_images/test_2551.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b0\u221e \u222bt2\u221e \u222b0t2\u221e \u222b0t2\u221e \u222b0\u221e \u222b0t2\u221e \u222b0\u221e \u222b0t2\u221e \u222b0t2\u221e (e^(t2/2) - 1)e^(-t2/2)dt2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{3x + 4y}{7}$.",
        "gt_answers": "x = - \\frac { 1 2 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_2554.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$ f(x) = \\frac{1}{2} \\left( x - \\frac{1}{2} \\right)^2 + \\frac{1}{4} \\left( x - \\frac{1}{2} \\right)^4 $",
        "gt_answers": "( \\sqrt { 2 } - 1 , 0 )\n",
        "image_path": "./data/HME100K/test_images/test_2555.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of the shape shown in the image is:\n\nA = \u222b\u03c0r\u00b2d\u03c0 \\cdot r^2 \\cdot d\u03c0A=\u222b\u03c0r\u00b2d\u03c0\u200bThe area of the shape is given by the integral of pi times the square of the radius over pi.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\\begin{equation} \\mathrm{H}\\_\\phi = \\frac{\\mathrm{d}}{\\mathrm{d}t}(\\mathrm{L}\\_\\phi - \\mathrm{L}\\_\\phi^\\mathrm{0}) \\end{equation} This is the formula for the energy balance of a control volume. The left side of the equation is the change in specific heat of the fluid, which is a function of temperature and specific volume. The right side of the equation is the rate of heat transfer into or out of the control volume, which is a function of the temperature difference and the heat transfer coefficient.\n\nIn this formula",
        "gt_answers": "( 9 - c ) ^ { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_2557.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is A = l \\* w, where l is the length and w is the width. The formula for the perimeter of a rectangle is P = 2l + 2w. Using these formulas, we can find the area and perimeter of the rectangle in the image.\n\nFirst, we need to find the length and width of the rectangle. We can do this by looking at the image and measuring the length and width of the rectangle. Let's say the length is 4 cm and the width is 3 cm.\n\nNext, we can use the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write out the expression for the formula in the image using LaTeX format. Here's the expression:$$ \\frac{a+b}{c+d}$$where a, b, c, and d are variables. This is a simple fraction that can be used to solve various mathematical problems.",
        "gt_answers": "C _ { 4 } ^ { 1 } \\cdot C _ { 6 } ^ { 3 } \\cdot = 8 : 0\n",
        "image_path": "./data/HME100K/test_images/test_2559.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x^{3}}{x+5}+\\frac{5x^{2}}{x+3}+\\frac{3x}{x+1}$",
        "gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2560.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{equation}\n\\begin{aligned}\n5 + 3 = 8\n\\end{aligned}\n\\end{equation}\n\\end{center}\n\nThis equation is simply adding 5 and 3 to get 8. The image shows that the number 5 is written in red ink and the number 3 is written in blue ink, with a plus sign between them to indicate the addition operation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX representation of the expression in the image:\n\n\\begin{align\\*}\nx + 2x + 3x + 4x &= 10x \\\n&= 10 \\\n&= 5 \\\n&= 5 + 3 \\\n&= 8 \\\n&= 8 - 3 \\\n&= 5 \\\n&= 5 \\* 2 \\\n&= 10 \\\n&= 10 \\* 2 \\\n&= 20 \\\n&= 20 \\* 2 \\\n&= 40 \\\n&= 4",
        "gt_answers": "2 0 + 2 3 = 4 3 ( s\n",
        "image_path": "./data/HME100K/test_images/test_2563.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a blackboard with the following equation written on it: 5 + 3 = 8. The equation is written in red chalk on a white background. The number 5 is written above the plus sign, and the number 3 is written below the equals sign. The number 8 is written below the equals sign. The equation is written in the standard mathematical notation for addition.",
        "gt_answers": "x = \\frac { 3 } { 4 } - \\frac { 2 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_2564.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$P\\_a = 10 \\times \\frac{x}{100}$\n\nThe pressure of the gas in the cylinder is given by the formula:\n\nP\\_a = F\\_a \\* rho\\_a\n\nwhere F\\_a is the force applied on the piston and rho\\_a is the density of the gas in the cylinder. The force applied on the piston is given by:\n\nF\\_a = P\\_a \\* A\n\nwhere A is the area of the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a line in a 3D space can be expressed as:y = mx + bwhere m is the slope of the line and b is the y-intercept of the line. In this case, the slope is 3, and the y-intercept is 5. Therefore, the equation for the line in the image is:y = 3x + 5To graph this equation, we can use the following steps:1. Plot the x-axis and y-axis with appropriate scales.2. Plot the slope of the line (3) on the x-axis.3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula for calculating the area of a triangle. The formula is: (1/2) \\* (base x height). The base is represented by the number 2.5 and the height is represented by the number 3.5.",
        "gt_answers": "\\cos \\alpha = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2567.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is given by:\n\n$$\\text{b}=\\frac{2n}{a}+\\frac{n^2}{a^2}$$\n\nwhere $n$ is the number of people in the classroom.",
        "gt_answers": "b = \\frac { 7 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2568.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\nwhere A, B, C, and D are constants.",
        "gt_answers": "b ^ { 2 } y ^ { 2 } + y ^ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_2569.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tabular}{ccc}\n$x$ & $y$ & $z$ \\\n\\end{tabular}\n\\end{center}\nwhere $x$, $y$, and $z$ are variables.",
        "gt_answers": "y = \\frac { 5 1 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_2570.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is given below:\n\n$$\\begin{aligned} \\text{Image} = \\frac{\\text{sum of the numbers in the first row} + \\text{sum of the numbers in the second row}}{\\text{number of terms in the first row} + \\text{number of terms in the second row}} \\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX equation for the expression given in the image:\n\n\\begin{equation}\nE = mc^2\n\\end{equation}\n\nIn this equation, E represents the energy of an object, m represents its mass, and c represents the speed of light in a vacuum. The equation states that the energy of an object is equal to the product of its mass and the speed of light squared. This equation is a fundamental concept in physics and is used to describe the relationship between energy, mass, and velocity.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n\\begin{align}\n& \\text{Area of the rectangle with length } x = 4 \\text{ and width } y = 5 = x \\times y = 20 \\text{ square units} \\\n\\end{align}",
        "gt_answers": "- \\frac { 1 } { 2 } x = 1 6\n",
        "image_path": "./data/HME100K/test_images/test_2574.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "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![](https://www.youtube.com/watch?v=eGKgTvPQR1Y)\n\nThe red line represents the equation of the parabola y = x^2, and the blue line represents the equation of the hyperbola x^2 + y^2 = 4xy. The point where the two lines intersect is the point of inflection, where the concavity of the parabola changes to the other side.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format would be:\n\n$$ 2x^2 + 4x - 8 = 0 $$\n\nwhere $x$ is an arbitrary variable.",
        "gt_answers": "2 A g N O _ { 3 } + F e = F e ( N O _ { 3 } ) _ { 2 } + 2 A g\n",
        "image_path": "./data/HME100K/test_images/test_2576.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{a + 2b + 3c}{4}$.\n\nHere's how to derive it:\n\n1. Simplify the expression by factoring out the greatest common factor of 4: $\\frac{a + 2b + 3c}{4} = \\frac{2(a + b + c)}{2}$.\n2. Factor the numerator: $\\frac{2(a + b + c)}{2} = 2a + 2b + 2c$.\n3. Simpl",
        "gt_answers": "2 [ \\frac { 4 } { 3 } x - \\frac { 2 } { 3 } x + \\frac { 1 } { 2 } ] = \\frac { 3 } { 4 } x\n",
        "image_path": "./data/HME100K/test_images/test_2577.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a diameter of 6 cm is:\n\nA = (\u03c0r^2)\n\nwhere r is the radius of the circle, which is half of the diameter, or 3 cm.\n\nSo the area of the circle is:\n\nA = (\u03c0(3 cm)^2)\n= 3\u03c0 cm^2\n= 9\u03c0 cm^2\n= 9.5\u03c0 cm^2",
        "gt_answers": "0 . 0 8 = \\frac { 8 } { 1 0 0 } = 8 \\%\n",
        "image_path": "./data/HME100K/test_images/test_2578.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is shown in LaTeX format as follows:$$\\begin{aligned}x^2+3x+1=0\\end{aligned}$$In this equation, the variable x is raised to the power of 2, plus 3, and 1, and is equal to 0.",
        "gt_answers": "\\frac { 1 7 } { 3 } y = \\frac { 1 7 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2579.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is not clear, as the image does not contain any mathematical expression.",
        "gt_answers": "0 . 5 m o l\n",
        "image_path": "./data/HME100K/test_images/test_2580.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length 5 and width 3 is:\n\nA = l x w\n= 5 x 3\n= 15 square units\n\nThe area of the rectangle is 15 square units.",
        "gt_answers": "\\frac { A B } { B D } = 0 . 5\n",
        "image_path": "./data/HME100K/test_images/test_2581.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a triangle is:\n\nA = (1/2)bh,\n\nwhere b is the base of the triangle, h is the height of the triangle, and A is the area of the triangle.",
        "gt_answers": "x = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2582.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\nThis is a mathematical expression written in LaTeX format.\n\nThe expression represents a rational number as the sum of two integers.\n\nTo evaluate the expression, we can substitute the values of the variables:\n\nn = 5\np = 7\n\nThen, we can simplify the expression using the rules of algebra:\n\n4(p + 3n) - 5(2n + 3) = 4p + 14n - 15n + 6 = 4p + 14n - 15n = 4p -",
        "gt_answers": "\\frac { 3 } { 1 + 1 } - \\frac { x } { x - 1 } + 1 = 0\n",
        "image_path": "./data/HME100K/test_images/test_2583.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we first need to determine the formula. The formula is given by:\n\n![Image](https://i.imgur.com/e0qzv3r.png)\n\nThe formula is the sum of the first n terms of an arithmetic series, given by:\n\nS\\_n = (n + 1) / 2 \\* (2a + (n - 1)d)\n\nwhere a and d are the first and last terms of the series, respectively.\n\nIn this case, a =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$a = \\frac{x+y}{2}$$\n\nwhere x and y are the numerical values of the variables in the formula.",
        "gt_answers": "1 2 x = 1 2 \\times 5 = 6 0\n",
        "image_path": "./data/HME100K/test_images/test_2586.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by: 6 \\* 5 + 6 \\* 2 + 0 \\* 0 = 60.",
        "gt_answers": "6 . 6 . 7 . \\sqrt { 3 } 8 \\sqrt { 2 } - 1 9 1 0 1 0 7\n",
        "image_path": "./data/HME100K/test_images/test_2588.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the expression for the sum of the first n positive integers. The formula is written as:1+2+3+4+...+n=n(n+1)2where n is a positive integer.",
        "gt_answers": "x = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2589.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula using LaTeX format is:\n\n$$\\begin{aligned}\n&\\text{Given Formula: } \\frac{1}{2}\\left( \\frac{1}{4} + \\frac{1}{5} \\right) \\\n&\\Rightarrow \\frac{1}{2}\\left( \\frac{1}{4} + \\frac{1}{5} \\right) = \\frac{1}{8} + \\frac{1}{10} \\\n&\\Rightarrow \\frac{1}{2}\\left( \\frac{1}{4} + \\frac{1",
        "gt_answers": "P _ { a } : P _ { b } = 4 : 1\n",
        "image_path": "./data/HME100K/test_images/test_2590.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$\\sum\\_{i=1}^{n}x\\_i$where $x\\_1, x\\_2,..., x\\_n$are the variables in the formula.\n\nNote: This is a LaTeX formula. To see it in plain text, you may need to enable LaTeX rendering in your browser or use a LaTeX editor.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n![](https://www.quickchart.io/chart?bkg=white&c=%7B%0Atype%3A%20%27image%27%2C%20name%3A%20%27%E3%80%81%E3%81%99%20%E3%81%8B%20%E3%81%8D%27%2C%20width%3A%205",
        "gt_answers": "\\angle 2 + \\angle B C F = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2592.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "1 2 x + m - 1 1 \\leq 3\n",
        "image_path": "./data/HME100K/test_images/test_2593.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not clear, as it appears to be a mathematical equation written in a different language. To write it out in LaTeX format, you would need to know the specific mathematical symbols used in the equation. If you can provide the image, I can try to write out the formula for you.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the image is A = (1/2) \\* (4/5) \\* (1/3) \\* (1/4) \\* (5/6) \\* (1/2) = 1/12.\n\nThe formula for the area of a rectangle is A = l \\* w, where l is the length and w is the width. The area of a rectangle with length 4 and width 5 is 4 \\* 5 = 20.\n\nTherefore, the area of the image is 1/12",
        "gt_answers": "3 . 6 : x = 4 8 \\% : \\frac { 3 } { 2 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2595.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a quadratic formula for the solution to the differential equation dy/dx = x^2. The equation can be written as:dy/dx = x^2dx/dx = 0dx/dx = 0dx/dx = 0dy/dx = x^2dx/dx = 0dx/dx = 0dx/dx = 0dy/dx = x^2dx/dx = 0dx/dx = 0dy/dx = x^2dx/dx = 0dy/dx = x^2dx/dx = 0dy/",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is: \\frac{x - 3y + 5z}{x - 2y + 5z}.",
        "gt_answers": "( 3 ^ { \\frac { 1 } { 3 } } \\times 5 ^ { \\frac { 1 } { 3 } } ) ^ { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_2597.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\n\u222b[\u222by(x)dx]y(x)dx=\u222b[\u222by(x)dx]y(x)dx\\int \\left[\\int y(x)dx\\right] y(x)dx = \\int \\left[\\int y(x)dx\\right] y(x)dx\u222b[\u222by\u200b(x)dx]y\u200b(x)dx\u200b=\u222b[\u222by\u200b(x)dx]y\u200b(x)dx\u200bUsing the property of the integral, the left-hand side can be",
        "gt_answers": "2 x - 3 y = 6 2 x - . 3 y\n",
        "image_path": "./data/HME100K/test_images/test_2598.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n& 2x + 3y - 4xy \\\n\\end{align\\*}\nThis formula represents the sum of the products of two variables, x and y, and the sum of those products multiplied by another variable, x.",
        "gt_answers": "5 S _ { 1 } + 3 S _ { 2 } = 2 S _ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2600.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the given expression:\n\n$$\\frac{1+x^2+3x+5}{1+x+3}$$\nThis expression is a ratio of two polynomials, where the numerator is a polynomial of degree 4 and the denominator is a polynomial of degree 2. The image shows the coefficients of the polynomials in the numerator and denominator. The constant term of the numerator is 1, the constant term of the denominator is 1, and the variable terms are x^2, x, 3x, and 5 in the numerator",
        "gt_answers": "< ^ { 2 } - \\frac { 1 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_2601.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is given below:\n\n\\begin{center}\n$ 2x^2 - 4x + 1 = 0 $\\\n\\end{center}\n\nThis is the equation of a parabolic function with vertex at the origin and zeros at $\\frac{1}{2}$ and $\\frac{1}{2}$.",
        "gt_answers": "y _ { 2 } = \\frac { 2 } { k } + 4\n",
        "image_path": "./data/HME100K/test_images/test_2602.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the equation in the image is: 4x + 8y = 14. This equation represents a line that passes through the point (3, 4) and has a slope of 2.",
        "gt_answers": "\\frac { 4 } { x ^ { 2 } - 4 } = \\frac { x + 1 } { x + 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2603.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is $A = \\pi r^2$, where $r$ is the radius of the circle.",
        "gt_answers": "a = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2604.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a triangle with sides of length 4, 5, and 6 is:\n\nA = 0.5 \\* (4 + 5 + 6) \\* 0.5 \\* (4 + 5 + 6)\nA = 15 \\* 15\nA = 225\n\nTherefore, the area of the triangle is 225.",
        "gt_answers": "\\frac { 1 } { 3 } y - y = - \\frac { 1 } { 3 } - 2\n",
        "image_path": "./data/HME100K/test_images/test_2605.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image in LaTeX format is:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=1]\n\\draw[line width=1pt, fill=white] (0,0) rectangle (1,1);\n\\node[right] at (1,0.5) {$\\frac{1}{2}$};\n\\node[above] at (0.5,1) {$\\frac{1}{2}$};\n\\draw[line width=1pt, fill=black] (0.5,0) rectangle (1,0.5);",
        "gt_answers": "( 3 a + 1 ) ( 6 a - 1 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_2606.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be expressed as:x^2 + x + 1 = 0This is a quadratic equation in one variable, with a leading coefficient of 1 and a constant term of 1. The solutions to this equation are x = - 1 and x = 1.",
        "gt_answers": "x _ { 1 } = 0 , x _ { 2 } = \\frac { - 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2607.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n\\begin{center} 4x + 2 = 12 \\end{center}\n\nThis is a linear equation with one variable, x. The solution to the equation is x = 4, which can be verified by substituting x = 4 into the equation and verifying that it is true.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{x^2 + 2x - 3}{x + 1}$.\n\nIn LaTeX format, the formula can be written as: $\\frac{x^2 + 2x - 3}{x + 1}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b(\u222b(f(x)dx)g(x)dx)dx=\u222b\u222bf(x)g(x)dxdx",
        "gt_answers": "2 = \\frac { 1 } { 2 } \\times 2 \\times Q H\n",
        "image_path": "./data/HME100K/test_images/test_2612.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a fraction line with the numerator being the sum of two terms, 4 and 6, and the denominator being 12.\n\nThe fraction can be written as:\n\n4/12 + 6/12 = 10/12\n\nor simplified to:\n\n5/12\n\nSo the answer to the question is 5/12.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \\frac{e^3 - 2}{e - 1}.\n\nHere is the LaTeX format for the expression:\n\n\\frac{e^3 - 2}{e - 1}",
        "gt_answers": "A C = 2 ( \\sqrt { 3 } + 1 ) m\n",
        "image_path": "./data/HME100K/test_images/test_2615.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$m\\_x + m\\_y = \\frac{m\\_xm\\_y}{m\\_x + m\\_y}$$\nwhere $m\\_x$ and $m\\_y$ are the mass of the two blocks.",
        "gt_answers": "m _ { 1 } = 1 0 m _ { 2 } = 1 1\n",
        "image_path": "./data/HME100K/test_images/test_2616.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can follow these steps:\n\n1. Determine the variables and constants in the formula.\n2. Write out the formula using the appropriate LaTeX commands for each operation.\n3. Simplify the expression by factoring out common factors and canceling out extraneous terms.\n\nUsing these steps, we can write out the formula as follows:\n\nThe formula for d^2/dx^2 is given by the equation. We can simplify this expression by factoring out x^2, which is a common factor:",
        "gt_answers": "\u3001 D \u3001 B ^ { \\prime } C = 5 c m\n",
        "image_path": "./data/HME100K/test_images/test_2617.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![](https://www.quickmath.com/jc/images/formula-1.png)\n\nWhere:\n\n* A is the number of apples in the basket\n* B is the number of bananas in the basket\n* C is the number of oranges in the basket\n* D is the number of grapes in the basket\n* E is the number of pears in the basket\n* F is the number of peaches in the basket\n* G is the number of plums in the basket\n* H",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b0^\u221e \u222b\u2212\u221e^x 1x\u22121dx + \u222b0^\u221e \u222b\u2212\u221e^x (1\u2212x)dx = \u222b0^\u221e \u222b\u2212\u221e^x (x\u22121)dx + C, where C is a constant of integration.\n\nThe image shows the graph of the function f(x) = x^2. The integral on the left represents the area under the curve from x = 0 to x = \u221e, and the integral on the right represents the area from x =",
        "gt_answers": "\\frac { 2 1 } { x } = \\frac { 2 . 5 } { 1 } = 2 . 5\n",
        "image_path": "./data/HME100K/test_images/test_2621.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is not specified, so it cannot be written in LaTeX format. The image appears to be a representation of a geometric shape, but without additional information, it is not possible to determine the formula for the shape or the equation that defines it.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a geometric shape, with lines and curves forming the contours of the shape. The shape is not labeled or identified, so it is not possible to determine its formula without additional information. However, the shape could be represented using LaTeX code as follows:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=0.5]\n\\draw[line width=1pt] (0,0) -- (1,1) -- (1,0) -- cycle;\n\\draw[line width=1pt] (0,0) -- (0,1) -- (1,",
        "gt_answers": "1 . ( x + y ) ^ { 2 } + 6 ( x + y ) + 9\n",
        "image_path": "./data/HME100K/test_images/test_2623.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{a}{b} = \\frac{b^2 - 4ac}{2b} $$\n\nwhere $a$, $b$, and $c$ are the sides of the triangle.",
        "gt_answers": "x = \\frac { 2 9 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2624.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the line of best fit in the given image is:\n\ny = 4x + 11\n\nThe equation of the line of best fit is derived from the equation of a line that passes through two or more points on the scatter plot. In this case, the line passes through the points (3, 10) and (5, 21). The slope of the line is calculated as the rise over run, which is 4 units for each unit of run. The y-intercept is 11. Therefore, the equation of the line of best fit is y =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 1 + 3x^2 + 5x - 12 = 0.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{aligned}\n  & (x + y) \\times (a - b) = xy + ax - by \\\n  \n& (x + y) \\div (a - b) = \\frac{xy + ax - by}{a - b} \\\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 1 + 1 = 2.\n\nIn LaTeX format, this can be written as:\n\n\\begin{equation}\n1 + 1 = 2\n\\end{equation}",
        "gt_answers": "S x _ { 1 } = \\sqrt { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_2628.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n$$ \\frac{4(x^2 + y^2)}{(x^2 - y^2)} $$\n\nThis formula represents the equation of a circle in polar coordinates with center at the origin and radius 2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: x = (y - 3) / 2.\n\nIn LaTeX format, this formula can be written as:\nx = \\frac{(y - 3)}{2}",
        "gt_answers": "8 + 3 = - \\frac { 1 } { 2 } - a\n",
        "image_path": "./data/HME100K/test_images/test_2630.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a mathematical expression in LaTeX format:\n\n$$\\begin{aligned} \\text{x} &= \\frac{a}{b} \\cdot \\frac{c}{d} \\cdot \\frac{e}{f} \\cdot \\frac{g}{h} \\cdot \\frac{i}{j} \\cdot \\frac{k}{l} \\cdot \\frac{m}{n} \\cdot \\frac{o}{p} \\cdot \\frac{q}{r} \\cdot \\frac{s}{t} \\cdot \\frac{u}{v} \\cdot \\frac{w}{x",
        "gt_answers": "x ^ { 2 } - x y + 4 = 0\n",
        "image_path": "./data/HME100K/test_images/test_2631.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: sin(cos(x)) = 0.\n\nNote: This expression assumes that the cosine of x is less than 1.",
        "gt_answers": "\\cos ( \\frac { \\pi } { 2 } + x ) = - \\sin x\n",
        "image_path": "./data/HME100K/test_images/test_2633.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n\\begin{align\\*}\n\\frac{1}{2}\\cdot\\frac{1}{2}\\cdot\\frac{1}{2} + 1 = \\frac{1}{2}\\cdot\\frac{1}{2}\\cdot\\frac{1}{2} + 1 = \\frac{1}{2}\\cdot\\frac{1}{2}\\cdot\\frac{1}{2} + 1 = \\frac{1}{2}\\cdot\\frac{1}{2}\\cdot\\frac{1}{2} + 1 = \\frac{",
        "gt_answers": "x = - 3\n",
        "image_path": "./data/HME100K/test_images/test_2634.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: (b + c)d = (b + c)d(b + c)d, which can be expressed mathematically as follows: (a + b)c = ac(a + b)c(a + b)c.",
        "gt_answers": "\\frac { . O B } { O E } = \\frac { O D } { O C }\n",
        "image_path": "./data/HME100K/test_images/test_2635.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a diameter of 2cm is given by:\n\nA = \u03c0r^2A = \\pi r^2A=\u03c0r2\u200bwhere r is the radius of the circle.\n\nGiven the diameter of 2cm, the radius of the circle is:\n\nr = diameter2cm = 2 cm = 0.02 mr = \\frac{diameter}{2} = 2 \\ cm = 0.02 mr = diameter22\u200bcm0.02\u200bmTherefore, the area of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression for the formula in LaTeX format:$$\\begin{aligned} 5 & = & \\frac{2}{3}+\\frac{2}{3}+\\frac{2}{3} \\\n\n\\end{aligned}$$This formula represents the average of three numbers: 2, 2, and 2. The sum of these three numbers is 6, which is the numerator of the fraction in the formula. The denominator of the fraction is 3, which is the number of terms in the sum.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the formula in the image:\n\n\\begin{align\\*}\nx &= \\frac{b}{2a} \\\\\ny &= \\sqrt{\\frac{a^2 - b^2}{a^2 + b^2}}\n\\end{align\\*}\n\nIn this formula, `a` and `b` are constants. The variable `x` is defined as the ratio of `b` to `2a`, and the variable `y` is defined as the square root of the expression $\\frac{a^2 - b^2}{a^2 +",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is A = (b/2) \\* h, where b is the base of the triangle and h is the height. To find the area of the triangle in the image, we can use the formula and substitute the values given in the image for b and h.\n\nFirst, we know that the base of the triangle is 2.2 cm. Next, we know that the height of the triangle is 3.7 cm. Using the formula, we can calculate the area of the triangle as follows:\n\nA = (2.2/2) \\*",
        "gt_answers": "C _ { 2 } = y = - x ^ { 2 } + 2 x + 3\n",
        "image_path": "./data/HME100K/test_images/test_2639.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\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} \\\n\\end{aligned}\n\\end{center}\n\nThe expression is simply the sum of the letters A through L.",
        "gt_answers": "- x ^ { 2 } + 6 x + x ^ { 2 } - x - 4 = k\n",
        "image_path": "./data/HME100K/test_images/test_2640.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nEM = \u2211[1/(i-1)]\u2211[j/(m-j)]\u2211[k/(m-k)]\u2211[1/(n-k)]\u2211[1/(n-i)]\u2211[1/(m-n)]\u2211[1/(n-m)]\u2211[1/(j-k)]\u2211[1/(j-i)]\u2211[1/(m-j)]\u2211[1/(m-n)]\u2211[1/(n-m)]\u2211[1/(n-i)]\u2211[1/(j-",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{V}=\\frac{1}{2}m(u+v)^2$$\n\nwhere V is the variance, m is the mass, u and v are the upper and lower limits of the distribution, respectively.",
        "gt_answers": "x _ { 1 } = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2642.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is written as follows in LaTeX format:\n\n\\begin{align\\*}\nc\\_s = \\frac{g\\_s}{h\\_s}\n\\end{align\\*}",
        "gt_answers": "C u O + H _ { 2 } S O _ { 4 } = C u S O _ { 4 } + H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_2643.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Can you please provide it again?",
        "gt_answers": "4 x ^ { 2 } + ( 4 n - 4 ) x + n ^ { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_2644.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ (1000\\times 0.25) + (200\\times 0.25) + (150\\times 0.25) + (100\\times 0.25) = \\ 300 + 50 + 75 + 100 = \\ 225 $$\n\nThis formula calculates the total cost of 1000 computers, each with a cost of $200, along with 200 computers with a cost",
        "gt_answers": "1 2 c m = 1 2 0 0 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_2645.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is not provided, so I cannot write the expression for the formula. Please provide the image so I can assist you.\n\nThe LaTeX code for the expression is:\n\n$$ f = \\frac{1}{2} \\cdot \\frac{5 + 7}{2} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: 4x^2 + 12x + 6.",
        "gt_answers": "\\frac { 1 } { C _ { 1 0 } ^ { 2 } } = \\frac { 1 } { 4 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2647.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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: $y = 2x + 3$.",
        "gt_answers": "S _ { n - 1 } = \\frac { 3 n - n ^ { 2 } - 2 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2648.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can follow these steps:\n\n1. Select the text in the image that represents the formula. In this case, it is the number 3 in the middle of the image.\n2. Use the LaTeX command '\\frac'to write the fraction. So, we have $\\frac{3}{5}$.\n3. Use the LaTeX command '\\sum' to write the sum. So, we have $\\sum\\_{i=1}^5 3$.\n4. Use the LaTeX command '\\prod' to write the product. So, we",
        "gt_answers": "z = - \\frac { 1 7 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2649.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a schematic diagram representing a digital electronic circuit. The circuit has two inputs (A and B) and an output (Q). The circuit also has a voltage source V1, a current source I1, and a resistor R1. The circuit is designed to perform a logical operation on the inputs A and B.",
        "gt_answers": ": 3 \\times 3 \\times 6 = 5 4 c m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2650.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{a^2+b^2}{2ab}=\\frac{1}{2}\\sqrt{a^2+b^2}$$",
        "gt_answers": "\\frac { x } { 1 5 } = \\frac { 1 . 5 } { 0 . 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2651.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\ud83d\udcca The formula for the derivative of a function f(x) = x^2 is given by \ud835\udc53'(x) = 2x.\ud835\udc53(x)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following code:\n\n\\begin{center}\n\\begin{equation}\n\\text{Number of heads in 6 tosses} = 3 + 3 + 3 + 3 + 3 + 3 = 18\n\\end{equation}\n\\end{center}\n\nHere, we have used the LaTeX equation environment to write out the formula. We have also used the $\\text{number of heads in 6 tosses}$ variable to represent the number of heads obtained in 6 toss",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n\\begin{center}\n\\begin{minipage}{0.4\\textwidth}\n\\begin{align*}\n& 10 + 5i - 3j + 2k & = & 10 + 5i - 3j + 2k \\\n\\end{align*}\n\\end{minipage}\n\\end{center}\n\nThis formula can be read as \"the sum of 10 and 5i, minus 3j and 2k is equal to the sum of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\ny = (x^2)\\*2x - (2x^3) - x^2\\*3\n\nThis is a quadratic equation with the variable x. The leading coefficient is 2x^2, and there are two other terms involving x, x^3 and x^2\\*3. The constant term is - (2x^3) - x^2\\*3.",
        "gt_answers": "y = 2\n",
        "image_path": "./data/HME100K/test_images/test_2655.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is $\\frac{3x^2 - 9x + 7}{2x - 3}$.",
        "gt_answers": "9 7 \\div 3 0 = 3 \\cdots 7\n",
        "image_path": "./data/HME100K/test_images/test_2656.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$x + 3 = 5$$This is a linear equation with one variable, x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I don't have access to the image you provided. Please provide the LaTeX code or formula for the image so I can help you.",
        "gt_answers": "a ^ { 2 } + b ^ { 2 } - a b = 4 0\n",
        "image_path": "./data/HME100K/test_images/test_2658.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: (x + 3) / (x - 2) = 2.\n\nTo derive this formula, we can use the following steps:\n\n1. Multiply both sides of the equation by x - 2 to get x + 3 = 2(x - 2).\n2. Simplify the left side of the equation by factoring out x - 2: x + 3 = 2.\n3. Divide both sides of the equation by x - 2 to get 3 = 2 / x - 2.",
        "gt_answers": "\\sqrt { 3 x + 1 } = 1 + \\sqrt { 5 x - 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2659.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\sum\\_{i=1}^n i^2 + 3n^2 = 5n^3 + 1$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX formula for the expression: $\\frac{5x^2+7x-3}{2x+1}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is 4/2.",
        "gt_answers": "L _ { 7 } = \\frac { 6 V } { 6 0 \\Omega } = 0\n",
        "image_path": "./data/HME100K/test_images/test_2662.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2x\u00b2 + 4x - 8 = 0.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is 3(x + 5) - 12.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the sum of two terms, each of which is the square of a number. The first term is 64, which is the square of 8, and the second term is 128, which is the square of 16.\n\nThe sum of 64 and 128 is 192.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula in the image using LaTeX format, we can use the following code:\n\n\\begin{center}\n$d=r\\_{1}-r\\_{2}$\n\\end{center}\n\nwhere $d$ is the distance between the two points $r\\_1$ and $r\\_2$, and $r\\_1$ and $r\\_2$ are the coordinates of the two points in 3D space.",
        "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": "MiniGPT4"
    },
    {
        "question": "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: x = (3 \\* y) / (4 - y).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$x^2 + 2x - 5 = 0$\n\\end{center}\n\nThis equation represents a quadratic equation with a constant term of 5 and a leading coefficient of 2. The solutions to this equation can be found by completing the square or by using the quadratic formula.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$ 1234\\frac{890}{765} = \\frac{1234\\times 890}{765} = \\frac{1234\\times 890}{765} = \\frac{963890}{765} = \\frac{963890}{765} = \\frac{1234\\times 890}{765} = \\frac{1234\\times",
        "gt_answers": "\\frac { 8 0 } { 1 1 } = 7 \\frac { 2 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_2671.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image provided. Can you please send it to me?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x^2 - 2x + 1}{x + 3}$.",
        "gt_answers": "- 2 . 5 + a = - 1 5 + 7\n",
        "image_path": "./data/HME100K/test_images/test_2673.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:\n\n$$\\frac{m \\cdot g}{r^2}$$",
        "gt_answers": "f ( x ) - m \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_2674.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$ \\frac{1}{2}(2x + 3) - \\frac{1}{3}(x + 1) = \\frac{1}{2}(4x + 2) - \\frac{1}{3}(2x + 1)$$\n\nThis formula represents the difference between two expressions involving x. The first expression is $\\frac{1}{2}(2x + 3)$, which can be simplified using algebra to $\\frac{1}{2}(2x + 3) = \\frac{1}{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \\frac{x}{x^2 + 6x - 8}\n\nThe expression is in the form of a fraction, where the numerator is x and the denominator is x^2 + 6x - 8. The variable x is raised to the power of 2 in the denominator and to the power of 1 in the numerator. The constant value 6x appears in both the numerator and denominator. The constant value - 8 appears only in the denominator.\n\nThe function is a rational function,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression for the formula in the image:\n\n$$\\text{tan}\\left(\\frac{\\theta}{2}\\right) = \\frac{\\sin\\left(\\theta\\right)}{\\cos\\left(\\theta\\right)}$$\n\nThis formula calculates the tangent of half the angle $\\theta$. The sine and cosine functions are used to calculate the ratios of the sine and cosine of the angle to the cosine of half the angle.\n\nI hope this helps! Let me know if you have any further questions.",
        "gt_answers": "\\tan ( \\frac { \\pi } { 4 } - x ) = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2677.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the image:\n\n$$\\frac{300\\sqrt{300}+300\\sqrt{200}}{50\\sqrt{50}}=\\frac{300\\sqrt{300}+300\\sqrt{200}}{50}$$\n\nAlternatively, you can use the following LaTeX code to write the expression:\n\n$$\\frac{300\\sqrt{300}+300\\sqrt{200}}{50\\sqrt{50}}=\\frac{300\\",
        "gt_answers": "\\frac { 1 } { 2 } 6 0 = 3 0\n",
        "image_path": "./data/HME100K/test_images/test_2678.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{B} = \\frac{\\text{d}\\text{V}}{\\text{dt}} $$\n\nWhere:\n\n* B is the rate of change of the volume of the object (in liters per second)\n* dV is the change in the volume of the object (in liters)\n* dt is the change in time (in seconds)\n\nThe formula represents the rate of change of the volume of the object with respect to time.",
        "gt_answers": "1 2 0 = 2 . 5 k + b\n",
        "image_path": "./data/HME100K/test_images/test_2679.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is given below:\n\n$$\\text{SIN}\\_{t}\\left(\\frac{\\text{r}}{\\text{t}}\\right)=\\frac{\\text{r}}{\\text{t}}\\sin\\left(\\frac{\\text{r}}{\\text{t}}\\right)$$\nThis formula relates the sine of the ratio of the radius of the circle to its circumference at any time $t$ to the ratio itself. The sine of a ratio is the same as the cosine of its complement, which is $\\frac{\\pi}{2}-\\text{AR",
        "gt_answers": "y _ { 4 } = - \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2681.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a simple expression for finding the area of a rectangle. It is given by the product of its length and width, or Length x Width.",
        "gt_answers": "\\frac { 0 . 5 } { 1 . 5 } = \\frac { 1 . 5 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_2682.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\frac{4x^2+8x+2}{x^3-6x^2+11x-5}\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a number line with the numbers 4, 5, 6, 7, 8, 9, and 10 on it. The number 6 is highlighted in red.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given below:\n\n&#x2202;&#x2202;2x&#x2202;&#x2202;x&#x2202;&#x2202;2y&#x2202;&#x2202;2y&#x2202;&#x2202;x&#x2202;&#x2202;x&#x2202;&#x2202;2z&#x220",
        "gt_answers": "\\frac { C B } { B F } = \\frac { D B } { P C }\n",
        "image_path": "./data/HME100K/test_images/test_2685.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n<img>Image Content</img>\n\nThe expression is the sum of 6, 8, and 9, which is 23.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 2y + 2x - 4 = 0 $$\n\nwhere x and y are variables.",
        "gt_answers": "y _ { 2 } = - 2\n",
        "image_path": "./data/HME100K/test_images/test_2688.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression that is not in LaTeX format. However, assuming that it is a formula for a line in 2D space, the expression can be written as follows:y = mx + bwhere m is the slope of the line, x is the horizontal coordinate, and b is the y-intercept of the line. The formula can be rearranged into slope-intercept form as y = mx + b. The image also shows the equation of the line in slope-intercept form, which is y = 1x + 50.",
        "gt_answers": "( a + 5 ) ( a - 1 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_2689.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as follows:\n\n$$\\text{200}\\times\\frac{10}{250}+\\frac{300}{450}=\\frac{200}{3}$$\n\nThe image shows a diagram with three overlapping circles, where each circle has a radius of 250 and 450 units. The center of the circles are located at coordinates (0,0), (100,0), and (200,0), respectively. The lines intersecting the circles represent the overlaps between them.",
        "gt_answers": "2 0 0 + 3 0 0 = 5 0 0\n",
        "image_path": "./data/HME100K/test_images/test_2690.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Can you please provide the image so I can assist you with the LaTeX format?",
        "gt_answers": "k ( \\frac { 1 } { 2 } x , x + 2 )\n",
        "image_path": "./data/HME100K/test_images/test_2691.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot provide an answer without the image you requested. Please provide the image so I can assist you.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\nh(a) = 3(a - 1)\n\nh(b) = 4(b - 2)\n\nh(c) = 5(c - 3)\n\nThe function h(a) is defined as 3(a - 1), which means that it returns the result of 3 when the input is a - 1, and it returns the result of 0 when the input is any other number. Similarly, the function h(b) is defined as 4(b - 2),",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is not clear. It appears to be a mathematical equation, but it is difficult to read without the image.\n\nHowever, assuming that the equation is correct, we can write it in LaTeX format as:\n\n$$ \\frac{\\partial E}{\\partial t} = \\frac{1}{2}\\frac{\\partial}{\\partial t}(\\rho v^2) + \\rho \\nabla \\cdot \\mathbf{v} + \\frac{p}{\\rho} $$\n\nwhere $\\rho$ is the density of the fluid, $v$ is the velocity vector, $\\mathbf{v",
        "gt_answers": "A E = 2 \\sqrt { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2697.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:$$$$$$\\frac{\\frac{3}{4}}{\\frac{7}{4}} = \\frac{3}{7}$$$$$$$$\\frac{\\frac{3}{4}}{\\frac{7}{4}} = \\frac{3}{7}$$This can be written as:$$$$$$\\frac{3}{4}:\\frac{7}{4}=3:7$$$$$$\\frac{3}{4}:\\frac{7}{4}=3:7$$This means that the ratio of the width to the height of the image is 3:4 or",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\documentclass{article}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{align}\n\\frac{d^2x}{dt^2} + 2\\omega\\_n^2 x = \\omega\\_n^2 x\n\\end{align}\n\n\\end{document}\n```",
        "gt_answers": "\\frac { 2 5 } { 2 } n + n = \\frac { 1 } { 2 } - ( - 5 )\n",
        "image_path": "./data/HME100K/test_images/test_2699.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$x = 2 - \\frac{5}{x}$$This formula is an example of an iterative formula, as it involves the variable x on both the left and right side of the equation. The left side of the equation represents the number 2, while the right side represents the expression $\\frac{5}{x}$. When the equation is solved for x, the variable x is replaced with the value 4.5, which is the result of substituting the value 2 for x and 5 for $\\frac{5}{x}$.",
        "gt_answers": "( a + b ) = 2 5\n",
        "image_path": "./data/HME100K/test_images/test_2700.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n<LaTeX code>$\\frac{a^2+b^2}{2ab}=\\frac{1}{2}\\left(\\frac{a}{b}\\right)^2+\\frac{1}{2}\\left(\\frac{b}{a}\\right)^2\\right)$</LaTeX code>\n\nThis is a formula for the dot product of two vectors, a and b. The formula is calculated by dividing the sum of the squares of the magnitudes of the vectors by the product of their angles. The result is the dot product of the vectors.",
        "gt_answers": "2 ( x + y ) = 3 - 3 k\n",
        "image_path": "./data/HME100K/test_images/test_2701.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:$$\\frac{a\\*sin(x)+b\\*cos(x)}{c\\*t+d}$$where$$a$$is the slope of the line segment,$$b$$is the y-intercept of the line segment,$$c$$is the time interval over which the acceleration is measured, and$$d$$is the initial velocity of the object.\n\nThe formula calculates the average velocity of an object over a given time interval. The slope of the line segment represents the change in velocity over time, while the y-",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{1}{2} x^2 + \\frac{3}{2} x - \\frac{1}{2}$$",
        "gt_answers": "\\cos ^ { 2 } \\alpha = \\frac { 3 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_2704.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by the formula:\n\n$$ I = \\frac{1}{2}\\left(\\frac{1}{2} + \\frac{1}{2}\\right) $$\n\nor,\n$$ I = \\frac{1}{4} $$\nThis formula represents the brightness or intensity of the image, which is defined as the luminance of the image multiplied by the contrast of the image. The contrast of the image is defined as the ratio of the luminance of the brightest part of the image to the luminance of the darkest part of the image",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression of the formula in the image using LaTeX format:\n\n\\begin{align\\*}\n\\text{Image Content}\n&= \\frac{1}{2} \\cdot \\frac{2}{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 \\",
        "gt_answers": "x _ { 1 } = - \\frac { 2 } { 3 } , x _ { 2 } = - 4\n",
        "image_path": "./data/HME100K/test_images/test_2706.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the formula for the expression in the image, we can use LaTeX format. The formula is given by:\n\n$$ \\frac{a^2 - b^2}{a - b} = \\frac{(2a - b)(2a - b)}{(2a - b)} = 4a - 2b $$\n\nTherefore, the formula is 4a - 2b.",
        "gt_answers": "\\frac { 1 } { 2 } x = 2\n",
        "image_path": "./data/HME100K/test_images/test_2707.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot write out the expression of the formula in the image as it does not provide any information about the formula or its variables. Can you please provide more information about the formula or its variables?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{center}\n\\frac{(a+b)^2-ab}{a^2+b^2}\n\\end{center}\n\nThis is the formula for the dot product of two vectors a and b.",
        "gt_answers": "\\frac { 7 } { 2 1 } = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2709.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$ a = \\frac{-b\\sqrt{1-\\frac{4ac^2}{b^2}}}{\\sqrt{1-\\frac{4ac^2}{b^2}}}$$\n\nThis formula is derived from the quadratic formula for a quadratic equation of the form ax^2 + bx + c = 0. The values of a, b, and c in the formula are determined by the given values in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $ a = \\frac { 2x - 3y + 4z } { x + y + z } $.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression in LaTeX format, use the following code:\n\n$$\\begin{aligned} 2\\times 10^6 + 0.2 &= 2.2 \\times 10^7 \\end{aligned}$$\nIn LaTeX format, the mathematical operators are represented by the following symbols:\n\n* Plus sign: $\\+$\n* Minus sign: $\\-$\n* Times sign: $\\times$\n* Division sign: $\\div$\n* Exponentiation sign: $\\^n$ or $\\x^n$\n* Square root sign: $\\sqrt$\n* Square",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is an equation in LaTeX format: $ \\frac{3}{4}x^{2}+5x-15 $\n\nExplanation:\n\n* The fraction $ \\frac{3}{4} $ is the numerator of the fraction.\n* The variable $x$ is the variable in the equation.\n* The superscript $2$ indicates that the variable $x$ is raised to the power of $2$.\n* The coefficient $5$ is added to the variable $x$.\n* The constant $5$ is subtracted from the equation.\n\nSo the equation is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\begin{aligned}\ny & = \\frac{3x^2}{2} + 2x - \\frac{5}{4} \\\\\nx & = \\frac{1}{2}(y + 5)\n\\end{aligned}$$",
        "gt_answers": "t = \\frac { \\Delta s } { V } = 0 . 5 s\n",
        "image_path": "./data/HME100K/test_images/test_2715.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of the triangle shown in the image is A = 1/2bh, where b is the base of the triangle and h is the height.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: lg(hghb)l.\n\nTo write it out in LaTeX format, you would use the following code:\n\nlg(hghb)l\n\nThe l is a lowercase letter L, and the g is a lowercase letter g. The hghb is the variable in the formula, which represents a hypothetical number. The l at the end of the formula indicates that the logarithm is taken to the base 10.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n$$\\begin{aligned}m = \\frac{1}{4\\sqrt{2}}\\end{aligned}$$\n\nThis formula is derived using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.\n\nUsing this theorem, we can find the length of the hypotenuse of the triangle in the image, which is given by:\n\n$$\\begin{aligned}c = \\sqrt{",
        "gt_answers": "\\frac { N } { N a } = n = \\frac { m } { M }\n",
        "image_path": "./data/HME100K/test_images/test_2718.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n\\begin{align\\*}\n\\frac{\\text{mass}}{\\text{volume}} = \\frac{\\text{density}}{\\text{mass}}\n\\end{align\\*}\n\nThis formula is derived from the ideal gas law, which states that the pressure of a gas is directly proportional to its volume and inversely proportional to its mass. The formula above shows that the density of a gas is equal to its mass per unit volume.",
        "gt_answers": "( x ^ { \\cdot } - \\frac { 1 } { 2 } ) ^ { 2 } + 2 - \\frac { 1 } { 4 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_2719.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given formula:\n\n$$\\begin{align\\*}\nf(x) = \\frac{1}{x+2}\n\\end{align\\*}$$\n\nNote that this formula is defined for all real numbers x, except x = -2, because the denominator would be zero at that value.",
        "gt_answers": "4 \\times ( x - 2 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_2720.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{480}{8} = 60$.",
        "gt_answers": "\\frac { 7 } { 1 6 } = \\frac { 2 1 } { 4 8 }\n",
        "image_path": "./data/HME100K/test_images/test_2723.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\nkd = kh \\* hd\n\nwhere kd is the constant of proportionality for the isochronous movement, kh is the constant of proportionality for the horizontal movement, and hd is the constant of proportionality for the vertical movement.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\nx + 3y &= 7 \\\n\\end{align\\*}\nThis is a linear equation in two variables, where x and y are the variables, and the constant value 7 represents the target output.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: v = v / 2. This is a basic formula for velocity in a circular path.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{center} $\\frac{1}{2}(x + y) + 2xy$ \\end{center}\n\nThis formula calculates the sum of the products of x and y and the sum of x and y.",
        "gt_answers": "x < \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2727.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n&#x2208;&#x2208;&#x2202;&#x2208;&#x2208;&#x2202;&#x2208;&#x2208;(x)=&#x2212;&#x2211;&#x2208;&#x2202;&#x2208;&#x2208;&#x2202;&#x220",
        "gt_answers": "A D = 2 \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2728.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $\\frac{1}{4} + \\frac{1}{6} + \\frac{1}{8} + \\frac{1}{10}$ which simplifies to $\\frac{1}{4} + \\frac{1}{5}$ using the distributive property.",
        "gt_answers": "\\angle B E F = 1 5 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2730.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following code:\n\n\\begin{equation}\nx + 2y = 6\n\\end{equation}\n\nThis equation represents the line passing through the point (2, 4) and intersecting the x-axis at x = 6.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image can be written as follows using LaTeX format:\n\n\\begin{align\\*}\nc &= \\frac{1}{4} \\\\\n&= \\frac{1}{4} + \\frac{1}{4} + \\frac{1}{4} + \\frac{1}{4} \\\\\n&= \\frac{1}{2} + \\frac{1}{2} + \\frac{1}{2} + \\frac{1}{2} \\\\\n&= 2\n\\end{align\\*}",
        "gt_answers": "C _ { n } S O _ { 4 } + M g ( O H ) _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2732.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is:\n\nA = \u03c0r^2A = \\frac{\\pi}{r^2}A=\u03c0r2\u200bwhere r is the radius of the circle. To find the area of the circle in the image, we need to first find the radius.\n\nWe can use the Pythagorean theorem to find the length of the radius. Let's call the length of the radius \"r\". The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle)",
        "gt_answers": "\\frac { 1 } { 2 } m + 3 = 1\n",
        "image_path": "./data/HME100K/test_images/test_2733.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as:\n\n$$ d = \\frac{t^2}{2} + 1 $$\n\nwhere $t$ is the time in seconds and $d$ is the distance in feet.",
        "gt_answers": "D E ^ { 2 } = D O \\cdot D B .\n",
        "image_path": "./data/HME100K/test_images/test_2734.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:\n\n$$\\text{ImageContent}$$\n\nHere, the image content can be represented using the mathematical notation.",
        "gt_answers": "V ^ { \\prime } _ { 2 } = V - V _ { 1 } ^ { \\prime } = V - V _ { 0 }\n",
        "image_path": "./data/HME100K/test_images/test_2735.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is \\frac{1886\\textsuperscript{5003} + 1871\\textsuperscript{5003} + 1865\\textsuperscript{5003} + 1858\\textsuperscript{5003} + 1848\\textsuperscript{5003} + 1839\\textsuperscript{5003} + 1825\\textsuperscript{5003} + 181",
        "gt_answers": "1 8 0 ^ { \\circ } - 1 6 5 ^ { \\circ } = 1 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2736.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by the equation\n\n$$x = \\frac{1}{3}(2y + 4z)$$\n\nThis equation can be used to determine the value of x when given the values of y and z.",
        "gt_answers": "\\vert A B \\vert = \\frac { \\sqrt { 3 2 - 6 m ^ { 2 } } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2737.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the image you provided:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick, blue] (0,0) -- (2,0) node[midway, below] {$ b $};\n\\draw[thick, red] (2,0) -- (4,0) node[midway, below] {$ a $};\n\\draw[thick, green] (4,0) -- (6,0) node[midway, below] {$ c $};\n\\draw[thick, orange] (6,0",
        "gt_answers": "A D ^ { 2 } + B D ^ { 2 } = A B ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2739.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$ \\frac{x\\sqrt{x}}{x+2}+\\frac{x\\sqrt{x}}{x+4}+\\frac{x\\sqrt{x}}{x+6}=\\frac{9x\\sqrt{x}}{3(x+2)(x+4)(x+6)}$$The image shows a formula written in the form of a fraction with the numerator being the product of two terms, each of which is the square root of x raised to a power less than one and the denominator being the sum of three terms, each of which is",
        "gt_answers": "x _ { 2 } = - \\frac { \\sqrt { m - 1 } } { m - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_2740.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is: A = (1/2)bh, where b is the base and h is the height. The area of a right triangle with sides of length 5 units and height 7 units is: A = (1/2) \\* 5 \\* 7 = 35.\n\nThe volume of the prism is: V = Bh, where b is the base and h is the height. The volume of the prism with base 8 units and height 5 units is: V = 8 \\* 5 = 40.",
        "gt_answers": "- x = - \\frac { 1 6 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2741.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{\\frac{\\text{Image Content}}{\\text{Image Content}}}{\\frac{\\text{Image Content}}{\\text{Image Content}}}=\\frac{\\text{Image Content}}{\\text{Image Content}}$$",
        "gt_answers": "\\angle B + \\angle A D B + \\angle B A D = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2742.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{x^3+3x^2+x+1}{x^2+2x+1} $$\n\nHere, the variable x is being raised to the third power and added to the numerator, while the denominator is the sum of x squared and two x's.",
        "gt_answers": "\\sqrt { \\frac { 2 } { 3 } } = \\frac { \\sqrt { 6 } } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2743.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a formula for the moment of inertia of a solid sphere with respect to its rotation axis.\n\nmoment of inertia of a solid sphere with respect to its rotation axis = (1/12) \\* (4/3) \\* pi \\* r^2\n\nwhere r is the radius of the sphere.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$E = h \\cdot f$\n\nwhere $E$ is the energy of the electron, $h$ is Planck's constant, and $f$ is the frequency of the photon.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n2x + 10y = 22\n\\end{center}\n\nThis is a linear equation in two variables, where the constant term is 22 and the slope of the line is 2x + 10y. The y-intercept is 10y.",
        "gt_answers": "2 x - 1 0 = 1 5 x + 3 - 3 3\n",
        "image_path": "./data/HME100K/test_images/test_2748.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "x ^ { 2 } + 4 x y + 4 y ^ { 2 } = 9\n",
        "image_path": "./data/HME100K/test_images/test_2749.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by the following LaTeX formula:\n\n$$\\begin{aligned} x &= \\frac{1}{2} \\cdot \\sqrt{2} + \\frac{1}{2} \\cdot \\sqrt{10} - \\frac{1}{2} \\cdot \\sqrt{6} + \\frac{1}{2} \\cdot \\sqrt{8} \\\n&= \\frac{1}{2} \\cdot \\sqrt{2} + \\frac{1}{2} \\cdot \\sqrt{10} - \\frac{1}{2} \\cdot \\",
        "gt_answers": "\\angle B O D = \\angle D O E = 2 8\n",
        "image_path": "./data/HME100K/test_images/test_2751.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} \\text{COS} &= \\text{sin} \\frac{\\theta}{2} \\cdot \\text{cos}\\frac{\\theta}{2} \\ &= \\text{sin}\\theta \\cdot \\text{cos}\\theta \\ \\ &= \\text{sin}\\frac{\\theta}{2} \\cdot \\text{cos}\\frac{\\theta}{2} \\ &= \\frac{1}{2}\\text{sin}2\\theta \\ &= \\frac{1}{2}\\cdot\\frac{1}{2",
        "gt_answers": "\\cos c = \\frac { \\sqrt { 5 } } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2752.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is: $\\frac{a}{b}$. In LaTeX format, this can be written as: $\\frac{a}{b}$.\n\nThis formula represents the ratio of the quantity of a substance to the quantity of another substance. The variables 'a' and 'b' represent the quantities of the substances being compared. This formula can be used to compare the ratios of different substances, such as in chemical reactions or in other scientific applications.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\ntan\u2061\ud835\udc65=\u2212\ud835\udc65+2\ud835\udc65\u22121\ud835\udc65+4\ud835\udc65\u22123\ud835\udc65+5\ud835\udc65\u22124\ud835\udc65+3\ud835\udc65\u22122\ud835\udc65+1\ud835\udc652\u2212\ud835\udc65+12\ud835\udc65\u22125\ud835\udc65+9\ud835\udc65\u22123\ud835\udc65+2\ud835\udc65\u22121\ufffd\ufffd\ufffd",
        "gt_answers": "\\tan \\angle A C D = \\frac { A D } { C D }\n",
        "image_path": "./data/HME100K/test_images/test_2754.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\nThe formula for the area of a rectangle is $A = lw$, where $l$ is the length and $w$ is the width.\n\nTo calculate the area of the rectangle in the image, we can use the formula:\n\nA = 3x2 - 4x + 5\n= 3x(2 - 4x + 5)\n= 3x(2 - 2x - 4x + 5)\n= 3x(-6x + 5)\n= 3x(-2x + 5)\n=",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\text{f(x) = \\frac{1}{2}x^2 + 3x - 4}$$",
        "gt_answers": "\\therefore 0 = - 3 k + 3 \\therefore k = 1\n",
        "image_path": "./data/HME100K/test_images/test_2758.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the parabola with equation \ud835\udc66 = 3\ud835\udc65^2 + 4\ud835\udc65 + 1 can be written as follows:\n\n\ud835\udc66 = 3\ud835\udc65^2 + 4\ud835\udc65 + 1\n\nThis equation can be graphed by plugging in different values of \ud835\udc65 into the equation and plotting the corresponding values of \ud835\udc66 on a graph. For example, if \ud835\udc65 = 0, then \ud835\udc66 = 3(0)^",
        "gt_answers": "x = \\frac { 4 } { 3 } \\cdot y = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2761.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n\\frac{x^4 - 6x^3 + 11x^2 - 8x + 3}{x^2 + 2x - 1}\n\\end{center}\n\nThis is a quadratic formula with a leading coefficient of 1 and a constant term of 3, and it has a single root at x= - 1.",
        "gt_answers": "x ^ { 2 } + k ( x + 1 ) = x ^ { 2 } + x\n",
        "image_path": "./data/HME100K/test_images/test_2763.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is given by:\n\n`f(x) = ((4x^3 - 6x^2 + 4x) / (2x^2 - 2x + 1))`",
        "gt_answers": "7 2 c = D ^ { \\prime } B\n",
        "image_path": "./data/HME100K/test_images/test_2764.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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{1296 \\* 256 + 16777216}{16777216} \\times 100$$\n\nThis formula computes the percentage of the image that is covered by the blue square. The numerator of the fraction is the sum of the products of each pixel in the image with the corresponding value in the blue square. The denominator is the total number of pixels in the image. The result is then multiplied by 100 to obtain the percentage.",
        "gt_answers": "2 0 k g \\times ( 1 m - 0 . 1 m / s t ) = 3 0 k g \\cdot 0 . 1 m / s . t\n",
        "image_path": "./data/HME100K/test_images/test_2765.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\begin{aligned}x &= \\frac{100}{400} \\times \\frac{400}{300} \\times 0.7 \\times 1.2\\end{aligned}$$\n\nwhere x is the number of red balls in the given image.",
        "gt_answers": "A B ^ { 2 } = A C \\cdot A E\n",
        "image_path": "./data/HME100K/test_images/test_2767.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a diagram with a letter C in the center, surrounded by various mathematical expressions and equations. The text in the image says `cab = 150. 60`, which means that the capital of Alabama is equal to 150.60.\n\nThe following LaTeX code can be used to render the diagram in the image:\n\n\\begin{center}\\begin{tikzpicture} \\draw[fill=white] (0,0) circle (2cm); \\node[anchor=center] at (0,0) {$ c\\_a $}; \\draw[->] (",
        "gt_answers": "\\angle A B D = 1 8 0 - \\angle A B C\n",
        "image_path": "./data/HME100K/test_images/test_2769.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle is given by:\n\nA = l x w\n\nwhere l is the length and w is the width.\n\nTo find the area of the rectangle in the given image, we can measure the length and width of the rectangle. Let's assume that the length is 4 cm and the width is 3 cm. Then,\n\nA = 4 x 3 = 12 cm^2\n\nTherefore, the area of the rectangle in the given image is 12 cm^2.",
        "gt_answers": "4 A l + 3 O _ { 2 } = 2 A l _ { 2 } O _ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2770.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $latex $\\frac{1}{x^2+3x+1}$$latex$ which can be written as: $\\frac{1}{(x+3)^2}$ in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the image:\n\n$$\\text{Given the image: } \\quad \\text{with the expression } $$\n$$x^2 + 2x + 1 = 0$$\n$$\\text{Solving for } x:$$\n$$x = -\\frac{1\\pm\\sqrt{2}}{2}$$\n$$\\text{Therefore, } \\quad \\text{and } $$\n$$x = -\\frac{1+\\sqrt{2}}{2}$$\n$$\\text{or } \\quad \\text{and } $$\n$$",
        "gt_answers": "x _ { 1 } = - \\frac { 4 } { 7 } \\sqrt { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_2773.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n\\frac{1}{\\sqrt{2}} + \\frac{1}{\\sqrt{3}} = \\frac{1}{\\sqrt{2}} + \\frac{1}{\\sqrt{3}}\n\\end{align\\*}\n\nwhich simplifies to:\n\n\\begin{align\\*}\n\\frac{2}{\\sqrt{2}} + \\frac{2}{\\sqrt{3}} = \\frac{2}{2} + \\frac{2}{3}\n\\end{align\\*}",
        "gt_answers": "( 2 - 7 + \\frac { 1 } { 2 } ) a\n",
        "image_path": "./data/HME100K/test_images/test_2775.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle with width 3 and height 4 can be written as:\n\nA = l \\* w = 3 \\* 4 = 12 square units\n\nThe area of a rectangle with width 5 and height 7 can be written as:\n\nA = l \\* w = 5 \\* 7 = 35 square units\n\nThe area of a rectangle with width 4 and height 6 can be written as:\n\nA = l \\* w = 4 \\* 6 = 24 square units\n\nThe area",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not written in LaTeX format, but it can be written as follows:\n\nLet x be the number of pizzas sold in a day and y be the number of slices served in each pizza. Let x + y be the total number of slices sold in a day. The function f(x) = 3x + 4y represents the total cost of selling x pizzas and y slices. The cost of each pizza is 3x slices and the cost of each slice is 4y. Therefore, the total cost is 3x +",
        "gt_answers": "0 < \\frac { b } { a } < 1\n",
        "image_path": "./data/HME100K/test_images/test_2777.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is $\\frac{m\\_3}{m\\_1 + m\\_2}$.",
        "gt_answers": "P A + \\frac { 3 } { 5 } P M\n",
        "image_path": "./data/HME100K/test_images/test_2778.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{Electric current in a wire is proportional to the amount of charge flowing through it per unit time, given by the formula:$$I = Q/t$$Where $I$ is the electric current, $Q$ is the charge, and $t$ is the time.}$$\n\nThe image shows the formula for electric current, with the variable on the left side of the equation and the constant on the right side. The formula states that the electric current in a wire is proportional to the amount of charge flowing through it per unit",
        "gt_answers": "\\angle B A E = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2779.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in LaTeX format, we can use the following steps:\n\n1. Choose the appropriate math mode. In this case, we can use the \"math mode\" in LaTeX.\n2. Write the formula using the appropriate symbols and operators.\n3. Use the \"LaTeX compiler\" to convert the LaTeX code into an image.\nHere is the LaTeX code for the given formula:\n\n\\begin{center}\n\\begin{equation}\nx^2 + 2x + 1 = 0\n\\end{equation}\n\\end{center}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\ns=kA+B(s\u2212A)s = \\frac{k}{A+B(s-A)}s=kA+B(s\u2212A)where:\ns: the number of people in the group\nA: the number of people in the group who do not get along with each other\nB: the number of people in the group who do not get along with each other\nk: a constant that represents the intensity of disagreement between the people in the group",
        "gt_answers": "S _ { n } < \\frac { 3 } { 1 9 }\n",
        "image_path": "./data/HME100K/test_images/test_2781.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a quadratic function can be written as: y = ax2 + bx + c, where a, b, and c are constants and x is the independent variable. This formula represents a parabolic curve in the x-y plane.\n\nThe graph of a quadratic function has a U-shape, with the vertex at the minimum or maximum point. The axis of symmetry is the vertical line passing through the vertex. The maximum or minimum value of the function is located at the vertex of the parabolic curve.\n\nTo solve a quadratic equation, we can use the quadratic formula: x = (-b",
        "gt_answers": "\\frac { 4 } { 3 } x - \\frac { 3 } { 4 } x = - 1\n",
        "image_path": "./data/HME100K/test_images/test_2782.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 1 + 2i + 3j + 4k = 6 $$\n\nwhere $i$, $j$, and $k$ are the imaginary units.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n<img src=\"https://www.mathworks.com/help/supportpkg/images/mupad1.jpg\" width=\"500\">x^2 + 4x + 4 = 0</img>\n\nwhere the variable x is raised to the second power, with a coefficient of 2, and then added to 4x and 4, resulting in the equation shown in the image.",
        "gt_answers": "\\therefore F O = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2785.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\filldraw[black] (0,0) circle (2);\n\\filldraw[black] (0,2) circle (2);\n\\filldraw[black] (2,0) circle (2);\n\\filldraw[black] (2,2) circle (2);\n\\draw[thick] (0,0) -- (0,2) -- (2,2) -- (2,0);\n\\filldraw",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n<LaTeX code>x^2 + (a - 3)x + 5 = 0</LaTeX code>",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image is:$$ \\frac{P\\_n}{P\\_n+Q\\_n} $$This formula is a ratio of two polynomials, $P\\_n$ and $Q\\_n$. The numerator $P\\_n$ is a polynomial of degree $n-1$ and the denominator $P\\_n+Q\\_n$ is a polynomial of degree $n$. The expression evaluates to the fraction of the sum of the roots of $P\\_n$ and $Q\\_n$ that are less than or equal to $-1$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the derivative of a function f(x) with respect to x is given by:$\\frac{d}{dx}f(x) = \\frac{df(x)}{dx}$The derivative of a function f(x) with respect to x is given by:$\\frac{df(x)}{dx} = \\frac{d}{dx}f(x)$The derivative of a function f(x) with respect to x is given by:$\\frac{d^2f(x)}{dx^2} = \\frac{d}{dx}\\left(\\frac{df(x)}{dx}\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{x^2}{4}+\\frac{x}{2}$.",
        "gt_answers": "5 x ^ { 2 } + y ^ { 2 } = 5\n",
        "image_path": "./data/HME100K/test_images/test_2790.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not provided, so I cannot write it out using LaTeX format. However, the formula can be written as follows:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "x = - 2 \\pm 2 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2791.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the sum of the first n natural numbers, denoted by the sum symbol $\\sum \\_{i=1}^n i$. The formula is written in LaTeX format as follows:\n\n\\begin{equation}\n\\sum\\_{i=1}^n i\n\\end{equation}\nIn this formula, the variable $i$ takes on the values $1, 2, \\ldots, n$, and the sum is taken over all those values. The result is the sum of the first $n$ natural numbers.",
        "gt_answers": "\\frac { S _ { 1 } } { S _ { 2 } } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2793.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} r &= \\frac{v^2}{2g} \\\\ &= \\frac{v^2}{2g} \\end{aligned}$$\n\nIn this formula, `v` is the velocity of the object at the bottom of the ramp, `g` is the acceleration due to gravity, which is approximately 9.81 meters per second squared. The formula shows that the radius of curvature of the path of the object is equal to the velocity squared divided by two times the acceleration due",
        "gt_answers": "P = \\frac { F } { S } = \\frac { 2 0 1 x } { 0 . 8 \\times 1 0 ^ { - 4 } m ^ { 2 } } = 2 . 5 \\times 1 0 ^ { 5 } P a\n",
        "image_path": "./data/HME100K/test_images/test_2795.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2x + 3y = 6.",
        "gt_answers": "\\frac { 6 2 } { 1 5 } = 4 \\frac { 2 } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2797.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula can be written as follows using LaTeX format:\n\n$$\\text{C}=\\frac{b \\* t}{2}\\left(\\frac{c}{b}+\\frac{d}{2t}\\right)\\left(\\frac{a}{b}+\\frac{c}{2t}\\right)$$\n\nwhere $a, b, c, d$ are constants.",
        "gt_answers": "6 x = 6 ( 1 + 6 + 6 ^ { 2 } + 6 ^ { 3 } + \\cdots + 6 ^ { 1 0 0 } )\n",
        "image_path": "./data/HME100K/test_images/test_2798.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the LaTeX expression for the given formula:\n\n$$\\begin{aligned} \\text{b} = \\frac{\\text{a}+\\text{c}}{\\text{c}-\\text{a}} \\end{aligned}$$\n\nIn this expression, the variable $\\text{b}$ is defined as a ratio of two expressions, $\\frac{\\text{a}+\\text{c}}{\\text{c}-\\text{a}}$. The variables $\\text{a}$ and $\\text{c}$ are defined elsewhere in the formula.",
        "gt_answers": "\\angle B A D = 9 0 ^ { \\circ } - \\angle B = 9 0 ^ { \\circ } - 7 5 ^ { \\circ } = 1 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2799.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is:A=bh/2where b is the base of the triangle, h is the height, and A is the area. In LaTeX format, this can be written as:A=bh/2\\[A = \\frac{b}{2}h\\]The formula for the area of a trapezoid is:A=bh(i+h)2where b is the base, h is the height, and i is the height of the isosceles triangle formed by the base and the line connecting the apex to the base. In",
        "gt_answers": "y _ { 2 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2800.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\begin{equation}\nP = \\frac{1}{2}mv^2 - \\frac{1}{2}mv^2\n\\end{equation}\n```",
        "gt_answers": "0 . 4 \\div 2 = 0 . 2 ( m )\n",
        "image_path": "./data/HME100K/test_images/test_2801.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the triangle in the image is:\n\n$$ A = \\frac{1}{2}bh $$\n\nwhere b is the base length of the triangle, h is the height of the triangle, and A is the area of the triangle.\n\nTo find the area of the triangle, we can substitute the given values into the formula:\n\n$$ A = \\frac{1}{2}(10)(5) $$\n\n$$ A = \\frac{1}{2}(10)5 $$\n\n$$ A = 25 $$\n\nTherefore, the area",
        "gt_answers": "\\sin 6 0 ^ { \\circ } = 3 0 ( \\sqrt { 3 } - 1 ) c m\n",
        "image_path": "./data/HME100K/test_images/test_2802.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a mathematical expression for the derivative of a function f(x) with respect to x. The derivative is represented by the red arrow pointing to the right, which is the direction of the change in the function's value with respect to x. The blue arrow pointing to the left represents the negative derivative, which is the direction of the change in the function's value with respect to x. The red arrow pointing up represents the increase in the function's value with respect to x, and the blue arrow pointing down represents the decrease in the function's value with respect to x.\n\nIn LaTeX",
        "gt_answers": "3 8 5 - 3 2 5 1 \\div 3 = 2 0 ,\n",
        "image_path": "./data/HME100K/test_images/test_2803.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$ d = \\frac{2r}{5} $$\n\nwhere $d$ is the diameter of the circle, $r$ is its circumference, and $5$ is a constant factor.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX code for the formula in the image:\n\n\\begin{align\\*}\nx + 2 = 5\n\\end{align\\*}\n\nThis formula is saying that the variable x is equal to 5 minus 2. The equal sign (=) is used to indicate that the two sides of the equation are equal. The backslash character (\\) is used to display the formula in LaTeX format.",
        "gt_answers": "x = \\frac { 1 7 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_2805.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is \\frac{5}{4}.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not shown. Can you provide the image?",
        "gt_answers": "A C = A E + C E = 5 + 5 = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_2807.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a diameter of 36 cm is given by: \u03c0r^2, where r is the radius of the circle. The radius of the circle is half of the diameter, so it is 18 cm. Therefore, the formula for the area of the circle is: \u03c0(18)^2 = 18\u03c0^2 cm^2.",
        "gt_answers": "x ^ { 2 } = \\frac { 4 9 } { 8 1 }\n",
        "image_path": "./data/HME100K/test_images/test_2810.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the given image is not clear and I cannot see any formula in it. Please provide a clear image with the formula written on it.",
        "gt_answers": "O A = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2811.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be expressed as: $ H\\_2O + CO\\_2 \\to H\\_2CO\\_3 $\n\nHere, H\\_2O represents water, CO\\_2 represents carbon dioxide, and H\\_2CO\\_3 represents carbonic acid. The equation shows that water and carbon dioxide react to form carbonic acid.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{a}{b + 8}$.\n\nLaTeX format: $\\frac{a}{b + 8}$",
        "gt_answers": "B A C = 8\n",
        "image_path": "./data/HME100K/test_images/test_2814.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX format for the given expression:\n\n\\begin{center}\n\\begin{minipage}{0.5\\textwidth}\n\\begin{align*}\nx^2 + 3x - 5 &= 0 \\\\\\\nx &= \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\n\\end{align*}\n\\end{minipage}\n\\end{center}\n\nIn this expression, x is the variable that we want to find. The expression is a quadratic equation in x, which",
        "gt_answers": "\\frac { 1 - 2 m } { 5 } \\geq 3 m + 2\n",
        "image_path": "./data/HME100K/test_images/test_2815.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression in the image:\n\n\\begin{center}\n$\\frac{6483}{9000}$\n\\end{center}\n\nIn this formula, the numerator is 6483, which is the area of the rectangle, and the denominator is 9000, which is the base. The fraction is simplified by dividing both numerator and denominator by 300, which gives the final answer.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is $\\frac{1}{3}$x$\\frac{2}{5}$y.",
        "gt_answers": "\\frac { x - 1 } { 2 } = \\frac { - x + 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2818.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we need to first convert the image into a mathematical equation.\n\nThe formula in the image is a function that takes two inputs, x and y, and returns their sum. We can represent this function using the following LaTeX code:\n\n$$ f(x,y) = x + y $$\n\nwhere x and y are variables representing the inputs to the function. The function is defined as the sum of x and y.\n\nOnce we have written out the formula in LaTeX format, we can use it to perform mathematical operations on the function.",
        "gt_answers": "x = \\frac { 4 . 5 } { 7 . 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2819.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "O B = C D \\cdot O C = O D\n",
        "image_path": "./data/HME100K/test_images/test_2820.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the formula in the image:\n\n$$\\text{f(x) = \\frac{a\\left(1 - x^2\\right)}{b + x^3}}$$\n\nwhere $a$ and $b$ are positive constants.",
        "gt_answers": "\\therefore B F = 1 0 0\n",
        "image_path": "./data/HME100K/test_images/test_2822.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$latex = \\frac{m}{t^2}$\n\\end{center}\n\nwhere $m$ is the mass of the object and $t$ is its period of oscillation.",
        "gt_answers": "\\vert a + \\frac { 1 } { a } \\vert = a + \\frac { 1 } { a }\n",
        "image_path": "./data/HME100K/test_images/test_2825.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:$$\\frac{1}{2} + \\frac{3}{4} - \\frac{1}{4}$$This can be written as follows:$$\\frac{1}{2} + \\frac{3}{4} - \\frac{1}{4}=\\frac{1}{2}+\\frac{3}{4}-\\frac{1}{4}$$The expression represents the sum of the fractions $\\frac{1}{2}$ and $\\frac{3}{4}$, with the fraction $\\frac{1}{4}$ subtracted from the sum.",
        "gt_answers": "1 - 2 \\sin ^ { 2 } c = - \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2826.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is given by the equation: ( t ) = ( v ) / ( t ) = ( 5 ) / ( 3 ) = 1.67 m/s.",
        "gt_answers": "V = \\frac { s } { t } = \\frac { 1 3 5 0 } { 4 5 } = 3 0 0 k m / h\n",
        "image_path": "./data/HME100K/test_images/test_2827.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe expression for the given image is:\n\n$$\n\\text{ImageContent} = \\frac{1}{2}(x + y) + \\frac{1}{4}(x - y)\n$$\n\nWhere x and y are the coordinates of the black and white squares, respectively.\n```\n\nThe expression uses the two coordinates to find the sum of the black and white squares and divides it by 2 for the black square and 4 for the white square.",
        "gt_answers": "1 . 3 5 t > 0 . 7 5 t > 0 . 3 5 t > 2 2 8 k g > 3 5 k g\n",
        "image_path": "./data/HME100K/test_images/test_2828.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$\\begin{aligned} \\frac{1}{3} \\cdot \\frac{5}{9} \\cdot \\frac{7}{11} &= \\frac{2333}{1218} \\ \\mathrm{or} \\ \\ \\frac{2333}{1218} \\cdot 100% \\end{aligned}$$The above code will display the fraction as: $\\frac{2333}{1218}$. This means that",
        "gt_answers": "1 8 . 7 5 = 7 5 k + b\n",
        "image_path": "./data/HME100K/test_images/test_2829.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{1}{a + 2b}$$where a and b are constants.",
        "gt_answers": "a < b = c\n",
        "image_path": "./data/HME100K/test_images/test_2830.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the formula:\n\n$$\\frac{a + 2b + 4c}{b + 3c} = \\frac{1}{3}$$\n\nNote that the numerator is a sum of the variables a, b, and c, while the denominator is a sum of b and c. The fraction is simplified by canceling the common factor of 3 from the numerator and denominator.\n\nThe resulting expression evaluates to $\\frac{1}{3}$, which is the final answer.",
        "gt_answers": "( 2 x - 3 y ) - ( 2 x - 6 y ) = - 7 + 1 0\n",
        "image_path": "./data/HME100K/test_images/test_2831.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by the formula: A = \u03c0r^2, where r is the radius of the circle. The area of the circle is equal to the product of pi and the square of the radius.",
        "gt_answers": "x _ { 1 } = 0 , x _ { 2 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_2832.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$ 6 + 8 - 5 + 4 = 21 $$",
        "gt_answers": "\\frac { 1 0 } { 3 } < x < 6 .\n",
        "image_path": "./data/HME100K/test_images/test_2833.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:x^2+2x-3=0, where x is the variable.",
        "gt_answers": "2 m - 4 = 3 m - 1\n",
        "image_path": "./data/HME100K/test_images/test_2834.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle can be written as:\n\nA = lw + h\n\nWhere l is the length of the rectangle, w is the width of the rectangle, and h is the height of the rectangle.",
        "gt_answers": "A Q = \\frac { A B } { \\cos A } = \\frac { 2 0 } { \\frac { 1 } { 2 } } = 4 0\n",
        "image_path": "./data/HME100K/test_images/test_2835.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{2x}{x+5}$.",
        "gt_answers": "[ 3 2 8 - ( 3 5 4 - 3 1 ) ] \\times 7 2 0 = 3 6 0 0\n",
        "image_path": "./data/HME100K/test_images/test_2836.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the expression of the formula in the image using LaTeX format:$$\\begin{align}x^2+y^2&=r^2\\end{align}$$This formula is used to find the sum of the squares of two variables, x and y, and compare it to the square of a constant value, r. The equation can be used to solve for various problems involving squares and square roots.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: 2 + 2 = 4.\n\nIn LaTeX format, the expression is:$\\frac{2 + 2}{4}$",
        "gt_answers": "x = \\frac { 1 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2839.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{x + 3}{x - 2}$\n\nTo evaluate the function at x = 4, we substitute x = 4 in the function and simplify:\n\n$\\frac{x + 3}{x - 2}$ = $\\frac{4 + 3}{4 - 2}$ = $\\frac{7}{2}$ = 3.5\n\nSo the function evaluates to 3.5 at x = 4.",
        "gt_answers": "\\therefore x = \\frac { 1 2 + 2 G } { a - 3 . }\n",
        "image_path": "./data/HME100K/test_images/test_2840.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but there is no formula in the image provided. The image shows a whiteboard with a handwritten expression that appears to be a mathematical equation. Can you please provide the image with the formula you would like me to write out in LaTeX format?",
        "gt_answers": "7 + 4 - 6 = 5\n",
        "image_path": "./data/HME100K/test_images/test_2842.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "O E = x - \\sqrt { x ^ { 2 } - 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2843.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:\n\n$$\\text{y}=\\frac{x^2}{2}+\\frac{3x}{2}$$",
        "gt_answers": "\\frac { \\pi } { 4 } + x ) = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2844.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is an equation for the volume of a cylinder with a radius of 2 cm and a height of 5 cm. The volume of a cylinder is calculated by the formula V = (pi)r^2h, where V is the volume, r is the radius, and h is the height. Plugging in the given values, we get V = (3.14) (2)^2 (5) = 314.26 cm^3.",
        "gt_answers": "B ^ { \\prime } = ( 5 , 2 \\sqrt { 2 } - 2 \\sqrt { 2 } ) = ( 5 , 0 )\n",
        "image_path": "./data/HME100K/test_images/test_2845.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 5x^2 - 10x + 5.",
        "gt_answers": "1 0 0 0 0 \\times ( 1 + x ) ^ { 2 } = 1 2 1 0 0\n",
        "image_path": "./data/HME100K/test_images/test_2846.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$s = \\frac{mgh}{\\sqrt{r^2 + (d - h)^2}}$$\n\nwhere:\n\n* $s$ is the distance from the point of release to the point where the object lands on the ground\n* $m$ is the mass of the object\n* $g$ is the acceleration due to gravity\n* $h$ is the height of the object from which it is released\n* $r$ is the distance from the point where the object is released to the point where it lands on the ground\n*",
        "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",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as:\n\nA = \u03c0r^2\n\nWhere A is the area of the circle, r is the radius of the circle, and \u03c0 is the mathematical constant that is approximately equal to 3.14. To find the area of the circle in the image, you can use the formula above with the given radius of 1.5 cm:\n\nA = \u03c0(1.5)^2\n\nA = 4.71 cm^2\n\nTherefore, the area of the circle in the image is approximately 4",
        "gt_answers": "y = k x + b ( k \\neq 0 )\n",
        "image_path": "./data/HME100K/test_images/test_2848.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:\n\nA = l x w\n\nwhere l is the length and w is the width of the rectangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula is:\n\n`(1/4) \\* 2^(2x) + (1/2) \\* 2^(x)`",
        "gt_answers": "x = 0 . 8\n",
        "image_path": "./data/HME100K/test_images/test_2850.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:$$\\begin{aligned} a + 4b - 2c &= 14 \\\\ 2a + 3b + 2c &= 19 \\\\ 3a + 2b &= 9 \\end{aligned}$$This LaTeX code represents the system of linear equations given in the image:$$\\begin{aligned} ax + by &= bx + 4y \\\\ ax + bx &= 2ax + 3y \\\\ x + y &= 3y \\end{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ \\frac{100}{200} = \\frac{100}{200}\\cdot\\frac{200}{100} = \\frac{100}{200}\\cdot \\frac{200}{100}\\cdot \\frac{100}{200} = \\frac{100}{200}\\cdot \\frac{200}{100}\\cdot \\frac{100}{200}\\cdot \\frac{100}{20",
        "gt_answers": "D F = \\frac { \\sqrt { 5 } } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2852.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the equation:\n\nA = l \\* w\n\nwhere l is the length and w is the width of the rectangle.\n\nThe area of the rectangle in the image is 5x4. Therefore, the formula would be:\n\nA = 5 \\* 4 = 20\n\nThe area of the rectangle is 20 square units.",
        "gt_answers": "\\frac { A ^ { \\prime } B ^ { \\prime } } { A B } = \\frac { A ^ { \\prime } C ^ { \\prime } } { A C } = \\frac { B ^ { \\prime } C ^ { \\prime } } { B C } = k\n",
        "image_path": "./data/HME100K/test_images/test_2853.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{4x+4y}{6}$.\n\nThe numerator is $\\frac{4x+4y}{6}$ which means $\\frac{4\\times x+4\\times y}{6}$.\n\nThe denominator is $\\frac{4x+4y}{6}$ which means $\\frac{4\\times x+4\\times y}{6}$.\n\nTherefore, the expression is $\\frac{4x+4y}{6}$.",
        "gt_answers": "4 x = - 4\n",
        "image_path": "./data/HME100K/test_images/test_2854.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{x^2}{9} - \\frac{3x}{2} - 1 $$",
        "gt_answers": "\\cos B = \\frac { 1 } { 5 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2855.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{a + b} = \\text{c}$$where $\\text{a}$ and $\\text{b}$ are the coefficients for the variables in the formula, and $\\text{c}$ is the constant term.",
        "gt_answers": "x = \\frac { 5 } { 2 1 }\n",
        "image_path": "./data/HME100K/test_images/test_2856.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:ms5 \\* 4ms5 + 12ms5 + 24ms4 - 28ms5 - 4ms5.",
        "gt_answers": "m \\leq \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2857.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n$$\\frac{2400}{500+300}=\\frac{2400}{800}\\Rightarrow 3$$",
        "gt_answers": "F \\times 1 0 0 c m = 9 0 0 N \\times 3 0 c m\n",
        "image_path": "./data/HME100K/test_images/test_2858.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}(4x + 3) = 10$",
        "gt_answers": "x = 2 4 3 0 \\div 1 . 0 S\n",
        "image_path": "./data/HME100K/test_images/test_2859.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\begin{center}\n\\frac{1}{2} x^2 + 4x - 8 = 0 \\\\\ny = \\frac{1}{2} x^2 + 4x \\\\\ny = \\frac{1}{2} x^2 + 4x + 8\n\\end{center}\n```",
        "gt_answers": "3 6 \\times 3 1 4 = 1 1 3 . 0 4 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_2860.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula can be written as:$$\\text{w}=\\frac{E}{V}$$where w is the work done, E is the energy expended, and V is the volume of the substance expelled.",
        "gt_answers": "W = 1 5 0 0\n",
        "image_path": "./data/HME100K/test_images/test_2861.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 5.6 cm is $\\pi r^2$, where $\\pi$ is the mathematical constant approximately equal to 3.14. The area of the circle is therefore given by:\n\n$\\text{Area} = \\pi (5.6 \\text{ cm})^2 = 19.04 \\text{ cm}^2$\n\nAlternatively, you can use the LaTeX code:\n\n$\\text{Area} = \\pi r^2 = \\pi (5.6 \\text{ cm})^2 = 19",
        "gt_answers": "x = \\pm \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2863.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle is given by the formula: \u03c0r^2, where r is the radius of the circle. Using LaTeX format, the equation can be written as: $\\pi r^2$.",
        "gt_answers": "y _ { 1 } = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2864.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not visible as it is a black and white image.",
        "gt_answers": "\\frac { 2 } { 3 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2865.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{e}^{-\\frac{1}{2}}\\left( \\frac{\\text{e}^{-\\frac{1}{2}}}{\\sqrt{2 \\pi}} \\right)$$",
        "gt_answers": "1 0 N \\cdot O A = F _ { 2 } \\cdot 2 O A\n",
        "image_path": "./data/HME100K/test_images/test_2866.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the following LaTeX expression:\n\n$$\\frac{E\\_{max}}{E\\_{min}} = \\frac{h \\_{ max}}{h \\_{ min}} = \\frac{2 \\cdot 3}{1 \\cdot 4} = \\frac{6}{4} = 1.5$$\n\nThe image shows a ratio of maximum energy to minimum energy in the form of an equation. The numerator is 2x3, which represents the maximum energy, and the denominator is 1x4, which represents the minimum energy. The expression simplifies",
        "gt_answers": "\\angle A B D = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2867.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: 3x + 2y = 10. This is a linear equation with two variables, x and y. The solution to the equation is found by setting the equation equal to zero and solving for x and y. The solution is x = 4 and y = 3.",
        "gt_answers": "2 \\sqrt { S _ { 2 } } = \\sqrt { S _ { 1 } } + \\sqrt { S _ { 3 } }\n",
        "image_path": "./data/HME100K/test_images/test_2868.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is given by\n\n$$ E = mc^2 $$\nwhere E is the energy of the object, m is its mass and c is the speed of light in a vacuum.",
        "gt_answers": "\\frac { 2 } { 5 } x - 7 = 9\n",
        "image_path": "./data/HME100K/test_images/test_2869.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$\\frac{1}{2} \\times \\frac{1}{4} \\times \\frac{3}{5}$\n\nwhich simplifies to:\n\n$\\frac{3}{10}$",
        "gt_answers": "\\frac { 2 } { 5 } + \\frac { 1 } { 2 } = \\frac { 4 } { 1 0 } + \\frac { 5 } { 1 0 } = \\frac { 9 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_2870.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe expression is:\n\n$$\\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6}$$\n\n$$\\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6} = \\frac{3 + 4 + 5 + 6}{6} = \\frac{17}{6} = \\boxed{2.8333}$$\n```",
        "gt_answers": "A C = 1 6 , A B = 2 0\n",
        "image_path": "./data/HME100K/test_images/test_2871.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ x^2 + 3x + 2 = 0 $$This is a quadratic equation that can be solved using the quadratic formula:$$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$$In this case, a = 1, b = 3, and c = 2, so the solutions to the equation are:$$ x = \\frac{-3 \\pm \\sqrt{9 - 4(1)(2)}}{2(1)} = \\frac{-3 \\pm \\sqrt{5}}{",
        "gt_answers": "x _ { 1 } = \\frac { 3 \\sqrt { 2 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2872.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a black hole is given by:\n\n$$ M = \\frac{c^3}{G}$$\n\nwhere $M$ is the mass of the black hole, $c$ is the speed of light, and $G$ is the gravitational constant.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x = (5 - 2) \\* 2 + 11 = 9.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula can be written as follows in LaTeX format:\n\n\\begin{align\\*}\nd^2x/dt^2 &= -1/m \\* d/dt(mgx) \\\n   &= -1/m \\* mg \\* d/dt(x) \\\n   &= -1/m \\* mg \\* dx/dt \\\n   &= -mg \\* dx/dt.\n\\end{align\\*}\nIn this expression, we have used the chain rule to find the second derivative of the position of the object with respect",
        "gt_answers": "A O \\bot B O\n",
        "image_path": "./data/HME100K/test_images/test_2876.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{x^4 + 4x^3 + 6x^2 + 4x + 1}{x^4 - 4x^3 - 6x^2 + 4x + 1} $$",
        "gt_answers": ", x = 4 + m\n",
        "image_path": "./data/HME100K/test_images/test_2878.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image can be written as follows:\n\n$$\\text{Imag}\\_{cat} = \\frac{\\text{Imag}\\_{left} + \\text{Imag}\\_{right}}{2}$$\n\nwhere $\\text{Imag}\\_{cat}$ is the category of the image, $\\text{Imag}\\_{left}$ is the left part of the image, and $\\text{Imag}\\_{right}$ is the right part of the image. The division by 2 is used to obtain the average value of the left and right parts of the image.\n\nNote that",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for finding the area of a circle with a diameter of 7 inches is: A = \u03c0r^2, where r is the radius of the circle. To find the radius of the circle, we can use the formula: r = d/2, where d is the diameter of the circle. Therefore, the formula for finding the area of the circle is: A = \u03c0(d/2)^2.",
        "gt_answers": "S _ { \\Delta } A P D = \\frac { 1 } { 2 } P R\n",
        "image_path": "./data/HME100K/test_images/test_2881.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be expressed in LaTeX format as follows:\n\n$$ \\frac{5 + 3i}{7 - 2i} = \\frac{8 + 5i}{15 - 5i} $$\n\nThe equation is a rational expression, where the numerator is the sum of the complex numbers 5 + 3i and the denominator is the difference of the complex numbers 7 - 2i and 15 - 5i.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} y &= \\frac{x}{2} \\ \\ \\text{if} \\ x \\geq 0 \\ \\&\\& x \\leq 1 \\ \\&\\& y \\leq 2\\end{aligned}$$\n\nThis formula is written in LaTeX format with the help of the `aligned` environment. The `\\frac` command is used to denote the fraction, and the `$` symbols are used to denote the variables `x` and `y`. The `&` symbol is used to denote logical conditions.",
        "gt_answers": "3 = \\frac { 2 } { 8 } x - ( - \\frac { 4 } { 8 } x )\n",
        "image_path": "./data/HME100K/test_images/test_2883.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am unable to see the image as there is no image provided in your message. Could you please provide the image so that I can assist you in writing out the expression of the formula?",
        "gt_answers": "2 3 x - 2 1 x = 4 0\n",
        "image_path": "./data/HME100K/test_images/test_2884.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\n$ $ $\\frac{m\\_2^2 - m\\_1^2}{m\\_2^2 - m\\_1^2 + \\sqrt{m\\_1^2 - (m\\_1^2 - m\\_2^2)}} \\leq \\frac{1}{2}$\n\nwhere $m\\_1$ and $m\\_2$ are the masses of the two particles involved in the process.",
        "gt_answers": "m = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2885.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ \\frac{k\\sin\\theta - mg\\sin\\theta}{k + mg}$$\n\nThe expression represents the kinetic equation for an object falling under the influence of gravity and friction. The frictional force acting on the object is given by $$F\\_f = \\mu F\\_n$$ where $\\mu$ is the coefficient of friction and $F\\_n$ is the normal force acting on the object. The net force acting on the object is the sum of the gravitational force and the frictional force, which",
        "gt_answers": "( x - 2 0 ) ( x - 4 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_2886.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n$$ 2x - 3y = 12 $$\n\nwhere x and y are variables.",
        "gt_answers": "( 3 x + y ) ( 3 x - y ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_2887.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{100}{\\sqrt{200}}$.\n\nHere's how to derive it:\n\nThe formula for the area of a circle with radius $r$ is $\\pi r^2$. To find the area of the circle in the image, we can substitute $r$ with $\\sqrt{200}$, since it is the radius of the circle.\n\nSo, the area of the circle is $\\pi \\sqrt{200}^2$.\n\nTo simplify the expression, we can divide both numerator and denominator by $\\",
        "gt_answers": "E A \\cong \\Delta O E A\n",
        "image_path": "./data/HME100K/test_images/test_2888.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the provided image does not contain a mathematical expression or formula. It appears to be a piece of text written in a handwriting style, but it is not clear what the intended message or content is. If you have a specific question about the mathematical expression you want to write using LaTeX format, please provide the expression itself, along with any relevant details or context.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the image:\n\n$$\\frac{2+3}{4-1}$$\n\nThis equation represents the ratio of the sum of two numbers to the difference of those numbers. The numerator is $2+3$, which is the sum of $2$ and $3$. The denominator is $4-1$, which is the difference of $4$ and $1$. This results in a ratio of $2+3 : 4-1 = 7 : 3$, which can be simplified to $\\frac{7}{3}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we need to follow these steps:\n\n1. Click on the image to enlarge it.\n2. Right-click on the image and select `Copy Image Address`.\n3. Paste the image address into an LaTeX editor, such as Overleaf.\n4. Type the following LaTeX code to display the formula:\n\n$$\\text{The number of people per household is 2.5.}$$\n\n5. Compile the LaTeX code to display the formula in the image.\n\nThe formula will be displayed in the image",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we need to follow the following steps:\n\n1. Select the equation in the LaTeX editor and highlight the text.\n2. Press the keyboard shortcut 'ctrl + c' (Windows) or 'command + c' (Mac) to copy the text.\n3. In the image, select the area where you want to place the equation and paste the copied text.\n4. Format the equation using LaTeX syntax, including the use of variables, operators, and functions.\n\nThe formula in the image is:\n\n$$\\frac{x",
        "gt_answers": "\\frac { 2 x } { 7 } + \\frac { x } { 3 } = - 1 0\n",
        "image_path": "./data/HME100K/test_images/test_2892.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Please provide a valid image for me to perform the requested task.",
        "gt_answers": "3 0 5 - 1 4 9 \\approx 2 0 0\n",
        "image_path": "./data/HME100K/test_images/test_2893.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=0.5]\n\\draw[thick] (0,0) -- (2,0) -- (2,2) -- (0,2) -- cycle;\n\\fill[white] (0,2) circle (1.5cm);\n\\node at (1,1.5) {$ $\\\\text{4x+3}\\ $};\n\\end{tikzpicture}\n\\end{center}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle can be written as:\n\nA = \u03c0r^2\n\nwhere A is the area of the circle, r is the radius of the circle, and \u03c0 is the mathematical constant pi (approximately equal to 3.14159).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the given image:\n\n\\begin{align\\*}\nx^2 - 5 &= 10 \\\n\\end{align\\*}\n\nThis equation represents a quadratic equation with a constant term of 10 and a leading coefficient of 1. To solve for the value of x, we can use the quadratic formula:\n\nx = $\\frac{b \\pm \\sqrt{b^2 - 4ac}}{2a}$\n\nwhere a, b, and c are the coefficients of the quadratic equation:\n\na = 1\nb",
        "gt_answers": "x = - \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2896.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a calculation in LaTeX format. The equation is: $6 \\times 7 + 8 = 42 + 8 = 50$.",
        "gt_answers": "x = \\frac { 4 } { 7 } \\times \\frac { 1 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_2898.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a LaTeX code for the formula given in the image:\n\n$ \\\\frac{x^2 + 3x + 5}{x^2 - 4x + 8}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the derivative of a function f(x) with respect to x. The equation is given by:f'(x) = f(x) - 110xf(x) - 99xf(x) - 99xf(x) - 99xf(x) - 99xf(x) - 99xf(x) - 99xf(x) - 99xf(x) - 99xf(x) - 99xf(x) - 99xf(x) -",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:\n\n$$\\frac{a}{b}=\\frac{c}{d}\\Rightarrow \\frac{a}{c}=\\frac{b}{d}$$\n\nwhere a, b, c, and d are any positive integers.",
        "gt_answers": "\\textcircled { 1 } \\div \\textcircled { 2 } = \\frac { 2 7 } { 3 6 } = \\frac { s - 2 7 } { s - 1 8 . }\n",
        "image_path": "./data/HME100K/test_images/test_2901.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, you would need to perform the following steps:\n\n1. Identify the variables in the formula: x, y, and z.\n2. Write the formula using LaTeX syntax: f(x, y, z) = x^2 + 2y^2 + 3z^2.\n3. Replace the variables with their corresponding symbols: f(x, y, z) = x^2 + 2y^2 + 3z^2.\n4. Write the function using LaTeX syntax: f(x)",
        "gt_answers": "\\frac { x + 1 } { 3 } - \\frac { x - 2 } { 2 } = \\frac { 4 + x } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_2902.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\frac{3\\times 5}{2\\times 4} = \\frac{3}{2} \\times \\frac{5}{4} = \\frac{3}{2} \\times \\frac{5}{8} = \\frac{3}{4} \\times \\frac{5}{8} = \\frac{3}{4} \\times \\frac{25}{8} = \\frac{375}{64} = \\frac{375}{32} = \\frac{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression in the image:\n\n$$ 3x^2 + 2y^2 = 9 $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle can be written as:\n\nA = \u03c0r^2A = \\pi r^2A=\u03c0r2where r is the radius of the circle.",
        "gt_answers": "\\angle A E F = \\angle 3 = 7 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2906.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{aligned}\n\\text{n(A)} &= \\frac{\\text{n(B)}}{\\text{n(B) + 2}} \\\n\\end{aligned}\n\\end{center}\n\nThe expression is using the formula for the sum of two numbers, where the numerator is the number of elements in set B and the denominator is the sum of the number of elements in set B and 2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{distance} = \\sqrt{(x\\_2-x\\_1)^2+(y\\_2-y\\_1)^2}$$\n\nThe formula is the distance between two points, represented by the variables $x\\_1$ and $y\\_1$ for the first point, and $x\\_2$ and $y\\_2$ for the second point.",
        "gt_answers": "\\frac { y ^ { 2 } } { 2 } - \\frac { x ^ { 2 } } { 4 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_2909.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is 0 + 0 = 0.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression for the formula. The expression is given by the following LaTeX code:\n\n$$\\begin{aligned} 5x + 6y &= 20 \\ \\text{for all real numbers } x \\text{ and } y\\end{aligned}$$\n\nThis equation represents a linear equation in two variables, x and y, with a constant term of 20. The symbol $\\leftrightarrow$ indicates the equivalence of the equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\text{E} = \\frac{m}{2}$$\n\nwhere E represents the electric potential energy of the charged particle at equilibrium, m represents the mass of the charged particle, and v represents the velocity of the charged particle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we need to identify the function being evaluated at a specific point and the value of the independent variable at that point. From the given image, we can see that the formula is f(x) = 2x^2 + 8x - 90.\n\nThe value of the independent variable x at the point where the function is evaluated is 10. Therefore, the value of the function at that point is f(x) = 2(10)^2 + 8(10) - 90 = 20",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$ 2(10 - 3) + 5 = 18 $$",
        "gt_answers": "\\frac { 1 5 } { 5 0 } = \\frac { 3 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_2915.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression for the formula in the image using LaTeX format:\n\n$$\\begin{align\\*} \\text{P}=\\text{16}\\times\\text{3}\\times\\text{5}\\times\\text{0.5} \\times \\frac{1}{4}\\times\\text{0.6}\\times\\text{0.25}\\times\\text{0.5}\\times\\text{0.1}\\times\\text{0.4}\\times\\text{0.1}\\times\\text{0.1}\\times\\text{0.1} \\",
        "gt_answers": "F _ { 1 } L _ { 1 } = F _ { 2 } L _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2916.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given formula:\n\n$$\\frac{x^2}{x+5}$$",
        "gt_answers": "- \\frac { 3 } { 5 } = - 0 . 6\n",
        "image_path": "./data/HME100K/test_images/test_2917.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I don't have access to the image you provided. Can you please provide the image so I can assist you with the LaTeX format?",
        "gt_answers": "x _ { 1 } + x _ { 2 } = - \\frac { b } { a }\n",
        "image_path": "./data/HME100K/test_images/test_2918.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by the formula:\n\n![](https://i.imgur.com/img)\n\nwhere C is a constant and the rest of the terms are as described in the previous answer.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n![sb/b^1] \\* (2 - s2) / (s3 + 1)\n\nwhere s1 and s2 are the two vertices of the triangle and s3 is the third vertex.",
        "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": "MiniGPT4"
    },
    {
        "question": "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\ny = x^2 - (2x/x + 1)\n\nwhere x is any real number.",
        "gt_answers": "y = - \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2921.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with base 3 and height 4 can be written as:\n\nA = (3)(4) = 12cm\u00b2\n\nor, in LaTeX format:\n\n$ A = 3 \\times 4 = 12 \\text{ cm}^2 $",
        "gt_answers": "\\angle E H D = \\angle 1 = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2922.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ \\frac{4 - 2\\sqrt{3}}{5 + 3\\sqrt{2}} $$\n\nThis formula can be simplified to:$$ \\frac{1}{2} $$\n\nThe image shows a piecewise function that is defined on the intervals [0, 2], [3, 4], and [4, 6]. The function is linear on the first interval, constant on the second interval, and constant on the third interval. The slope of the function is 1 on the first interval, - 2 on the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image with the formula is: $\\frac{1}{2}\\cdot \\frac{1}{2} + 2 = \\frac{1}{2}(1 + 2) = 1$. This can be written in LaTeX format as $\\frac{1}{2}\\cdot \\frac{1}{2} + 2 = \\frac{1}{2}(1 + 2) = 1$.\n\nHere's a breakdown of the formula:\n\n* $\\frac{1}{2}$ is a fraction that represents half of a quantity. In this case, it",
        "gt_answers": "\\overrightarrow { C M } = 2 \\overrightarrow { M B }\n",
        "image_path": "./data/HME100K/test_images/test_2924.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{3x^2+5x+6}{x^3+4x^2+6x+8}$. This can be written in LaTeX format as: $\\frac{3x^2 + 5x + 6}{x^3 + 4x^2 + 6x + 8}$.",
        "gt_answers": "D P = 3 - t\n",
        "image_path": "./data/HME100K/test_images/test_2925.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a function that maps each element of the set to an element of the set of real numbers. The domain of the function is the set of all real numbers, and the range is the set of all real numbers greater than or equal to 0. The function is continuous and differentiable at all points in its domain.\n\nThe function can be written in LaTeX format as follows:\n\n$$ f(x) = \\begin{cases} 0 & x = 0 \\\\ x^2 & x \\neq 0 \\end{cases} $$\n\nwhere $x$ is a real variable.",
        "gt_answers": "O B = \\frac { 1 } { 2 } B D = \\frac { 1 } { 2 } \\times 6 = 3\n",
        "image_path": "./data/HME100K/test_images/test_2926.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is:\n\n$$ \\text{Img} = \\frac{1}{2} x^2 + \\frac{1}{2} y^2 + \\frac{1}{2} z^2 $$\n\nThe image is a 3-dimensional representation of a sphere with radius 1. The x, y, and z axes are perpendicular to each other and pass through the center of the sphere. The formula represents the sum of the squares of the distances from the origin to each of the three points on the sphere along the x, y, and z axes.",
        "gt_answers": "5 u - 3 v = 1\n",
        "image_path": "./data/HME100K/test_images/test_2927.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ x\\_{1} + 2x\\_{2} = 6 $$\nThis equation represents a line in the Cartesian plane with slope 2 and y-intercept 6. The equation can be graphed by plotting the points (x, y) that satisfy the equation and connecting them with a line. The slope of the line is 2 and the y-intercept is 6.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{aligned}\n\\frac{a^2 + 2b^2}{a^2 - 2b^2} &= \\frac{a^2 + 2b^2}{a^2 - 2b^2} \\\n&= \\frac{a^2 + 2b^2}{a^2 - 2b^2} \\\n&= \\frac{a^2 + b^2}{a^2 - 2b^2} \\\n&= \\frac{a + b}{\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image with the given equation can be written as follows:\n\n\\begin{center}\n4x^2 + 16x - 8 = 0\n\\end{center}\n\nThis is a quadratic equation in standard form with a constant term of 8 and a leading coefficient of 4. The solutions to this equation are the values of x that make the equation true. One of these solutions is x = 2, which can be found by setting the equation equal to zero and solving for x:\n\n\\begin{center}\n4(2)^2 + 16",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{area} = \\frac{1}{2}bh$$\n\nwhere $b$ is the base of the trapezoid and $h$ is its height.",
        "gt_answers": ". \\angle A O B = 1 8 0 ^ { \\circ } - \\angle A B O - \\angle B A O = 1 5 0 ^ { \\circ } .\n",
        "image_path": "./data/HME100K/test_images/test_2932.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a mathematical expression that represents the formula for the area of a triangle with an altitude of 8 units and a base of 10 units.\n\nThe formula for the area of a triangle is:\n\nA = (bh)/2\n\nWhere b is the base and h is the altitude.\n\nSo, the formula for the area of this triangle would be:\n\nA = (10)(8)/2\n\nWhich simplifies to:\n\nA = 40/2\n\nA = 20\n\nTherefore, the area of this triangle is",
        "gt_answers": "a + b + c = - 5 . 2\n",
        "image_path": "./data/HME100K/test_images/test_2933.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I cannot see the image. Please provide the image.",
        "gt_answers": "\\angle B D C = \\frac { 1 8 0 - 6 1 } { 2 } = 5 9 . 5 ^ { \\circ } = \\angle B C D\n",
        "image_path": "./data/HME100K/test_images/test_2934.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:\n\n$$\\frac{\\frac{1}{2}\\cdot100}{4}$$\n\nThe numerator is the sum of the fractions of the numbers 1 and 2, and the denominator is the product of 4 and 100.",
        "gt_answers": "\\frac { x - 2 } { 2 } \\leq 1 = \\frac { 7 - \\pi } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2935.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a mathematical expression written in LaTeX format:\n\n\\begin{align\\*}\nf(x) = \\frac{2}{x+3}\n\\end{align\\*}\n\nThis formula calculates the value of the function f(x) for any given input value of x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the formula in the image is: $\\frac{1}{2}x^2 + \\frac{1}{2}x + \\frac{1}{4}$\n\nThe steps to derive the formula are:\n\n1. Start with the equation of a line given by $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.\n2. Substitute $x = \\frac{1}{2}$ to get $y = \\frac{1}{2} \\times \\frac{1}{2} + b = \\frac",
        "gt_answers": "( 1 - a ) x ^ { 2 } - 4 x + 6 > 0 _ { \\cdot }\n",
        "image_path": "./data/HME100K/test_images/test_2939.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a number line with numbers from 0 to 100. The numbers are marked in red in the first 20 digits, in yellow for the next 20 digits, and in green for the last 10 digits. The numbers are marked in blue at the bottom of the image.\n\nTo write the expression for this number line, we can use the following formula:\n\nn(100) + n(90) + n(80) +... + n(20) + 10\n\nwhere n(x) represents the number x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is given by:\n\nP = (1 - c) / (1 - c)\n\nwhere c is the probability of a success in one trial.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{x^2 + 2x - 12}$\n\nThe LaTeX format for this expression is: $\\frac{1}{x^2 + 2x - 12}$\n\nThis expression represents a parabolic function with vertex at the origin and a minimum value of $\\frac{1}{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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle can be expressed using LaTeX as follows:\n\n\\begin{equation}A = ab\\end{equation}\n\nwhere A is the area of the rectangle, a is the length of the rectangle, and b is the width of the rectangle.\n\nThe area of a rectangle can be found by multiplying its length and width:\n\n\\begin{equation}A = ab\\end{equation}\n\nSo, in this case, the area of the rectangle is 8 x 5 = 40.",
        "gt_answers": "( x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2945.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the given image:\n\n\\begin{align\\*}\n\\frac{454 - 329}{454 + 275} &= \\frac{125}{389} \\approx 0.323\\\n\\end{align\\*}\n\nThis formula is finding the fraction of the image on the right side of the expression. The numerator is the difference between the two numbers in the image, and the denominator is the sum of the two numbers in the image. The fraction is then approximated to three decimal",
        "gt_answers": "2 - 1 . 5 - \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2946.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the expression:\n\nA = l \\* w\n\nwhere l is the length of the rectangle and w is the width of the rectangle.\n\nTo find the area of the rectangle in the image, we can use the formula above with the given values:\n\nl = 3\nw = 4\n\nA = 3 \\* 4 = 12\n\nTherefore, the area of the rectangle in the image is 12 square units.",
        "gt_answers": "\\overrightarrow { a } + ( 2 - m ) \\overrightarrow { b }\n",
        "image_path": "./data/HME100K/test_images/test_2947.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n\\begin{align\\*}\ny & = \\frac{a}{b} \\cdot \\frac{c}{d} \\cdot \\frac{e}{f} \\cdot \\frac{g}{h} \\cdot \\frac{i}{j} \\cdot \\frac{k}{l} \\cdot \\frac{m}{n} \\cdot \\frac{o}{p} \\cdot \\frac{q}{r} \\cdot \\frac{s}{t} \\cdot \\frac{u}{v} \\cdot \\",
        "gt_answers": "y = 5\n",
        "image_path": "./data/HME100K/test_images/test_2948.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the given formula using LaTeX format, we can write it as follows:$$\\text{F}=\\frac{a\\_1b\\_1+a\\_2b\\_2}{a\\_1b\\_1+a\\_2b\\_2}\\text{.}$$Here, $a\\_1$ and $b\\_1$ are the coefficients of the first equation and $a\\_2$ and $b\\_2$ are the coefficients of the second equation. The fraction on the right-hand side represents the ratio of the two expressions.",
        "gt_answers": "\\frac { 1 } { 2 } a c c m 1 2 0 ^ { \\circ } = \\frac { 1 } { 2 } a s m 6 : + \\frac { 1 } { 2 } c s m 6\n",
        "image_path": "./data/HME100K/test_images/test_2949.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the expression of the formula in the image is:$$ 4x^2 + 9x - 12 = 0 $$In LaTeX format, this equation would be written as:$$ 4x^2 + 9x - 12 = 0 $$The solution to this equation is x = -3 or x = 4.",
        "gt_answers": "k - 2 = - \\frac { 1 2 } { 7 } - 2 = 3 \\frac { 5 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_2950.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX code for the given formula:\n\n$$c = \\frac{1}{1 + \\sqrt{2}}$$\n\nThe above code will render the formula as:c = 11+\u220f\u200b2\u200b\u200b\u200b\u200b\u200b1\u200b1\u200b\u200b1\u200b+\u200b2\u200b\u200b1\u200b\u200bc = \\frac{1}{1 + \\sqrt{2}}c=1+1+2\u200b\u200b1\u200b\u200bc = \\frac{1}{\\frac{1}{\\sqrt{2}}}\n\nThis formula represents the value of c, which is a constant in calculus",
        "gt_answers": "N a _ { 2 } C O _ { 3 } + 2 H C l = 2 N a C l + H _ { 2 } O + C O _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2951.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n\\begin{center}\n$e^ {-} \\frac{1}{2} x^2 + \\frac{1}{3} x^3$\n\\end{center}\n\nThis is the formula for the quadratic function with constant term $-\\frac{1}{2}$ and linear term $\\frac{1}{3}$. The constant term has been added to make the formula easier to read.",
        "gt_answers": "\\angle D O B = \\angle D B E + \\angle A E D = 7 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2952.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$\\text{Im}\\left(\\text{C}\\right)=\\text{I}\\left(\\text{C}\\right)$$\n$$\\text{Re}\\left(\\text{C}\\right)=\\text{R}\\left(\\text{C}\\right)$$\n$$\\text{Abs}\\left(\\text{C}\\right)=\\sqrt{\\text{Re}\\left(\\text{C}\\right)^2+\\text{Im}\\left(\\text{C}\\right)^2}$$\n\n$$\\text{arg}\\left(\\text{C}\\right)=\\frac{\\text{Im}\\left(\\text{",
        "gt_answers": "x _ { 1 } = \\frac { \\sqrt { 5 } - 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2955.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:$$$ 1 \\cdot 1 \\cdot 3 = 3$$$The image shows three objects, with one object in each row. The first row has one object, the second row has one object, and the third row has three objects. The formula shows that the product of one object and one object is equal to three objects.",
        "gt_answers": "\\cos B = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_2957.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n\\begin{align\\*}\n\\frac{100}{40} + \\frac{100}{25} &= \\frac{100 \\times 4}{40 \\times 25} \\\n&= \\frac{200}{1000} \\\n&= \\frac{1}{5}\n\\end{align\\*}\n\nAlternatively, you can use the following LaTeX code:\n\n$$\\frac{100}{40} + \\frac{100",
        "gt_answers": "( y + 2 ) ^ { 2 } + y ( y + 2 ) - y ^ { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_2958.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "\\sqrt { 3 } x = \\sqrt { 2 } x + 5\n",
        "image_path": "./data/HME100K/test_images/test_2959.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length L and width W is A = L \\* W.\n\nThe formula for the area of a rectangle with length L and height H is A = L \\* H.",
        "gt_answers": "\\sqrt { \\frac { 4 9 } { 2 5 } } = \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_2960.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not clear, as the formula is not provided. However, assuming the formula is y = mx + b, we can write it in LaTeX format as follows:\n\n$y = mx + b$",
        "gt_answers": "x = 3 m o l\n",
        "image_path": "./data/HME100K/test_images/test_2961.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$\\pi\\_{2004}=\\frac{2004}{3}\\cdot\\frac{3004}{4}\\cdot\\frac{4004}{5}\\cdot\\frac{5004}{6}\\cdot\\frac{6004}{7}\\cdot\\frac{7004}{8}\\cdot\\frac{8004}{9}\\cdot\\frac{9004}{10}\\cdot\\frac{10004}{11}\\cdot\\frac{11",
        "gt_answers": "x = \\sqrt [ 5 ] { \\frac { 1 6 } { 3 } }\n",
        "image_path": "./data/HME100K/test_images/test_2963.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\text{t} = \\text{1.43 s} - \\frac{\\text{0.68 s}}{\\text{V}\\_0}\\text{ln}\\left(\\frac{\\text{t}\\_0}{\\text{t}}\\right)$$where $\\text{t}$ is the time of the ball after it has been thrown, $\\text{t}$0 is the initial time of the ball, $\\text{V}\\_0$ is the initial velocity of the ball, and $\\text{ln}$ is the natural logarithm.##",
        "gt_answers": "x > 2 0 x < 2 0\n",
        "image_path": "./data/HME100K/test_images/test_2964.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ a = \\frac{0.002}{2} $$\n\nThe formula in the image is $a = 0.002r$, which can be written as $a = \\frac{0.002}{2}r$.",
        "gt_answers": "A = [ ( O _ { 1 } + O 2 ) \\div 2 ] ^ { 2 } - R - r\n",
        "image_path": "./data/HME100K/test_images/test_2965.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not provided, so I cannot write it out in LaTeX format. However, I can give you an example equation using LaTeX format.\n\nSuppose we want to write the equation for the area of a circle with radius r, denoted by A. We can use the formula:\n\nA = \u03c0r^2\n\nIn LaTeX format, this equation would be written as:\n\n$A = \\pi r^2$\n\nThis equation states that the area of a circle is equal to the product of pi and the square of its radius.",
        "gt_answers": "B P = \\sqrt { 3 ^ { 2 } + ( a - 1 ) ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_2966.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center} $\\frac{\\frac{\\frac{20}{x}+\\frac{x}{x+1}}{\\frac{x}{x+2}}}{\\frac{2}{x+1}}$ \\end{center}\n\nNote: In the LaTeX format, the function is written as $\\frac{a}{b}$, where $a$ is the numerator and $b$ is the denominator.",
        "gt_answers": "a x ^ { 2 } + ( 2 b - 9 ) x + c = 0\n",
        "image_path": "./data/HME100K/test_images/test_2967.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the equation for the dot product of two vectors, A and B. The dot product is a scalar quantity that measures the angle between two vectors. The formula is as follows:\n\n$$ dot\\_product(A,B) = A \\cdot B $$\n\nWhere $\\cdot$ is the dot product operator.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} f(x) &= \\frac{1}{1+e^{-x}} \\ \\left(\\frac{1}{2}\\right) \\\\\\ &= \\frac{2}{3+e^{-2x}} \\ \\left(\\frac{1}{2}\\right) \\end{aligned}$$\n\nThe above expression can be derived by applying the formula for the natural logarithm of a sum to the expression given in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\text{ImageContent}$$\n\nwhere,\n\n$$\\text{ImageContent} = 5 + 2\\sqrt{6}$$",
        "gt_answers": "x = - \\frac { 5 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_2970.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$ \\text{bl}\\_h = \\frac{1}{2} + \\sqrt{2} \\sqrt{\\text{bl}\\_h^2 - 1} $\n\nThis formula is known as the brahmagupta identity.",
        "gt_answers": "b < 0\n",
        "image_path": "./data/HME100K/test_images/test_2971.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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\nwhere r is the radius of the circle and c is the circumference of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written as follows in LaTeX format:\n\n\\begin{aligned}\n\\frac{a^2 + b^2}{2ab} - \\frac{a^2 + b^2}{2a} + 2\\sqrt{ab} &= 4a^2 - 2b^2 \\\n\\end{aligned}\nThe left side of the equation is the sum of two numbers, a and b, divided by their product, and the right side is the sum of a and b, minus a divided by a, plus 2 times the square root of a",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $ (x + 2) \\cdot (y - 1) = xy - 2y + 2 $.",
        "gt_answers": "x _ { 1 } = 3 , x _ { 2 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_2975.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 3 \\* ( 10 + 4 \\* 3 ) - 5.",
        "gt_answers": "- 3 + 1 = a - 1 , 4 + 0 = b + 1\n",
        "image_path": "./data/HME100K/test_images/test_2976.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\nx = 433 - 4(y + z)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:$$ a = \\frac{r^2}{r^2 + h^2} $$This is a formula for the area of a circle with radius $r$ and height $h$.",
        "gt_answers": "a = \\frac { 2 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2978.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not visible in the provided image. It is likely a mathematical equation or formula written in a text format. Can you please provide the image or the mathematical expression?",
        "gt_answers": "\\angle F = \\angle A C B = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_2982.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n\\text{Area of the circle} &= \\pi \\* r^2 \\\\\n&= \\frac{4}{9} \\* \\pi \\* (3 + 2\\sqrt{2})^2 \\\\\n&= \\frac{4}{9} \\* \\pi \\* (3 + 4) \\\\\n&= \\frac{4}{9} \\* \\pi \\* 7\n\\end{align\\*}",
        "gt_answers": "y - \\frac { 1 } { 4 } = - \\frac { \\sqrt { 5 } } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_2984.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{5x + 3y - 2z}{4xy + 3y^2 + 9xz - 4x - 2y}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a rectangle is: A = l x b, where l is the length and b is the width. For an equilateral rectangle, all sides are equal, so the formula simplifies to A = l x l / 2. The area of the rectangle is then A = l x b / 2.",
        "gt_answers": "\\therefore \\angle P E C = \\angle A P E\n",
        "image_path": "./data/HME100K/test_images/test_2987.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as:\n\n$$ c = \\frac{a - b}{a + b} $$\n\nwhere $a$ and $b$ are the coefficients of the equation and $c$ is the constant term.",
        "gt_answers": "\\frac { O B } { C D } = \\frac { A B } { A C }\n",
        "image_path": "./data/HME100K/test_images/test_2988.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ $x$ = $\\frac{4m}{2}$$ $x$ = $\\frac{m}{2}$$x$ = $\\frac{m}{2}$$$\\frac{x}{2} = \\frac{m}{2}\\frac{x}{2} = \\frac{m}{2}\\frac{x}{2} = \\frac{2m}{2}$$$\\frac{x}{2} = \\frac{2m}{2}$$which can be simplified as:$$ $\\frac{x}{2} = m$$$x =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is not provided, so I cannot write it out using LaTeX format. However, if you provide the formula, I can write it out using LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{sin}\\left(\\frac{\\text{x}}{\\text{2}}\\right) = \\frac{1}{2}\\left(\\frac{\\text{x}}{\\text{2}}\\right) + \\frac{1}{4}\\left(\\frac{\\text{x}}{\\text{2}}\\right)^2 - \\frac{1}{12}\\left(\\frac{\\text{x}}{\\text{2}}\\right)^3 + \\frac{1}{32}\\left(\\frac{\\text{x}}{\\text{2}}\\right)^4 - \\frac",
        "gt_answers": "\\angle B O C = 9 0 ^ { \\circ } - 2 0 ^ { \\circ } = 7 0\n",
        "image_path": "./data/HME100K/test_images/test_2991.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $ x = \\frac{b}{a} + \\frac{c}{b} $",
        "gt_answers": "A D \\bot B C\n",
        "image_path": "./data/HME100K/test_images/test_2992.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\frac{200\\sin(120^\\circ)}{75}$$",
        "gt_answers": "V _ { y } = a t\n",
        "image_path": "./data/HME100K/test_images/test_2994.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:3x5x3x10x5=30x5x3x10x5.",
        "gt_answers": "A B ^ { 2 } = A E ^ { 2 } + B E ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_2995.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{\\sqrt{x^2 + y^2}}$",
        "gt_answers": "\\frac { 1 } { 2 } \\leq m \\leq 5\n",
        "image_path": "./data/HME100K/test_images/test_2996.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$x = \\frac{a\\sin(t)}{c}$$\n\nwhere $a$ is the amplitude of the wave, $t$ is time, $c$ is the speed of the wave, and $x$ is the position of the wave at any given time.",
        "gt_answers": "1 2 8 - 1 0 0 . 4 8 = 2 7 5 2 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_2997.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we need to identify the variables and constants in the equation.\n\nThe equation is a quadratic equation with the variables x and y, and a constant coefficient of 2. The equation can be written as:\n\n2x^2 + 2y^2 = 10x + 10y\n\nUsing LaTeX format, we can write this equation as:\n\n$$ 2x^2 + 2y^2 = 10x + 10y $$\n\nThis equation represents a parabolic graph with",
        "gt_answers": "x = 3 9\n",
        "image_path": "./data/HME100K/test_images/test_2998.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format, but it can be written as follows: $\\text{a}^{2}+\\text{b}^{2}=\\text{a}^{2}+\\text{b}^{2}+\\text{2ab}$",
        "gt_answers": "6 4 \\div 4 ( < ) 6 4 \\div 2\n",
        "image_path": "./data/HME100K/test_images/test_2999.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{1}{2}(x + 3) - \\frac{1}{3}(x - 5)$\n\nNote: The formula is written in LaTeX format with proper syntax and spacing.",
        "gt_answers": "( x y = 8\n",
        "image_path": "./data/HME100K/test_images/test_3000.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\frac{dV}{dt} = \\frac{kV}{m} - \\frac{V^2}{2C}\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is:\n\n(3x\u00b2 + 2x) / (x\u00b2 - 4)\n\nThis can be written in LaTeX format as:\n\n$\\frac{3x^{2} + 2x}{x^{2} - 4}$",
        "gt_answers": "1 ^ { \\circ } m > 0\n",
        "image_path": "./data/HME100K/test_images/test_3002.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a perimeter of 12 and a width of 4 is:\n\nArea = Base x Height\nArea = 4 x 3\nArea = 12\n\nSo the area of the rectangle is 12 square units.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a group of numbers written in a table, with the sum of the first two numbers and the sum of the last two numbers. The formula for the sum of these numbers can be written as:\n\n(5 + 7) + (10 + 5) = 12 + 10 = 22\n\nSo the sum of the first two numbers is 12 and the sum of the last two numbers is 10, which gives a total sum of 22.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:$$ \\text{y} = \\frac{a + bx^2}{cx}$$This is a quadratic equation in the form of a parabola. The variables are $a, b, c, and x$. The constant is $y$.",
        "gt_answers": "x = 3 0 0 ( x - \\frac { 5 } { 1 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_3005.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not shown as it does not provide enough information to determine the formula. The image shows a mathematical expression involving variables and an equals sign, but it does not show the specific values for the variables or the operation being performed. To determine the formula, more information is needed.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n\u2211i=1\u221ei2=1\u221e\u2211i=1\u221ei4=1\u221e\u2211i=1\u221ei6=1\u221e...\n\nwhich is the sum of an infinite geometric series with first term 1 and common ratio i. The sum of the series is equal to the limit of the sum as i goes to infinity, which can be written as:\n\n\u2211i=1\u221ei2=1\u221e\u2211i=1\u221ei4=1\u221e\u2211i=1\u221ei6=1\u221e... = limi\u2192\u221e\u2211i=1",
        "gt_answers": "- 5 x = 3 \\frac { 4 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3007.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is the formula for the area of a circle. It is given by the formula:A=pir2, where p is the radius of the circle, r is the radius of the circle, and A is the area of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$ 2x + 3 = 7 $$\n\nWhere $x$ is an unknown integer.",
        "gt_answers": "\\frac { 2 - a - 1 } { 2 } = \\frac { \\sqrt { 2 } ( 1 - \\frac { 1 } { a } ) - \\sqrt { 2 } } { \\sqrt { 2 } ( 1 - \\frac { 1 } { a } ) }\n",
        "image_path": "./data/HME100K/test_images/test_3009.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:5x+6y=30\\begin{aligned} 5x + 6y &= 30 \\end{aligned}5x+6y=305x6y=30\u200bUsing LaTeX format.5x+6y=30\u200b5x+6y=30\u200b5x6y=30\u200b5x+6y=30\u200b5x6y=30\u200b5x6y=30\u200b5x+6y=30\u200b5x+6y=30\u200b",
        "gt_answers": "8 3 / 8 a = 0 . 4 5 b\n",
        "image_path": "./data/HME100K/test_images/test_3010.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the derivative of a function with respect to x is given by:\n\ndy/dx = (1/(y - 2x^2))",
        "gt_answers": "\\frac { 1 } { x } = \\frac { 1 } { 0 . 1 } x = 0 . 1 m o l\n",
        "image_path": "./data/HME100K/test_images/test_3012.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written on the image is:\n\n$$ 2x^2 + 5x - 10 = 0 $$\n\nThis is a quadratic equation in the form of a quadratic formula. The left-hand side of the equation is the sum of the square of two variables, $x^2$, and a linear expression in one variable, $5x$. The right-hand side of the equation is a constant term, $-10$, and the equals sign indicates that the two sides of the equation are equal. This equation can be solved using the quadratic formula, which gives the solutions $x = {-",
        "gt_answers": "x _ { 1 } = 5 0 x _ { 2 } = - 4 8\n",
        "image_path": "./data/HME100K/test_images/test_3013.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image you provided shows a geometric diagram of two overlapping circles with a shaded area representing the intersection of the two circles.\n\nTo write out the expression for this diagram using LaTeX format, we can use the following code:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\filldraw (0,0) circle (1);\n\\filldraw (1.5,0) circle (1);\n\\shade (intersection of 0,0--1.5,0) circle (0.25);\n\\end{tikzpicture}\n\\end{center",
        "gt_answers": "1 2 : 1 . 2 = 1 2 \\div 1 . 2 = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_3014.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{0.5}\\cdot (x + 3) = 4$$This is a linear equation with two variables, x and 3, and a constant term of 4. The coefficient of x is 0.5 and the constant term is 4. The solution to this equation is x = 4 - 0.5\\*3 = 1.5.",
        "gt_answers": "4 6 \\div ( 5 ) = 9 \\cdots 1\n",
        "image_path": "./data/HME100K/test_images/test_3016.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{equation}\\text{a + b = c}\\end{equation}\n\nIn this formula, 'a' and 'b' represent the two quantities being added together, and 'c' represents the sum of those quantities.",
        "gt_answers": "\\frac { 2 } { x + 1 } = a\n",
        "image_path": "./data/HME100K/test_images/test_3017.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula for a cubic function. The formula is written as follows: y = ax^2 + bx + c, where a, b, and c are constants. The formula represents a parabolic function with an equation of y = ax^2 + bx + c. The constant a represents the slope of the parabola, b represents the y-intercept, and c represents the constant term. The image shows the formula written out with LaTeX notation.\n\nThe image shows the formula for a cubic function. The formula is written as follows: y = ax^2 + bx",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression that shows the equation of a parabolic function in LaTeX format. The equation is y = x^2 + 4x - 6, which can be written as:y = \\frac{x^2}{2} + 2x - 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: $\\frac{2\\pi}{\\sqrt{2}}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is y = x^2, where x is a variable.",
        "gt_answers": "y _ { 1 } = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3021.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$ \\frac{1}{x+5} = \\frac{3}{2} $$\n\nThis can be rewritten in terms of the variable x as:\n\n$$ \\frac{1}{x+5} = \\frac{3}{2x+10} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: $\\frac{1}{2}x^2 + \\frac{1}{4}x - \\frac{3}{4}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX code for the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[line width=1pt] (0,0) -- (3,3) node[right] {$x$};\n\\draw[line width=1pt] (0,0) -- (0,3) node[above] {$y$};\n\\draw[line width=1pt] (3,0) -- (3,3) node[right] {$z$};\n\\draw[line width=1pt] (0,0) -- (3,",
        "gt_answers": "P ( A ) = \\frac { 1 } { 3 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3024.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Please ensure that the image is visible and accessible before asking a question.",
        "gt_answers": "y ^ { 2 } - 1 = 0 - y ^ { 2 } - 2 y + 5 = 0\n",
        "image_path": "./data/HME100K/test_images/test_3025.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as follows:\n\n<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><msup><mi mathvariant=\"normal\">t</mi></msup><mi mathvariant=\"normal\">t</mi></mrow><mrow><mi mathvariant=\"normal\">a</mi></mrow></mfrac></mrow><annotation encoding=\"application/x-tex\">n</annotation></semantics></math>",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:\n\nA = l \u00d7 w\n\nwhere l is the length of the rectangle and w is the width of the rectangle.\n\nThe area of the rectangle in the image is 15 cm2.\n\nl = 3 cm\nw = 5 cm\n\nA = l \u00d7 w = 3 \u00d7 5 = 15 cm2.\n\nSo, the formula for the area of the rectangle in the image is A = l \u00d7 w.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, you can use the following LaTeX code:\n\n\\begin{align\\*}\nx &= \\frac{4m}{7} \\\ny &= \\frac{7n}{9} \\\nz &= \\frac{9p}{11}\n\\end{align\\*}\n\nThis formula represents the following situation:\n\n* $x$ is the number of hours it takes to complete a task that requires $4$ people to work together.\n* $y$ is the number of hours it takes to complete a task that requires $",
        "gt_answers": "x _ { 3 } = \\frac { 4 \\sqrt { 7 } } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_3028.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{300 - 200}{200 - 100}$$This formula calculates the percentage increase in the difference between the two numbers. The result is that the percentage increase is 50%.",
        "gt_answers": "\\cot \\angle B C O = \\frac { C O } { D B } = \\frac { 2 } { 1 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_3029.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\node[draw, circle, inner sep=1pt] (img) at (0,0) {\\includegraphics[width=1cm]{Img.jpg}};\n\\end{tikzpicture}\n\\end{center}\n\nThis will display the image in the center of the page with a circle around it. The `tikzpicture` environment is used to position the image, and the `\\includegraphics` command is used to insert the image. The `[width=1cm]` argument specifies the",
        "gt_answers": "7 6 0 \\div 2 8 \\div 2 0 = 2 1 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_3030.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression for the formula in the image using LaTeX format:$$\\frac{1}{1+x^2}$$\n\nThis formula is used to calculate the area under the curve of a quadratic function, with the center at the origin. The area is denoted by $A$ and the vertex of the parabola is at the point $(0,0)$. The formula can be used to find the area of a square, which is given by $A = (x^2+y^2)^(1/2)$.",
        "gt_answers": "y _ { 4 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3032.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX format for the expression in the image:\n\n$$\\text{AB} + \\text{b} = \\text{a} + \\text{AB}$$",
        "gt_answers": "\\cos B = \\frac { B E } { A B } = \\frac { 4 } { 5 } .\n",
        "image_path": "./data/HME100K/test_images/test_3033.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n<img src=\" \"/><img src=\" \"/>",
        "gt_answers": "( x - 3 ) ( x + 2 ) + 4 = 2 x ^ { 2 } - 8\n",
        "image_path": "./data/HME100K/test_images/test_3034.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{align}\n&\\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} \\",
        "gt_answers": "\\angle P F O = 1 2 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3035.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation shown in the image is the formula for the area of a circle. The formula is given by:\n\nA = \u03c0r^2A = \\pi r^2A=\u03c0r2\u200bwhere r is the radius of the circle. The formula is based on the formula for the area of a circle, which is A = \u03c0r^2A = \\pi r^2A=\u03c0r2\u200bwhere r is the radius of the circle.",
        "gt_answers": "1 1 + 7 = 1 8 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_3036.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\begin{align\\*}\n\\frac{256 - 240}{240 - 200} &= \\frac{16}{40} \\\n&= \\frac{1}{2} \\\n&= 0.5\\\n&= 0.5 \\\n&= 0.5 \\\n&= 0.5 \\\n&= 0.5 \\\n&= 0.5 \\\n&= 0.5 \\\n&= 0.5 \\\n&= 0.5 \\\n&=",
        "gt_answers": "\\frac { y } { 4 } - \\frac { 1 } { y } = 0\n",
        "image_path": "./data/HME100K/test_images/test_3037.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{x^{2}+y^{2}}{2}$$The red arrow points to the variable x, which is squared and added to the variable y, which is also squared, and then the sum is divided by 2 to obtain the final result.",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3038.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for tan(a + b) can be written as follows: tan(a + b) = tan(a) + tan(b)Note that the addition of a and b is performed elementwise, so we can use the tangent formula for each element. Therefore, we have:tan(a + b) = tan(a) + tan(b)The result is the same as the sum of the tangents of the angles a and b, which we have already computed as tan(a) + tan(b) = 2.14 + 2.57 = 4.7",
        "gt_answers": "\\tan \\alpha = \\frac { B C } { A B } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3039.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the sum of 9 consecutive integers, each of which is a multiple of 7, can be written as follows:\n\nn + 9 \\* 7n + 89n + 7n + 6n + 5n + 4n + 3n + 2n + 1n + 09n + 89n + 7n + 6n + 5n + 4n + 3n + 2n + 1n + 09n + 89n + 7n + 6n +",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} \na &= \\frac{b+c}{d} \\\n\\end{aligned}$$\n\nThe variables in the formula are represented by the letters a, b, c, and d. The equals sign (=) is used to indicate that the left-hand side of the equation is equal to the right-hand side.",
        "gt_answers": "A ^ { \\prime } B = B\n",
        "image_path": "./data/HME100K/test_images/test_3042.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n\\begin{align}\n2(x + 3) - 5 &= 11 - 5 \\\n&= 6 - 5 \\\n&= 1 \\\n&= x + 1\n\\end{align}\n\nTherefore, the formula in the image is x + 1.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ m = \\frac{2}{3}\\times 30 + \\frac{1}{2}\\times 50 = \\frac{2}{3}\\times 30 + \\frac{5}{2}\\times 50 = \\frac{80}{3} + \\frac{50}{2} = 30 + 25 = 55$$",
        "gt_answers": "3 0 m = 3 0 0 0 c m\n",
        "image_path": "./data/HME100K/test_images/test_3046.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image:\n\n$$\\text{y} = \\frac{2000}{3} - \\frac{500}{4}$$",
        "gt_answers": "1 0 \\times 3 = 3 0 ( d m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_3047.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{center}\n$\\frac{\\text{number of boys}}{\\text{total number of students}}$\n\\end{center}\n\nThe image shows a ratio of 4:7, which means that there are 4 boys for every 7 girls in the class.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = l \\* w\n\nwhere l is the length and w is the width.",
        "gt_answers": "x = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3050.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows in LaTeX format:\n\n$$\\text{a + b + c}$$\n\nHere, a, b, and c are variables representing the quantities of three different elements present in the formula.",
        "gt_answers": "\\Delta B D E \\sim \\Delta E D O\n",
        "image_path": "./data/HME100K/test_images/test_3051.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is not clear, as the notation is not standard. Can you provide more details or the image itself?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not shown in LaTeX format, but it can be expressed as follows:\n\n$$\\text{v}=\\sqrt{3000 \\cdot \\frac{100}{50}}$$\n\nThis equation is based on the formula for velocity, which is the distance traveled by an object per unit time. In this case, the velocity is given as 3000 meters per second, and the time is given as 100 seconds. To convert the time to seconds, we divide by 50, which gives us 0.2 seconds. Then,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is not shown in the LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$c=\\frac{b}{a}$$\n\nwhere c, b, and a are the sides of the triangle with angle \u03b1 at the top, and angle \u03b2 at the bottom.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed as follows in LaTeX format:\n\n\\begin{center}\n$A = \\pi r^2$\n\\end{center}\n\nWhere $A$ is the area of the circle and $r$ is the radius of the circle. The value of $r$ is given as $r = 3.14$ in the image.",
        "gt_answers": "( 4 3 - 2 7 ) \\div 4 = 4\n",
        "image_path": "./data/HME100K/test_images/test_3056.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression in the image:\n\n$$\\frac{b+c}{2}$$\n\nwhere $b$ and $c$ are the two numbers in the image. The fraction bar separates the numerator (the sum of $b$ and $c$) from the denominator (2).",
        "gt_answers": "\\frac { B E } { C F } = \\frac { B C } { C E }\n",
        "image_path": "./data/HME100K/test_images/test_3057.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\text{3x^2 + 2x - 5}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for this image is not visible in the image. Can you please provide the image so I can write out the formula in LaTeX format?",
        "gt_answers": "y _ { 3 } = - \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3059.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the sum of the fractions is:\n\n\\frac{2}{4} + \\frac{2}{5} = \\frac{2 + 2}{4 + 5} = \\frac{4}{9}\n\nSo, the sum of the fractions is 4/9.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: f(x) = x^2 - x^4 + x^6.",
        "gt_answers": "a _ { m } = \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3063.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: 6x^3 - 15x^2 + 5x - 3.",
        "gt_answers": "\\textcircled { 1 } - 3 \\times \\textcircled { 4 } : 6 x = - 2\n",
        "image_path": "./data/HME100K/test_images/test_3066.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the derivative of f(x) with respect to x is given by:$$\\frac{d}{dx} f(x) = \\frac{4x^2 - 15x + 8}{x^3 - 5x^2 + 15x - 8}$$The derivative can be found using the chain rule of differentiation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:$$\\frac{x+y}{2}\\times\\frac{x-y}{2}\\times\\frac{x\\times y}{x+y}$$Therefore, the value of the formula for the given values of x and y is:$$\\frac{4+1}{2}\\times\\frac{4-1}{2}\\times\\frac{4\\times 1}{4+1}=6\\times\\frac{1}{4}\\times\\frac{4}{6}=3\\times\\frac{1}{2}=3$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n\\begin{aligned}\n\\text{Area of the rectangle } &= \\text{Length of rectangle } \\times \\text{ Width of rectangle } \\\\\n&= 5 \\times 4 \\\\\n&= 20 \\text{ cm}^2\n\\end{aligned}\n\nThe area of the rectangle is 20 cm^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format. Here is the formula in LaTeX format:\n\n$$ 10 + 9 = 19 $$\n\nThe formula is written in mathematical notation, with the numbers and operators in the correct positions. The equals sign (`=`), multiplication sign (`*`), addition sign (`+`), and subtraction sign (`-`) are all used in the correct places to indicate the operations being performed on the numbers. The resulting expression is 19, which is the correct result of adding 10 and 9.",
        "gt_answers": "\\angle D E B = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3070.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\frac{a+b}{c+d}$$\n\nwhere a, b, c, and d are any real numbers.",
        "gt_answers": "\\frac { 3 } { 6 } < \\frac { 2 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3071.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is: $\\frac{a+b}{c+d}=\\frac{b+d}{c+a}=\\frac{d+c}{b+a}=\\frac{c+d}{a+b}=\\frac{a+c}{b+d}=\\frac{b+a}{c+d}=\\frac{c+b}{a+d}=\\frac{a+c}{b+d}=\\frac{b+c}{a+d}=\\frac{d+c}{a+b}=\\frac{a+d}{b+c}=\\frac{b+d}{a+c}=\\",
        "gt_answers": "x = \\frac { a - 5 } { a - 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3072.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is $\\frac{1}{4}$.\n\nHere is the LaTeX code for the expression:\n\n\\frac{1}{4}",
        "gt_answers": "1 8 0 - 4 5 - 4 5 = 9 0\n",
        "image_path": "./data/HME100K/test_images/test_3073.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is given by:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "1 + ( 2 - a ) ^ { 2 } + 1 7 = 9 + ( 1 - a ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3074.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Determine the variables in the formula.\n\nIn the image, we have x, y, and z as variables.\n\n2. Write the formula using LaTeX notation.\n\nThe formula is given by:\n\n1. x + y + z = 12\n3. Solve for y.\n\nSubstituting x + y + z = 12 into the equation, we get:\n\ny = 12 - x - z\n4. Plot",
        "gt_answers": "1 2 \\times 6 = 7 2 ( d m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_3075.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the formula in the image:\n\n\\begin{center}\n$3x^2 + 2x - 4 = 0$\n\\end{center}\n\nThis is the equation of a parabolic curve that passes through the point $(-2,2)$. The x-intercepts of this curve are $\\frac{-b}{2a}$ and $\\frac{-b}{2a}$ where $a = 1$ and $b = 4$. The y-intercept is at the point $(0,2)$.",
        "gt_answers": "4 \\times 4 \\times 4 = 6 4 c m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3076.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the given image is given by:\n\n\\begin{aligned}\nx^3 + 5x^2 + 11x + 10 = 0\n\\end{aligned}\nThis is a cubic equation with the variable x. The solutions to this equation can be found by factoring the polynomial and solving for the roots. The factors of the polynomial are given by:\n\n\\begin{aligned}\n(x + 5)(x + 2)(x + 5)\n\\end{aligned}\nTherefore, the solutions to the equation are:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for this image is x^2 - 5x + 8.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: $\\sqrt{(\\frac{a}{b})^2 + (\\frac{c}{d})^2}$.",
        "gt_answers": "A E = 1 \\therefore A D = 2\n",
        "image_path": "./data/HME100K/test_images/test_3079.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 2x + 2y = 10.",
        "gt_answers": "x _ { 1 } + x _ { 2 } = - \\frac { b } { a } = 3\n",
        "image_path": "./data/HME100K/test_images/test_3080.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{T} = \\frac{m}{v}$$\n\nwhere T is the time, m is the mass of the object and v is the velocity of the object.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX code for the expression in the image:\n\n\\begin{align\\*}\n\\frac{d}{dt}\\left(\\frac{m}{2}\\right) + \\frac{d}{dt}\\left(\\frac{v^2}{2}\\right) = \\frac{d}{dt}\\left(\\frac{mv}{2}\\right)\n\\end{align\\*}\n\nwhere $m$ and $v$ are the mass and velocity of the object, respectively.",
        "gt_answers": "\\angle B O C = 1 2 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3082.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2 x 2 + 3 x 2 + 4 x 2 + 5 x 2 = 16x2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe expression for the area of a triangle with base b and height h is:\n\nA = (1/2)bh\n```",
        "gt_answers": "( x + 1 ) ^ { 2 } . = 4 8 \\div 3\n",
        "image_path": "./data/HME100K/test_images/test_3084.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nx4 + x3 - x2 + 3x - 5\n\nwhere x is the variable.",
        "gt_answers": "x - \\frac { 4 } { 5 } x = 1 0 + 3\n",
        "image_path": "./data/HME100K/test_images/test_3085.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x^2 + y^2}{x + y}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in LaTeX format using the image is:\n\n$$ 3x^2 + 4x - 5 = 0 $$",
        "gt_answers": "x _ { 2 } = \\sqrt { 3 } - \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3087.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with base (b) and height (h) can be written as:A=bhA = bhA=bhHere, the area (A) is equal to the product of the base (b) and height (h).",
        "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",
        "image_path": "./data/HME100K/test_images/test_3088.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ \\text{Image Content} = \\frac{3\\text{}}{\\text{2}}$$This is a formula for calculating the image content, which is the ratio of the number of pixels in the image to the number of pixels in the original image. The formula is written in LaTeX format, which uses the fraction bar to indicate the ratio and the slash to indicate the division operation.",
        "gt_answers": "( 3 - i ) ( t + 2 i ) \\in R\n",
        "image_path": "./data/HME100K/test_images/test_3089.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be expressed as:\n\n$$ \\frac{56}{84} = \\frac{56}{x} $$\n\nwhere $x$ is the denominator of the fraction, which is $84$ in this case.\n\nNote that this formula represents the ratio of the length of the rectangle's width to its height. The length of the rectangle is $56$, and its width is $x$. Therefore, the height of the rectangle is $\\frac{56}{x}$.",
        "gt_answers": "0 . 6 6 7 > \\frac { 2 } { 3 } > 6 . 6 \\% > \\frac { 4 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_3091.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression in the image:\n\n\\begin{equation}\n\\frac{dV}{dt} = \\frac{q}{\\sqrt{2mr}}\n\\end{equation}\n\nThis is the formula for the time derivative of the volume of a sphere with charge density $\\rho$ and radius $r$. The constant $q$ represents the amount of charge on the sphere.",
        "gt_answers": "x _ { 2 } = 4 y ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3092.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation 5(x^2 + 2x + 3) = 35. The equation can be written in LaTeX format as:\n\n$$5(x^2 + 2x + 3) = 35$$\n\nThis equation can be solved by factoring the left-hand side and simplifying the right-hand side, as follows:\n\n$$5(x + 5)(x + 3) = 35$$\n\nSimplifying the right-hand side, we get:\n\n$$5(x + 5) =",
        "gt_answers": "\\frac { 3 0 } { 1 5 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_3093.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: $\\frac{2}{4}+\\frac{1}{3}=\\frac{7}{12}$.",
        "gt_answers": "\\sqrt { ( 2 - x ) ^ { 2 } + ( 2 x + 1 - 3 ) ^ { 2 } } = 6\n",
        "image_path": "./data/HME100K/test_images/test_3094.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:$$\\frac{m\\_{1}}{m\\_{2}}$$where$m\\_1$and$m\\_2$are the masses of the two objects shown in the image. The formula represents the ratio of the mass of the first object to the mass of the second object.",
        "gt_answers": "N a _ { 2 } S O _ { 4 } + B a C l _ { 2 } = B a S O _ { 4 } l + 2 N a C l\n",
        "image_path": "./data/HME100K/test_images/test_3098.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{1}{2}\\left(\\frac{x}{10}\\right)^2 + \\frac{1}{4}\\left(\\frac{x}{5}\\right)^4 + \\frac{1}{6}\\left(\\frac{x}{10}\\right)^6$$",
        "gt_answers": "0 . 6 = \\frac { 6 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3099.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula for the area of a triangle with a base of 20 and a height of 30. The formula is:A = 1/2 x h x b. In this case, the area is 150 sq cm.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is $\\sqrt{3}+i\\sqrt{2}$.\n\nHere's how to derive the expression:\n\n1. Write the equation of the line in slope-intercept form:\ny = mx + b\n2. Identify the slope of the line:\nm = $\\frac{b}{a}$\n3. Calculate the value of the slope:\nm = $\\frac{2}{3}$\n4. Substitute the slope into the equation:\ny = $\\frac{2}{3}$x + 1\n5. Simplify the equation",
        "gt_answers": "x = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3101.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 5x5 + 10x5 + 3x5 + 8x5 + 15x5 + 7x5 + 6x5 + 4x5 + 2x5 + 1x5 + 0x5 + 1x5 + 1x5 + 0x5 + 1x5 + 0x5 + 0x5 + 0x5 + 0x5 + 0x5 + 0x5 + 0x5 + 0x5 +",
        "gt_answers": "\\frac { 3 } { 5 } : x = 2 5 \\% = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3102.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize, but the image provided does not contain any mathematical expression or formula. Please provide a different image with a mathematical expression for me to write out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{x^2 + 3x - 4}{x^2 - 5x + 6} = \\frac{x^2 + 3x - 4}{x - 2}$$\n\nThe denominator is $(x-2)$ which is a linear factor of the numerator $(x^2+3x-4)$. Therefore, the image represents a linear transformation of the form $T(x) = \\frac{x^2 + 3x - 4}{x - 2}$ which is represented by the equation",
        "gt_answers": "y - \\frac { 2 } { y } - 1 = 0\n",
        "image_path": "./data/HME100K/test_images/test_3104.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the sum of the first 30 terms of the sequence is given by:30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+6",
        "gt_answers": "( 8 9 - 2 5 ) \\div 8 = 8\n",
        "image_path": "./data/HME100K/test_images/test_3105.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}\\left(\\frac{x^2}{y^2}+\\frac{y^2}{x^2}\\right)\\left(\\frac{x}{y}+\\frac{y}{x}\\right)$.",
        "gt_answers": "2 [ \\frac { 4 } { 3 } x - ( \\frac { 2 } { 3 } x - \\frac { 1 } { 2 } ) ] = \\frac { 3 } { 4 } )\n",
        "image_path": "./data/HME100K/test_images/test_3107.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression of the formula in the image using LaTeX format:\n\n$$\\begin{aligned}\n&\\text{Image content: } \\frac{a}{b} \\rightarrow \\text{Image content: } \\frac{a}{b} \\left(\\frac{a}{b}\\right)^\\frac{1}{a} = \\frac{1}{b} \\rightarrow \\frac{a}{b}\\left(\\frac{a}{b}\\right)^\\frac{1}{a} = \\frac{a}{b} \\left(\\frac{a}{b}\\right)^\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{x^2+4x+3}{x-2}$. The formula is a quadratic equation with integer coefficients.",
        "gt_answers": "k ^ { 2 } x ^ { 2 } + ( 2 k - 4 ) x + 1 = 0\n",
        "image_path": "./data/HME100K/test_images/test_3109.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the expression in the image is given by:$$ y = x^2 + 2x + 1$$The variable x represents the independent variable and y represents the dependent variable in this equation.",
        "gt_answers": "x = - \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3111.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is the equation for the dot product of two vectors, u and v.\n\nUsing LaTeX format, the equation can be written as:\n\n$$u \\cdot v = \\left\\| u \\right\\| \\left\\| v \\right\\| cos(\\theta)$$\n\nwhere $\\left\\| u \\right\\|$ and $\\left\\| v \\right\\|$ are the magnitudes of the vectors u and v, respectively, and $\\theta$ is the angle between them.",
        "gt_answers": "a b + a c + b c ) \\times 2\n",
        "image_path": "./data/HME100K/test_images/test_3112.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n1) (a + b)2 + (c + d)2 = a2 + b2 + c2 + d2\n\n2) (a + b)2 + (c + d)2 = (a + b + c + d)2\n\n3) (a + b)2 + (c + d)2 = (a2 + 2ab + b2 + 2cd + c2 + d2)\n\n4) (a + b)2 + (c + d)2 = (a + b",
        "gt_answers": "a = - \\frac { 3 } { 2 } < - 1\n",
        "image_path": "./data/HME100K/test_images/test_3114.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a formula for the sum of the lengths of the edges of a shape with four sides. The formula is given by the equation:L = 2(a + b) + 3(c + d)where L is the sum of the lengths of the edges, a and b are the lengths of two adjacent edges, c and d are the lengths of two other adjacent edges, and the sum is taken over all four pairs of adjacent edges.",
        "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": "MiniGPT4"
    },
    {
        "question": "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$$ \\text{ImageContent} = \\frac{3 \\* 5 + 8 \\* 3}{4 \\* 5 + 7 \\* 3} $$\n\nwhere $\\text{ImageContent}$ is the image content.",
        "gt_answers": "( a - 3 ) x = 3 + a\n",
        "image_path": "./data/HME100K/test_images/test_3119.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not written in LaTeX format, so I cannot provide the expression of the formula. However, the image shows a mathematical expression that can be interpreted as follows:\n\n$$ \\frac{100 - 40}{50 + 20} = \\frac{100 - 40}{70} = \\frac{60}{70} = 0.857143 $$\n\nTherefore, the value of the expression is 0.857143.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is written in LaTeX format as follows:\n\n\\begin{align\\*}\nx + 2y &= 10 \\\n3x - 5y &= -12 \\\n\\end{align\\*}\n\nThis system of linear equations can be solved using the substitution method or the elimination method.",
        "gt_answers": "A P \\cdot C Q = A D \\cdot C D\n",
        "image_path": "./data/HME100K/test_images/test_3121.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n&#x2222;x + 1 = x + 1&#x2222;\" role=\"presentation\" style=\"position: relative;\">ax+1=x+1ax+1=x+1\\frac{a}{x}+1=\\frac{a}{x}+1ax+1\u200b=x+1\u200b\\frac{a}{x}+1=\\frac{a}{x}+1ax+1\u200b=x+1\u200ba\u200bx+1\u200b=x+1\u200b\\frac{a}{x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $\\frac{x}{y}$. This is a simple algebraic expression that represents the ratio of x to y. It can be used to solve various types of problems, including algebraic equations, inequalities, and proportions.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \\frac{6x - 4y + 2x + 4y - 6x}{4y - 6x}.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided as it appears to be incomplete or corrupted. Could you please provide the complete image or a clear explanation of the formula you would like me to write in LaTeX format?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\begin{aligned}\n\\text{Image Content} = 3x^2 + 2xy - y^2\n\\end{aligned}$$",
        "gt_answers": "x = \\frac { 6 } { 5 } \\div 3\n",
        "image_path": "./data/HME100K/test_images/test_3127.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{x^{2}}{x^{4}}$.\n\nHere's a breakdown of the formula:\n\n* $\\frac{x^{2}}{x^{4}}$ means we are dividing the square of $x$ by $x^4$.\n* $x$ is the variable that we are taking the square of and dividing by $x^4$.\n* The result of the calculation is the expression inside the parentheses.",
        "gt_answers": "4 = \\frac { m } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3128.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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 - 6 = 0.",
        "gt_answers": "x = \\frac { 5 } { 6 } \\div \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3129.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n$$\\begin{aligned} x = \\frac{5}{2} \\end{aligned}$$\n\nThis formula represents the solution to the equation $x^2 - 11x + 12 = 0$, which is the standard form of the quadratic equation. The coefficient of the squared term, $b = 11$, is the value of the constant term in the equation, and the coefficient of the linear term, $a = 5$, is the value of the leading coefficient. The solution to the equation is",
        "gt_answers": "\\frac { 2 } { 3 } x = \\frac { 1 7 } { 1 8 }\n",
        "image_path": "./data/HME100K/test_images/test_3130.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the expression in the image is given by:x^2+y^2=r^2where x and y are the coordinates of the point on the unit circle with radius r.",
        "gt_answers": "5 \\frac { 3 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3131.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n$$\\frac{t}{s+3}=\\frac{s^2-18s+36}{s^2+9s-24}$$",
        "gt_answers": "\\frac { \\sin \\alpha + \\cos \\alpha } { \\sin \\alpha - \\cos \\alpha }\n",
        "image_path": "./data/HME100K/test_images/test_3132.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but there is no image provided for me to write out the expression of the formula. Please provide the image so I can assist you.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{a + 2b} = 6 \\quad \\Rightarrow \\quad a = 2b - 3$$\n\nwhere a and b are variables representing the coefficients of the given equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as:\n\n$$\\text{ImageContent} = \\frac{1}{2} \\times \\left(\\frac{1}{4} + \\frac{1}{8}\\right)$$\n\nThis formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse has length 2, and the other two sides have length 1/4 and",
        "gt_answers": "\\frac { x } { 1 5 } = \\frac { 1 . 5 } { 0 . 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3135.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a mathematical expression that represents the formula for the sum of the infinite series:$\\sum\\_{n=1}^{\\infty } n\\cdot (-1)^{n-1}$",
        "gt_answers": "x _ { 2 } = - \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3136.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by: 1 / 2 \\* x^2 + y^2 = (x + y)^2.",
        "gt_answers": "2 . 4 \\div 4 = 0 . 6 ( d m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_3137.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with width w and length l is:\n\nA = w \\* l\n\nThis formula can be represented mathematically as:\n\nA = w \\* l\n\nwhere w is the width and l is the length of the rectangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given by the equation:\n\nP = A + B - ( C / d )\n\nwhere P is the pressure, A is the area of the head, B is the pressure in the head, C is the volume of the head, and d is the density of the liquid.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x^4 - 4x^3 + 6x^2 - 4x + 2.\n\nTo derive this expression, we can follow the steps shown in the previous question:\n\n1. Write out the polynomial for each term in the expression, using the exponents and coefficients given in the image:\nx^4 - 4x^3 + 6x^2 - 4x + 2\n2. Simplify the polynomial by combining like terms:\nx^4 - 4x^3 + 2x^",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is given by:\n\n$$\\begin{aligned} sin(x) = \\frac{e^(-i\\theta)}{i} \\ \\quad \\text{for} \\quad \\theta \\in \\left[\\frac{\\pi}{2},\\frac{3\\pi}{2}\\right] \\end{aligned}$$\n\nThis formula is derived from the unit circle definition of sine, which states that the sine of an angle $\\theta$ is equal to the y-coordinate of the endpoint of the line segment that shares the angle with the positive x-axis. In other words",
        "gt_answers": "\\sin \\theta = \\frac { d } { x }\n",
        "image_path": "./data/HME100K/test_images/test_3141.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is:\n\n$$ \\frac{1}{x} $$\n\nwhere x is the variable being substituted.",
        "gt_answers": "( x + y ) - 1 ) m - ( 2 x - 3 y + 6 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_3142.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:\n\n$$\\begin{aligned}\n& 4x^2 + 12x - 4\\\n\\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: 0.5\\*log(x) + 1.5\\*log(y) = log(z)where x and y are the input variables and z is the output variable.",
        "gt_answers": "\\angle A E D = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3144.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given formula:\n\n\\begin{align}\ny &= \\frac{250x^2}{64}+\\frac{16x}{8}-\\frac{5}{4}\\\n\\end{align}\n\nNote that I had to remove the angle brackets from around the formula, since LaTeX doesn't support them in mathematical expressions.",
        "gt_answers": "f ^ { \\prime } ( x ) > 0\n",
        "image_path": "./data/HME100K/test_images/test_3146.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n$$ E = mc^2 $$\n\nwhere $E$ is the energy of the object, $m$ is the mass of the object, and $c$ is the speed of light in a vacuum.\n\nThis formula is known as the mass-energy equivalence formula, which states that the energy of an object is equal to its mass times the speed of light squared.",
        "gt_answers": "O B = B D = C D = O C\n",
        "image_path": "./data/HME100K/test_images/test_3147.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed as:\n\nA = \u03c0r^2A = \\pi r^2A=\u03c0r2where r is the radius of the circle.\n\nTo write out the formula in LaTeX format, you can use the following code:\n\n$$A = \\pi r^2$$$A = \\pi r^2$$$A=\\pi r^2To display the formula in MathJax, you can use the following code:\n\n$$A = \\pi r^2$$$A = \\pi r^2$$$A=\\pi",
        "gt_answers": "2 N O + O _ { 2 } \\rightarrow 2 N O _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3148.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format.\n\nThe expression in the image is: \ud835\udc5f\ud835\udc4e4 + \ud835\udc5f\ud835\udc4e2\ud835\udc5f\ud835\udc4e2 + \ud835\udc5f\ud835\udc4e2 = \ud835\udc5f\ud835\udc4e\ud835\udc5f\ud835\udc4e4 + 2\ud835\udc5f\ud835\udc4e2\ud835\udc5f\ud835\udc4e2\ud835\udc5f\ud835\udc4e2 = 2\ud835\udc5f\ud835\udc4e",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$\\frac{a \\times b \\times c \\times d \\times e}{f}$$where a, b, c, d, e, and f are numbers.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n$$ m = \\frac{2mg}{v^2} $$\n\nwhere $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $v$ is the velocity of the object.\n\nThe formula states that the mass of an object is proportional to the square of its velocity divided by the acceleration due to gravity. In other words, if the velocity of an object is increased, its mass will also increase, but only if the acceleration due to gravity remains constant.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is:\n\n$$ \\frac{a}{b} + \\frac{c}{d} = \\frac{(a+c)}{(b+d)} $$\n\nThis is a simple expression for finding the sum of two fractions with unlike denominators.",
        "gt_answers": "\\frac { I _ { 1 } } { I _ { 2 } } = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3153.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: $\\frac{5+8}{2}$\\cdot$\\frac{4-3}{1}$\\cdot$\\frac{2-1}{1}$\\cdot$\\frac{9-5}{4}$\\cdot$\\frac{6-3}{2}$\\cdot$\\frac{8-5}{4}$\\cdot$\\frac{7-3}{1}$\\cdot$\\frac{4-1}{1}$\\cdot$\\frac{6-1}{2}$\\cdot$\\frac{9-1}{4}$\\cdot$\\frac{7-1}{2}$\\cdot",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n(Image)x=y+10x2\\frac{x}{y+10}x2\u200bwhere x and y are variables.",
        "gt_answers": "x _ { 2 } = - \\frac { \\sqrt { 1 0 } \\cdot } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3157.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{a^2 + 6b^2}{12}$.\n\nHere's how to derive the expression:\n\nThe given expression is $\\frac{4a^2 + 20b^2}{5}$. To simplify this expression, we can factor out 5 from the numerator and denominator:\n\n$\\frac{5(a^2 + 4b^2)}{5} = \\frac{a^2 + 4b^2}{1}$\n\nNext, we can cancel out the common factor",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is y = (a / x) + b.\n\nGiven the equation, the slope of the line is a / x. Since the equation is in slope-intercept form, the y-intercept is b. To find the x-intercept, we set y = 0 and solve for x:\n\n0 = (a / x) + b\nx = (a / a) + b / a\nx = 1 + b / a\n\nTherefore, the x-intercept is 1 + b / a. The equation passes through the point (",
        "gt_answers": "\\frac { 1 } { x + y } = a\n",
        "image_path": "./data/HME100K/test_images/test_3160.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written in LaTeX format would be: $\\frac{1}{2}(x + 4) - \\frac{1}{3}(y - 2) + 5 = \\frac{11}{3}$",
        "gt_answers": "- \\frac { 1 } { 2 } x + 4\n",
        "image_path": "./data/HME100K/test_images/test_3161.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{6364}{2058 + 6428} - \\frac{4626}{6826 + 2366}$",
        "gt_answers": "( 5 3 9 ) - ( 4 6 7 ) = ( 7 2 )\n",
        "image_path": "./data/HME100K/test_images/test_3162.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\begin{aligned}\n\\frac{2x^2 + 2x - 5}{x - 1} = \\frac{2x^2 + 2x + 3x - 5}{x - 1}\n\\end{aligned}$$",
        "gt_answers": "2 R = \\frac { b } { C M B } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3165.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$ 4 \\cdot 3 + 5 = 14 $\n\n$ 14 \\cdot 5 + 6 = 35 $\n\n$ 35 \\cdot 4 + 7 = 83 $\n\n$ 83 \\cdot 3 + 8 = 105 $\n\n$ 105 \\cdot 5 + 9 = 369 $\n\n$ 369 \\cdot 6 + 10 = 2169 $\n\n$",
        "gt_answers": "C = \\sqrt { 1 6 - 4 } = 2 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3166.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression for the derivative of a function with respect to x. The expression is dy/dx, which represents the rate of change of y with respect to x. The function is a simple polynomial function with a constant term of 2 and a variable term of x^2.",
        "gt_answers": "P C = B C - B P ^ { \\prime } = 1 6 -\n",
        "image_path": "./data/HME100K/test_images/test_3167.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n$$6\\times5\\times2 + 8 + 9 + 2 + 7 = 44$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is:<br> \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "4 u + 6 v = 3\n",
        "image_path": "./data/HME100K/test_images/test_3169.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is not specified. Can you provide the image?",
        "gt_answers": "x = - \\frac { 5 } { 1 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3170.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n\\begin{center}\n\\frac{5}{12} + \\frac{35}{12} = \\frac{87}{12}\n\\end{center}\n\nwhere the fraction 5/12 represents the numerator and 35/12 represents the denominator. The sum of these fractions is 87/12, which is the result of the image.",
        "gt_answers": "\\frac { 2 5 } { 3 5 } > \\frac { 2 4 } { 4 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3171.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is:$$m\\_n = \\frac{1}{2}\\left(\\frac{1}{2} + \\frac{1}{4}\\right) - \\frac{1}{4}\\left(\\frac{1}{4} + \\frac{1}{8}\\right)$$The equation can be rearranged as follows:$$m\\_n = \\frac{1}{2}\\left(1 - \\frac{1}{4}\\right) - \\frac{1}{4}\\left(1 - \\frac{1}{8}\\right)$$Alternatively, we can use the",
        "gt_answers": "\\frac { C N } { M N } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3172.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, you would use the following code: $\\frac{x^2 + 4x - 3}{x - 1} $. This is the same formula as the one provided in the previous answer. The only difference is that the variable x is denoted using the letter x with a caret on top, which is the standard notation for variables in LaTeX.\n\nHere is how the formula would look like in LaTeX format: $\\frac{x^2 + 4x - 3}{x - 1} $.\n\nIn this formula, the variable",
        "gt_answers": "x = \\frac { 2 } { 3 } \\times \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3173.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is \\frac{a^2 + b^2}{2ab}.",
        "gt_answers": "y = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3174.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The expression for the formula in the image using LaTeX format is: 150\\*0.0012+0.0012\\*0.021. This formula is used to calculate the time it takes for an object to fall to the ground from a certain height. The first term in the formula represents the time it takes for the object to fall from rest to half of its initial velocity, while the second term represents the time it takes for the object to fall from half of its initial velocity to the ground.\n\nIn LaTeX format, the",
        "gt_answers": "F _ { m } = 1 0 0 0 N = F _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3175.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$x + 2 = 5$$\n\nTo solve for x, we can subtract 2 from both sides of the equation:\n\n$$x = 5 - 2$$\n\nSimplifying the right side, we get:\n\n$$x = 3$$\n\nTherefore, the value of x is 3.",
        "gt_answers": "a + b = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3176.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{16}\\sum\\_{i=1}^{16}\\sum\\_{j=1}^{8}\\sum\\_{k=1}^{4}\\sum\\_{l=1}^{2}x\\_{i}y\\_{j}z\\_{k}w\\_{l}$.",
        "gt_answers": "A D / / B C\n",
        "image_path": "./data/HME100K/test_images/test_3178.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n\\begin{center}\n$ x^2 + 2x - 10 = 0 $\n\\end{center}\n\nThis is a quadratic equation in the form of $ ax^2 + bx + c = 0 $ where $ a = 1, b = 2, c = -10 $. To solve this equation, we can use the quadratic formula:\n\n\\begin{center}\n$ x = \\frac{-b \u00b1 \u221a(b^2 - 4ac)}{2a}",
        "gt_answers": "1 \\div 2 0 = \\frac { 1 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3179.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$ \\text{bc}\\_{002} $$\n\nwhere bc002 represents the given image.",
        "gt_answers": "B C = \\vert 2 - 0 \\vert = 2\n",
        "image_path": "./data/HME100K/test_images/test_3180.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear. Please provide a clear and legible formula for me to write it out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image can be written as:\n\n\\frac{2x + 3y - 5}{x + 2y + 3}\n\nwhere x and y are variables.",
        "gt_answers": "1 - \\frac { 1 } { 4 } = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3182.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:\n\n\\frac{1}{2} \\* 10 - \\frac{1}{4} \\* 3 + 1 = 5\n\nwhere,\n\n* 10 represents the number of squares in the first row\n* 3 represents the number of squares in the second row\n* 1 represents the number of squares in the third row.",
        "gt_answers": "\\frac { 8 } { 1 4 } \\textcircled { > } \\frac { 9 } { 2 1 }\n",
        "image_path": "./data/HME100K/test_images/test_3183.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by:\n\nx^4 + 5x^3 + 9x^2 + 11x + 7\n\nTo factor the polynomial, we can use the distributive property of multiplication over addition and the commutative property of addition.\n\nFirst, we factor the first and second terms:\n\nx^4 + 2x^3 + 3x^2 + 3x + 1\n\nNext, we factor the third and fourth terms:\n\n(x^2 + x) + 2(x + 1)",
        "gt_answers": "\\frac { 2 x } { 3 } = \\frac { 4 x - 8 } { 9 } - 5\n",
        "image_path": "./data/HME100K/test_images/test_3184.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image given is: y = x + 1.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\text{y}=\\frac{x^2+3x-5}{x+2}$$",
        "gt_answers": "x = \\frac { 1 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3187.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX formula for the expression shown in the image:\n\n$$\\frac{1000 \\times 400 + 2000 \\times 300}{1000 + 2000} = \\frac{120,000 + 200,000}{120,000 + 200,000} = \\boxed{160,000}$$\n\nI hope this helps! Let me know if you have any further",
        "gt_answers": "\\frac { 4 } { x ^ { 2 } - 4 } = 1 - \\frac { 1 } { x + 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3188.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image appears to show a mathematical expression written in LaTeX format. The expression is an equation involving the exponential function, exponential functions, and trigonometric functions. The equation is as follows:$$y = \\frac{2x^2 - 4x + 5}{x^2 - 4x + 3}$$This equation can be simplified to the form:$$y = \\frac{2x - 1}{x - 1}$$This is a standard form for an exponential function with a center of x = 1 and a slope of m = 2.",
        "gt_answers": "\\frac { C D } { C E } = \\frac { D O } { B O . }\n",
        "image_path": "./data/HME100K/test_images/test_3189.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 1 + 4 \u00d7 2 \u00d7 3 \u00d7 4 \u00d7 5 \u00d7 6 \u00d7 4 \u00d7 2 \u00d7 1 = 24. This can be written using LaTeX format as: $\\left(1 + 4 \\times 2 \\times 3 \\times 4 \\times 5 \\times 6 \\times 4 \\times 2 \\times 1\\right) = 24$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the region enclosed by the graph of y = x^2 from x = 1 to x = 3 is given by the integral of the area of the region under the curve from x = 1 to x = 3. The area of this region is given by the integral of the product of dx and dy over the region from x = 1 to x = 3, which is \u222b\u222b(1,3) (x^2)dx. Substituting x = 3 into the expression for y, we have y = 9. Therefore, the area of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image can be written as follows:\n\n$$\\begin{aligned} x &= 3.1416 \\\\ y &= 1.4142 \\\\ z &= 1.4142 \\times 3.1416 \\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$x = \\frac{2y}{3}$$\n\nwhere $x$ and $y$ are variables.",
        "gt_answers": "x = 3 \\pm 2 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3193.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{a+b}{c+d}$\n\nNote: This formula is derived from the given image.",
        "gt_answers": "\\lambda : y = k x - 1\n",
        "image_path": "./data/HME100K/test_images/test_3195.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the formula in the image using LaTeX format, you would need to use the LaTeX command `\\frac`.\n\nThe formula would be:\n\n$$\\frac{2x+5}{x^2-6x+8}=\\frac{2x+5}{x^2-11}$$\n\nThis simplifies to:\n\n$$\\frac{2x+5}{x^2-6x+8}=\\frac{2x+5}{x-3}$$\n\nThe left side of the equation is the original formula, and the right side is the simplified formula. The variable `x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is \\begin{aligned} a^2 + b^2 = c^2 \\end{aligned}.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Identify the variables: The variables in the formula are x, y, and z.\n2. Write the formula in LaTeX format: The formula is xy + yz.\n3. Replace the variables with their corresponding symbols: The symbols for x, y, and z are x, y, and z, respectively. Therefore, the formula in LaTeX format is xy + yz.\n4. Write the equation with the variables in parentheses: The equation is (xy + yz).",
        "gt_answers": "\\frac { 1 6 } { 6 8 } = \\frac { 4 } { 1 8 }\n",
        "image_path": "./data/HME100K/test_images/test_3198.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{\\sqrt{3}}{2}\\left(\\frac{2x+3y}{x^2+y^2}\\right) \\times \\frac{6z-4}{z^2+9z-12}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the number of integers that can be expressed as a sum of 4 and 5 is:535=105+535535=105+535535=105+535535=105+535535=105+535535=105+535535=105+535535=105+535535=105+535535=105",
        "gt_answers": "3 + 2 \\sqrt { 2 } P Q = 3 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3202.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "y _ { 4 } = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3204.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{aligned}\n\\frac{2000 + 100 \\* 5}{1000 + 500} &= \\frac{2000 + 500}{1000 + 500} \\times \\frac{100}{100} \\\n&= \\frac{2500}{1500} \\\n&= \\boxed{1}\n\\end{aligned}",
        "gt_answers": "0 : 2 0 0 = \\frac { 1 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3206.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:$$\\frac{a+b}{2}$$This is the formula for the average of two numbers, a and b. It is calculated by adding the two numbers together and dividing by 2. The result is an arithmetic mean, which is a number that represents the center of a dataset.",
        "gt_answers": "P _ { ( A ) } = 1 - \\frac { 4 } { 5 } = \\frac { 5 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_3207.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX format for the expression:\n\n\\begin{align} \\frac{64 - 4x^2}{9} = \\frac{64 - 4(x + 4)(x - 4)}{9} \\end{align}\n\nThe image shows a function with a hole at the bottom of the parabola. To find the derivative of this function, we can use the power rule of differentiation, which states that the derivative of a function f(x) = x^n is f'(x) = nx^(n-1). We can",
        "gt_answers": "\\frac { 2 } { 3 } : 8 = \\frac { 1 } { 2 } : 6\n",
        "image_path": "./data/HME100K/test_images/test_3208.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is: \\frac{b + \\frac{a}{c}}{d} - \\frac{c}{d}.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is $\\frac{a}{b} - \\frac{c}{d}$.",
        "gt_answers": "S _ { \\Delta A D B } = 3\n",
        "image_path": "./data/HME100K/test_images/test_3210.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not shown, as the image does not have any mathematical expression.\n\nHowever, assuming the image represents a function f(x), the formula for the derivative of the function f(x) with respect to x can be written as:",
        "gt_answers": "a = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3211.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$x^{2} + 2x + 1 = (x + 1)(x + 1)$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a graph with three points: x1, y1, and x2, y2. The equation of the line passing through these points is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The equation of the line can be written as y = (0.5)(0.8)x + 3, where 0.5 is the slope of the line and 3 is the y-intercept.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the region bounded by the curves y = x\u00b2 and y = x\u00b3 can be found by calculating the integral of the product of the two curves over the region. The region is the triangle with vertices at the points (0, 0), (0, 1), and (1, 0). Using the definite integral, we have:\n\n\u222b\u222b[0,1]y\u00b2(x)y\u00b3(x)dx=\u222b[0,1]x\u00b2(x)dx\u00d7\u222b[0,1]x\u00b3(x)dx=13[0,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is f(x) = x^2 + 3x - 4. This can be written in LaTeX format as follows:\n\n$$f(x) = x^2 + 3x - 4$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the area of a right triangle, which is: A = (b / 2) \\* h, where b is the base of the triangle and h is the height.",
        "gt_answers": "- 3 a ^ { 2 } - \\frac { 4 8 } { 2 5 } + 3 = 0\n",
        "image_path": "./data/HME100K/test_images/test_3218.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: x = (3y + 5z) / 2 \\* (x - 2y) - 5z.",
        "gt_answers": "x + y = - 6\n",
        "image_path": "./data/HME100K/test_images/test_3219.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is $\\frac{1}{a} + \\frac{1}{b} + \\frac{1}{c}$.",
        "gt_answers": "r A = 1 6\n",
        "image_path": "./data/HME100K/test_images/test_3220.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n\\begin{center}\n$$\\text{Width} = \\frac{\\text{Height}}{\\text{3}}$$\n\\end{center}\n\nThis formula states that the width of an object is equal to the height of the object divided by 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{Image Content} = \\frac{a \\times h}{400} + \\frac{f}{256} $$\n\nwhere $a$ is the amplitude of the pixel values, $h$ is the height of the image in pixels, $f$ is the frequency of the pixel values, and $400$ and $256$ are constants that depend on the specific implementation of the formula.",
        "gt_answers": "D A H = 4 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3222.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is given by the equation:\n\n<img src=\" \">\nwhere the variables x and y are given by the following equations:\n\nx = 3y + 2\ny = x - 5",
        "gt_answers": "x - 2 y = 0\n",
        "image_path": "./data/HME100K/test_images/test_3224.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I cannot see the image you provided. Please provide a clear and legible image so that I can assist you.\n\nOnce I have the image, I can write out the expression of the formula in LaTeX format as follows:\n\n\\begin{equation}\n\\frac{x^2 - 4x + 2}{x - 2} = \\frac{A}{B}\n\\end{equation}\n\nwhere $A = x^2 - 4x + 2$ and $B = x - 2$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe formula is given by:\n\ny = 2x + 1\n```",
        "gt_answers": "y = \\frac { \\dot { 8 } + 2 y } { 4 } + 1\n",
        "image_path": "./data/HME100K/test_images/test_3226.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{x+y}{2}$. This formula calculates the average of two numbers, x and y. To find the average, you add x and y and divide by 2.",
        "gt_answers": "x _ { 3 } = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3228.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{x + 2}{3x - 2} = \\frac{x}{3x - 2}$$\n\nThe solution is x = 1.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "y _ { 1 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_3230.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b \u222b \u222b (x 2 + 3x + 5) dx = ( \u222b \u222b x 2 + 3x + 5 dx ) + ( \u222b \u222b x 2 + 3x + 5 dx ) + ( \u222b \u222b x 2 + 3x + 5 dx ) + C\n\nwhere C is the constant of integration, which can be evaluated by applying the fundamental theorem of calculus.\n\n\u222b \u222b \u222b (x 2 + 3x + 5) dx",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \u222b[a, b]f(x)dx.",
        "gt_answers": "\\frac { b } { a } < 1\n",
        "image_path": "./data/HME100K/test_images/test_3234.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image can be written as:\n\n$$\\frac{a+b}{c+d} = \\frac{a-b}{c-d}$$\n\nwhere a, b, c, and d are any real numbers. This equation is known as the substitution method of algebraic fractions. It states that if we add or subtract the same nonzero number from both the numerator and denominator of a fraction, then the fraction remains unchanged.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression. The expression is written in LaTeX format as: $\\frac{1}{4}\\pi \\times \\frac{1}{2}r^2$.",
        "gt_answers": "\\angle 4 = \\angle 6 = \\angle B P\n",
        "image_path": "./data/HME100K/test_images/test_3236.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by $\\mathrm{A=}^{2}\\pi\\mathrm{r}^{2}$where A is the area of the circle and r is the radius of the circle.\n\nNow, let's use this formula to solve the given problem:\n\nGiven that $x$ is the diameter of the circle, we have $x=2r$. Substituting this into the formula for the area, we get:\n\nA=\u03c0r2=\u03c0(2r)2=4\u03c0r2\\begin{aligned}\nA &=",
        "gt_answers": "A P ^ { 2 } + B P ^ { 2 } = A B ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3237.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows an expression for the formula of a rectangle with a perimeter of 12 cm and an area of 9 cm. The formula is: Perimeter = 2 \\* (length + width) and Area = length \\* width. The perimeter of the rectangle is 12 cm and the area is 9 cm. The length is 4 cm and the width is 3 cm. Therefore, the perimeter is 8 cm and the area is 12 cm.",
        "gt_answers": "A P _ { 5 } = \\frac { 6 \\times 5 } { 2 } = 1 5\n",
        "image_path": "./data/HME100K/test_images/test_3238.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I can't see the image you provided. Can you please give me the formula?",
        "gt_answers": "0 . 9 8 = \\frac { n ^ { 2 } } { n ^ { 2 } \\pm 1 }\n",
        "image_path": "./data/HME100K/test_images/test_3240.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Can you please upload it to a public platform so that I can see it?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $ 4x^2 - 9x + 2x + 4 $.\n\nThe steps to derive this formula are:\n\n1. Simplify the expression 4(x+2)2 by completing the square:\n4(x+2)2 = 4(x^2 + 4x + 4)\n4(x+2)2 = 16x^2 + 12x + 16\n2. Factor the expression:\n16x^2 + 12x +",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the derivative of a function f(x) with respect to x, denoted by f'(x). The formula is written as: 12\\*3x^4\\*3x^2. This formula represents the slope of the tangent line to the graph of f(x) at a given point x. The slope is calculated by taking the derivative of f(x) with respect to x, which gives the slope of the tangent line at that point.\n\nThe formula is written in LaTex format, which is a typesetting system used for mathematical and scientific writing.",
        "gt_answers": "y ^ { 2 } - 6 y + ( 1 + 4 k ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_3244.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{aligned}\nx^2 - 4x + 4 &= 0 \\\n\n\\frac{x^2 - 4x + 4}{x - 2} &= \\frac{1}{x - 2} \\\n\n(x - 2)^2 &= 1 \\\n\nx - 2 &= \\pm \\frac{1}{2} \\\n\nx &= 2 \\pm \\frac{1}{2} \\\n\nx &= 2 \\pm 1 \\\n\nx &= 1 \\\n\nx &= 1 \\",
        "gt_answers": "- \\frac { b } { a } = - \\frac { 5 } { a } = 5\n",
        "image_path": "./data/HME100K/test_images/test_3246.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{5555 - 4444}{22}$.\n\nNote: The expression is written in LaTeX format, with the numerator and denominator separated by a forward slash (/) and the division symbol written as a fraction.",
        "gt_answers": "2 3 \\div 2 5 = \\frac { 2 3 } { 2 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3247.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a formula for a projectile motion problem, which can be written as:\n\n$$d = vt + \\frac{1}{2}gt^2$$\n\nwhere $d$ is the displacement of the projectile, $v$ is the initial velocity, $t$ is the time, and $g$ is the acceleration due to gravity.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image you provided does not contain any mathematical expression. It appears to be a piece of paper with some text written on it. To write out the expression of a formula in LaTeX format, you will need to provide a mathematical expression that can be written in LaTeX. Can you please provide a mathematical expression for me to write out in LaTeX format?",
        "gt_answers": "\\arccos x ( - 1 0 , \\pi )\n",
        "image_path": "./data/HME100K/test_images/test_3249.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$\\frac{x+y-z}{x-y}$.",
        "gt_answers": "x = \\frac { 5 } { 3 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3251.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the formula for finding the area of a circle:\n\nA = (\u03c0r^2)\n\nwhere A is the area, r is the radius, and \u03c0 is the constant value 3.14159. To calculate the area, you simply multiply the radius by itself. For example, if the radius of the circle is 5 cm, the area would be:\n\nA = (\u03c0r^2) = (3.14159 x 5^2) = 78 539.816 cm^2\n\nThis is the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I'm not able to see the image as it is not provided. Can you please provide the image so that I can assist you with the expression of the formula in LaTeX format?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{120 \\* 4} + \\frac{\\text{180}}{\\text{3}}$$\n\nwhere the variables are represented using the \\* symbol.",
        "gt_answers": "\\angle E K G = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3254.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as follows: x(y + z) - y = 2xz. This is the equation of a line in two variables with slope 2 and y-intercept 2z.",
        "gt_answers": "\\frac { x ^ { 2 } } { 3 } + \\frac { y ^ { 2 } } { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3256.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression for the formula in the image using LaTeX format:\n\n$$ \\frac{4 + 5 \\cdot 2}{6} = \\frac{13}{6} = \\frac{23}{12} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$ 2y + 3x = 9 $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{ImageContent} $$",
        "gt_answers": "3 + 5 + 6 = 1 4\n",
        "image_path": "./data/HME100K/test_images/test_3259.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by the formula:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a system of linear equations in two variables with the variable b and c being the coefficients of x and y, respectively.\n\na + bx + cy = 3xy + 2bx + 2cy\n\nbx + cy = ax + 2bx + 2cy\n\nThe solution to the system of equations is found by solving for x and y in terms of a and c:\n\nx = (2c - a) / (b + 2c)\n\ny = (a - 2c) / (b + 2c)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\ny & = 3x^2 + 2x - 4 \\\n\\end{align\\*}\n\nThis is the quadratic equation in standard form, where the coefficients of the variable x are 3 and 2, and the constant term is -4. The solution to the equation is found by completing the square, which gives:\n\n\\begin{align\\*}\ny & = 3x^2 + 2x + 8 - 4 \\\n\\end{align\\",
        "gt_answers": "x = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3262.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{1}{x^2}$where x is a variable.",
        "gt_answers": "x > \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3263.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the following LaTeX expression: $\\frac{x^2 - 5x + 8}{x - 2}$. This formula can be used to find the roots of the quadratic equation $ax^2 + bx + c = 0$, where $a = 1$, $b = 5$, and $c = 8$.",
        "gt_answers": "x + \\frac { 1 } { 4 } = \\frac { 4 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3264.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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:",
        "gt_answers": "\\frac { B E } { B F } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3265.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{PV} = \\frac{1}{2}\\rho v^2$$\nwhere $\\rho$ is the density of the fluid and $v$ is the velocity of the fluid.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 10 + 4\\*5 + 3 = 37. This is the sum of the expressions 10 and 4\\*5, with the addition of 3 at the end.\n\nTo write this in LaTeX format, you can use the following code:\n\n\\begin{align}\n10 + 4\\*5 + 3 &= 37 \\\n\\end{align}\n\nThis will produce the equation with the correct syntax for LaTeX.",
        "gt_answers": "x = \\frac { 2 0 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3267.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n$$5 \\times 3 + 3 = 15 + 3 = 18$$\n\nThis is a mathematical expression that represents the result of multiplying 5 by 3, adding 3, and then adding the result to 15 to get 18.",
        "gt_answers": "\\frac { 5 } { 8 } = \\frac { 2 5 } { 4 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3268.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation shown in the image is: $\\frac{1}{4} - \\frac{1}{2} + \\frac{3}{8} = \\frac{5}{8}$",
        "gt_answers": "8 \\div 5 = \\frac { 8 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3270.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:\n\n$$\\begin{aligned} \\text{Kh\u00f4ng} &= \\text{Kh\u00f4ng} + \\text{Kh\u00f4ng} \\end{aligned}$$\n\nwhere Kh\u00f4ng is the capital of Vietnam.",
        "gt_answers": "\\frac { 5 } { 4 } > \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3271.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the sum of the first n positive integers can be written as follows:$\\sum\\_{i=1}^{n} i=\\sum\\_{i=1}^{n} i2$This formula states that the sum of the first n positive integers is equal to the sum of the squares of the first n positive integers. The formula can be derived by using the formula for the sum of an arithmetic series, which is given by$\\sum\\_{i=1}^{n} ai=n\\frac{a}{2}$where a is the first term of the series and n is the number of terms. For the",
        "gt_answers": "y _ { 2 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3272.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a diameter of 4 cm is given by:\n\nA = \u03c0r^2, where r is the radius of the circle.\n\nThe formula for the volume of a sphere with a diameter of 4 cm is given by:\n\nV = 4/3\u03c0r^3, where r is the radius of the sphere.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$x = \\frac{a\\*b\\*c}{d}$$where $a$, $b$, $c$, and $d$ are constants.\n\nTo represent this equation in LaTeX format, you can use the following code:$$x = \\frac{a}{b} + \\frac{c}{d}$$Note that the division symbols are represented by the forward slash ($/$), and the multiplication symbols are represented by the asterisk (\\*). The constants $a$, $b$, $c$, and $d$ should be replaced with",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is given by:\n\n$$ \\frac{x+y+z}{x+y+z} = \\frac{600+800+400}{600+800+400} = \\frac{1400}{1600} = \\frac{1}{1} $$",
        "gt_answers": "6 0 0 \\times \\frac { 2 } { 3 } = 4 0 0\n",
        "image_path": "./data/HME100K/test_images/test_3275.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: 3x + 4y = 14xy + 6y = 14x2y = 14xy2 + 4y = 14xy2 + 4x2 + 2y = 14x2 + 4x2 + 2y = 14x + 4x2 + 2y = 14x + 4xy + 2y = 14x + 4xy + 2y = 14x + 4x2 + 2y =",
        "gt_answers": "\\frac { 1 } { a } < \\frac { 1 } { b }\n",
        "image_path": "./data/HME100K/test_images/test_3277.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX format for the formula in the image:\n\n$$\\frac{3x + 2y}{x + y}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:<br>\u222b(0, a) f(x) dx = (b)f(a) - f(0)<br>\u222b(a, b) f(x) dx = \u222b(0, b) f(x) dx + f(a)(b - 0)<br>\u222b(b, c) f(x) dx = \u222b(a, c) f(x) dx + f(b)(c - b)<br>\u222b(c, d) f(x) dx = \u222b(b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 1/3 \\* x^2 + 4x - 5. This can be written in LaTeX format as $\\frac{1}{3}x^2 + 4x - 5$.",
        "gt_answers": "y = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3280.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a linear function of the form y = mx + b, where m is the slope and b is the y-intercept. The slope of the line is -1/2, and the y-intercept is 3. To find the equation of the line, we can use the point-slope form of the equation:\n\ny - y1 = m(x - x1)\n\nwhere (x1, y1) is a point on the line. Substituting the given point (2, -5) into the equation, we get:\n\ny -",
        "gt_answers": "\\frac { 1 2 } { 1 6 } = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3281.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$ \\text{RMS} = \\frac{\\sqrt{\\frac{1}{N}\\sum\\_{i=1}^N\\left(\\frac{x\\_i - \\mu}{\\sigma}\\right)^2}}{\\sqrt{\\frac{1}{N}\\sum\\_{i=1}^N\\left(\\frac{x\\_i - \\mu}{\\sigma}\\right)^2}} $$\n\nwhere N is the number of data points, x\\_i is the i-th data point, $\\mu$ is the mean of the data points,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{1+x^2}$. This is the formula for the quadratic function, which is y = ax^2 + bx + c. In this case, the constant term c is zero and the coefficients a and b are 1 and -1, respectively.",
        "gt_answers": "x _ { 2 } = \\frac { 1 + \\sqrt { 1 0 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3283.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{x^2 + 2x - 4}{x - 2}$$\n\nThe equation in the image is a quadratic equation in the form of:\n\n$$ax^2 + bx + c = 0$$\n\nwhere $a = 1$, $b = 2$, and $c = -4$. Solving for the roots of the equation gives us:\n\n$$x = \\frac{-b \u00b1 \u221a(b^2 - 4ac)}{2a}$$\n\nPlug",
        "gt_answers": "3 : 1 . 5 = 4 : 2\n",
        "image_path": "./data/HME100K/test_images/test_3285.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a blackboard with the formula written in white chalk: $\\frac{a^2 + b^2}{2ab}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is x^2 - 3x + 5 = 0, which can be rewritten as x^2 - 3x = 5.",
        "gt_answers": "x = - \\frac { 1 2 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_3288.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: x2 + 3x - 10 = 0.",
        "gt_answers": "( 6 0 - 2 0 ) \\div \\frac { 4 } { 3 } = 3 0\n",
        "image_path": "./data/HME100K/test_images/test_3289.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$2x + 5 = 10$$To solve for x, we can isolate x on one side of the equation:$$2x + 5 = 10 \\rightarrow 2x = 10 - 5$$Substituting this value back into the equation, we get:$$2(10 - 5) + 5 = 10 \\rightarrow 15 + 5 = 20$$Therefore, the solution to the equation is x = 5.",
        "gt_answers": "x ^ { 2 } + y ^ { 2 } \\geq \\frac { 4 } { 2 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3290.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is written as: $\\frac{1}{2}$x + $\\frac{1}{4}$y = $\\frac{1}{4}$z.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n$m = \\frac{b}{a}$\n\nwhere $m$ is the image's mass, $b$ is the buoyant force acting on the image, and $a$ is the acceleration of gravity.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression involving the square root and trigonometric functions. The expression is given by:\n\nsqrt(3 + 4tan^2x)\n\nThis expression can be written in LaTeX format as:\n\n$\\sqrt{3 + 4\\tan^2x}$\n\nIn this expression, the square root function is applied to the expression 3 + 4tan^2x, which represents the difference between 3 and 4 times the square of the tangent of x. The tangent of x is a trigonometric function that varies with x, and its square is",
        "gt_answers": "\\frac { 1 } { 2 } m + 3 = 1\n",
        "image_path": "./data/HME100K/test_images/test_3293.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n 2x^2 + 2 = 10\n\\end{align\\*}\n\nThis formula is derived from the given expression by adding 2 to both sides of the equation and eliminating the x term on the left side.",
        "gt_answers": "\\frac { 1 } { 2 } x = - 2\n",
        "image_path": "./data/HME100K/test_images/test_3294.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given image:\n\n\\begin{align\\*}\n\\text{ImageContent} = \\frac{3\\left(x^2+y^2\\right)-r^2}{2xy}\n\\end{align\\*}\n\nThis formula represents a circle with center at the point $(x,y)$ and radius $r$.",
        "gt_answers": "x _ { 2 } = - \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3296.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$\\frac{a}{b}+\\frac{b}{c}+\\frac{c}{d}+\\frac{d}{e}+\\frac{e}{f}=x$\n\\end{center}\n\nwhere a, b, c, d, e, and f are the numerical values of the variables in the image, and x is the sum of the fractions.",
        "gt_answers": "t _ { 1 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_3298.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation shown in the image is:\n\n\u222ba&#x00D7;b f(x) dx = F(b) - F(a)\" role=\"presentation\">\u222ba\u226ab f(x) dx = F(b)\u2212F(a)\u222ba\u226ab f(x) dx = F(b)\u2212F(a)\\int\\_{a}^{b} f(x) dx = F(b) - F(a)\u222ba\u200bb\u200b f(x) dx = F(b)\u2212F(a)\n\nwhere F(",
        "gt_answers": "\\angle B = \\angle D = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3299.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is given by:\n\n$$\\text{ImageContent} = \\text{Black Hole}$$\n\nIn LaTeX format, this equation would be written as:\n\n$$\\text{ImageContent} = \\text{Black Hole}$$",
        "gt_answers": "y _ { 1 } = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3300.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n$$\\frac{1}{2}x^2 + \\frac{1}{3}x^3 = \\frac{1}{4}x^4$$\n\nThis formula represents the Taylor series expansion of the function $f(x) = x^4$ about the point $x = 0$. The formula shows that the partial sum of the series is equal to the value of the function at $x = 0$.",
        "gt_answers": "V A = \\frac { f t _ { 1 } } { m A + m B }\n",
        "image_path": "./data/HME100K/test_images/test_3301.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX format for the expression in the image:\n\n\\begin{align\\*}\nx &= \\frac{5}{2} - \\sqrt{2}\\sqrt{3} \\sqrt{5} \\\\\ny &= \\frac{1}{2} + \\sqrt{2}\\sqrt{3} \\sqrt{5}\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{x+3}{x-2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the expression$$C\\_{60}$$where C is a carbon atom and $60$ is the atomic number of carbon. This formula represents the structure of a fullerene, a type of molecule composed of 60 carbon atoms arranged in a sphere. The carbon atoms are bonded together by covalent bonds, forming a hollow sphere with the atoms at the vertices. The formula is a representation of the structure of a fullerene, which is a molecule composed of 60 carbon atoms arranged in a sphere. The carbon atoms are bonded",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n<math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<semantics><mrow><mover accent=\"true\"><mi>x</mi><mo stretchy=\"false\">+</mo></mover><mrow><mi mathvariant=\"normal\">2</mi></mrow></mover></semantics>\n</math>x+22\\_{10}x^2+11\\_{10}x+11\\_{10}",
        "gt_answers": "( 1 - \\frac { 5 } { 9 } ) x = \\frac { 8 } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3305.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Number of ways to choose 3 items from 8 items} = \\frac{8!}{3!5!} = \\frac{8!}{3\\times 5!} = \\frac{8!}{3\\times 5!} = \\frac{8!}{3\\times 5!} = \\frac{288}{15} = \\boxed{18}$$\n\nThis expression uses the factorial notation, where n! is equal to the product of all positive integers up to n. In",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the expression of the formula in the image using LaTeX format:\n\n$$\\begin{aligned} x &= \\frac{a}{b} \\Rightarrow xb = a \\ \\Rightarrow x = \\frac{a}{xb} \\Rightarrow x = \\frac{a}{ab} \\end{aligned}$$",
        "gt_answers": "( x - t _ { 1 } 1 ^ { 2 } = \\frac { 5 } { 1 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3308.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{r} = \\frac{\\text{b}}{\\text{a}} = \\frac{\\text{200 - 125}}{\\text{125 - 87}} = \\frac{35}{58} = 0 \\cdot 58 = 0$$\n\nThis formula calculates the ratio of two ratios, where the numerators are $\\text{b}$ and $\\text{a}$, respectively, and the denominators are $\\text{a}$ and $\\text{b}$,",
        "gt_answers": "R = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3309.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a sum of the squares of the digits in the number 24, which is 42+42+42+42+42=168. In LaTeX format, this can be written as follows:$$\\sum\\_{i=1}^{4} i^2 = 42 + 42 + 42 + 42 + 42 = 168$$In this formula, the sum symbol $\\sum$ indicates the sum of the four terms $i^2$, where $i$ ranges from 1 to 4.",
        "gt_answers": "\\rho = - \\frac { 4 } { 3 } x - \\frac { 8 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3311.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows in LaTeX format:\n\n\\begin{align\\*}\nP = \\frac{1}{n} \\sum\\_{i=1}^n x\\_i\n\\end{align\\*}\nwhere $P$ is the population mean of $x\\_1, x\\_2, \\ldots, x\\_n$, $n$ is the sample size, and $x\\_i$ is the $i$-th observation in the sample.",
        "gt_answers": "7 0 + 0 = 7 0\n",
        "image_path": "./data/HME100K/test_images/test_3312.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression in LaTeX format is: \u222b(x^3 + 2x^2 + 3x + 5)dx.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ff} = \\frac{\\text{g}}{\\text{h}}$$\n\nwhere $\\text{g}$ and $\\text{h}$ are constants that determine the rate of change of the function.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n\u222b \u222b (x^2 + 1) dx + \u222b (2x + 3) dy\n\u222b (x^2 + 1) dx = (x^3/3) + C1\n\u222b (2x + 3) dy = (2x^2/2) + C2\n\nTherefore, the expression is:\n\n[\u222b (x^3/3) + C1] + [\u222b (2x^2/2) + C2]\n\nThis expression is a definite integral that represents",
        "gt_answers": "\\tan A = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3315.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a geometric sequence with initial value x = 2 and common ratio r = 3.\n\nUsing the formula for the nth term of a geometric sequence, we have:\n\na\\_n = a\\_1r^(n-1)\n\nwhere a\\_1 = 2 and r = 3.\n\nSubstituting the values, we get:\n\na\\_3 = 2 \\* 3^2 = 12\na\\_4 = 2 \\* 3^3 = 56\na\\_5 = 2 \\* 3^",
        "gt_answers": "\\frac { 2 } { 3 } [ x - ( - 3 ) ] = \\frac { 2 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_3316.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$ \\frac{900 \\times 1200}{1440 \\times 1200} = \\frac{111.1111}{133.3333} $\n\nThis code produces the following output:\n\n$ \\frac{900 \\times 1200}{1440 \\times 1200} = \\frac{111.1111}{13",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=1.5]\n\\draw[->,black] (0,0) -- (2,0) node[below right] {$x$};\n\\draw[->,black] (0,0) -- (0,2) node[above right] {$y$};\n\\draw[black,fill=white] (1,1) circle (0.5);\n\\draw[black,fill=white] (1,0) circle (0.5);",
        "gt_answers": "1 0 ) - a + c - 2 b\n",
        "image_path": "./data/HME100K/test_images/test_3318.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a mathematical expression that represents the velocity of an object moving through space. The formula is: v = sqrt(2GM/r), where v is the velocity, GM is the mass of the object, and r is the radius of its orbit.\n\nThe formula states that the velocity of an object in space is equal to the square root of the gravitational force of the object (GM) divided by its radius (r). This formula is commonly used in physics to calculate the velocity of an object in space based on its mass and distance from the center of its orbit.",
        "gt_answers": "W _ { a } : W _ { b } : W _ { c } = 1 : 2 : 2\n",
        "image_path": "./data/HME100K/test_images/test_3319.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the equation in the image is:\n\n$$ \\frac{5+6}{3-4}=\\frac{11}{-1}=\\frac{11}{1}=\\boxed{5} $$\n\nwhere the variable x is 5 and the variable y is 6. The equation is in the form of a linear equation with a constant value of 3 on the left side and a variable on the right side. The constant value is subtracted from the variable, resulting in the equation $5-4=1$. The equation is then solved for x by dividing both sides by 1,",
        "gt_answers": "x = - \\frac { 5 5 } { 1 6 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3320.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression can be written as follows in LaTeX format:\n\n$$ \\left( \\frac{4\\times 4+3}{5\\times 5-2} \\right) + 6 $$\n\nwhere the parentheses are used to denote the order of operations and the multiplication and division symbols are used to perform the operations inside the parentheses. The result is 20.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you can use the following code:\n\n$$\\frac{x+4}{x-2}$$\n\nThe formula is the result of dividing x plus 4 by x minus 2. The fraction line can be written in LaTeX format by using the division symbol (`/`), the numerator (x), the denominator (x-2), and the fraction bar (`\\frac`).",
        "gt_answers": "\\frac { 5 } { 8 } \\times 4 = \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3322.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\frac{2x + 4y - 6xy}{x^2 + 4xy + y^2}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Select the image and right-click on it to copy it.\n2. Open a LaTeX editor, such as TeXstudio or Overleaf, and create a new document.\n3. Paste the image into the document.\n4. Use the LaTeX command \\includegraphics{} to insert the image into the document. This command takes two arguments: the first is the file name of the image, and the second is the label for the image.\n5. Write the formula using LaTeX syntax. For",
        "gt_answers": "\\vert - \\frac { 7 } { 1 0 } \\vert = \\frac { 7 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3324.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: $\\frac{a+b}{2}$ $\\frac{a-b}{2}$ $\\frac{a-b}{a+b}$ $\\frac{a+b}{a-b}$ where a and b are the number of heads and tails, respectively, in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:$\\frac{x}{2} + \\frac{y}{3} = \\frac{5}{6}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: f(x) = x^5 - x^4\\*6 + x^3\\*24 - x^2\\*48 + x\\*60 - 50.",
        "gt_answers": "a ^ { 2 } + 2 a - 3 = 0\n",
        "image_path": "./data/HME100K/test_images/test_3327.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the expression is given by:2x+y=4\\x+y=4\\x + y = 4x+y=4x+y=4x+y=42x+y=42x+y=42x+y=42x+y=4where x and y are variables. The equation is an equation of the line passing through the points (0,0) and (4,2).\n\nThe slope of the equation is given by the ratio of the change in y to the change in x. We can find this by substituting",
        "gt_answers": "( 0 = ) - \\frac { a } { 3 } < x\n",
        "image_path": "./data/HME100K/test_images/test_3328.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$x^4 + 6x^3 - 10x^2 + 15x - 5$",
        "gt_answers": "\\cdot x _ { 1 } = \\frac { \\sqrt { 3 a + 3 } } { a + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_3329.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression of the formula in the image:\n\n<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><msub><mi>a</mi><mrow><mi mathvariant=\"normal\">x</mi><mo>=</mo><msub><mi>b</mi><mi>c</mi></msub></mrow></msub></mrow></mmath>",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is:$$\\text{22}\\frac{1}{x}+\\frac{3}{x^2}=\\frac{13}{x}$$",
        "gt_answers": "b \\cos C + c \\cos B = 2 a \\cos A\n",
        "image_path": "./data/HME100K/test_images/test_3331.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ d = \\frac{a^2 + b^2}{2ab} $$\nwhere a and b are the lengths of the sides of the right triangle.",
        "gt_answers": "b _ { n + 1 } = \\frac { 6 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3333.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\text{Area of triangle } \\text{A} = \\frac{1}{2} \\cdot b \\cdot h$$where b is the base of the triangle and h is the height of the triangle.",
        "gt_answers": "( 4 n + 4 ) ^ { 2 } - 1 6 n ^ { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_3336.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length l and width w is given by: A = l \\* w.\n\nFor example, if the length is 12 and the width is 8, the area of the rectangle is 12 \\* 8 = 96.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 4\\sqrt{5}+\\sqrt{2}+\\frac{3}{4}$$",
        "gt_answers": "4 f + g + 5 g - 4 f = 1 2 .\n",
        "image_path": "./data/HME100K/test_images/test_3340.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: m\\_x = (a \\* x^2 + b \\* x + c)/x^3, where a, b, and c are constants.",
        "gt_answers": "D M = A M\n",
        "image_path": "./data/HME100K/test_images/test_3341.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression of the formula in the image:\n\n\\begin{align}\n\\text{Volume of revolution around the x-axis} &= \\int\\_1^2 \\pi y^2 dy \\\\\n&= \\frac{1}{3} \\pi \\left(\\frac{2}{1}\\right)^3 \\\\\n&= \\frac{2\\pi}{3}\n\\end{align}\n\nThis formula calculates the volume of revolution of a solid object around the x-axis, assuming that the cross-sectional area of the object is a circular disk with radius y.",
        "gt_answers": "x = - \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3342.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is not provided in the image. However, it can be written as follows:$$r= \\frac{d}{2t}$$where r is the radius of the circle, d is the diameter of the circle, and t is the time it takes for the circle to roll without slipping.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$r = \\frac{v^2}{2g}$$where v is the initial velocity and g is the acceleration due to gravity.",
        "gt_answers": "\\arcsin \\frac { \\sqrt { 5 } } { 5 } = \\beta\n",
        "image_path": "./data/HME100K/test_images/test_3344.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is as follows:\n\n\\begin{center}\n$ \\frac{dv}{dt} = \\frac{F}{m} $\\\n\\end{center}\n\nwhere\n\n$ v $ is the velocity of the object\n$ F $ is the force acting on the object\n$ m $ is the mass of the object\n\nThis is the equation of motion for an object under the influence of an external force. The force is equal to the change in momentum of the object with respect to time, which is given by the formula:\n\n\\begin{center}",
        "gt_answers": "f = \\frac { 5 } { 3 } n _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3345.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is: $\\frac{50}{100 \\* \\frac{45}{25}}=\\frac{50}{5000 \\* \\frac{9}{16}}=\\frac{50}{450 \\* \\frac{9}{16}}=\\frac{50}{729 \\* \\frac{9}{16}}=\\frac{50}{1080 \\* \\frac{9}{16}}=\\frac{50}{1920 \\* \\frac{9}{16",
        "gt_answers": "y _ { 2 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3347.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written in LaTeX format as follows:\n\n$$ \\begin{aligned} x &= 5 \\\\ y &= 10 \\end{aligned} $$\n\nThe equation represents a linear equation in two variables x and y, where x is equal to 5 and y is equal to 10.",
        "gt_answers": "\\frac { 1 } { 2 } x = 1 0 - 5\n",
        "image_path": "./data/HME100K/test_images/test_3348.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} f(x) &= 2x^2 + 5x - 3 \\\\ &= 2(x + 5) - 3 \\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![Image content](https://i.imgur.com/image_content.png)\n\nThe formula is:\n\n![Image content](https://i.imgur.com/image\\_content.png) = width x height x 100",
        "gt_answers": "\\omega = 1 0 r a d \\cdot l s .\n",
        "image_path": "./data/HME100K/test_images/test_3351.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of the circle with radius r is given by the formula:",
        "gt_answers": "\\frac { 1 } { x - y } = a\n",
        "image_path": "./data/HME100K/test_images/test_3353.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{2^4}{16}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n![Image Content](https://imgur.com/a/5JZ6Q8r)\n\n![Image Content](https://imgur.com/a/5JZ6Q8r)\n\nHere, the function f(x) = 2x + 3 is being integrated with respect to x from x = 0 to x = 3, and the lower limit of integration is being substituted with the function value at x = 3, i.e., f(3) = 12. The upper limit of integration is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{center}\n\\begin{equation}\n\\text{R} = \\frac{\\text{P}}{\\text{t}}\n\\end{equation}\n\\end{center}\n\nWhere:\n\n* R is the resistance of the object\n* P is the power consumed by the object\n* t is the time taken for the object to consume the power\n\nThis formula expresses the relationship between resistance, power, and time in a circuit. The resistance of the object affects the flow of electric current, and",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$\\frac{x+200}{250}$",
        "gt_answers": "2 5 \\times 8 = 2 0 0 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_3358.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by: $\\frac{a}{b}$ where $a$ and $b$ are the lengths of the sides of the triangle. The area of the triangle is given by: $\\frac{a}{2}$ $\\cdot$ $\\frac{b}{2}$ $\\cdot$ $\\frac{c}{2}$ $\\cdot$ $\\frac{1}{2}$ $\\cdot$ $\\frac{1}{2}$ $\\cdot$ $\\frac{1}{2}$ $\\cdot$ $\\frac{1}{2}$ $\\cdot$ $\\frac{1}{2}$ $\\cdot$ $\\frac{1}{",
        "gt_answers": "3 - \\frac { 2 x - 1 } { 5 } = \\frac { x + 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3359.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows an equation for the exponential function f(x) = 4x^3 - 4x^2. The formula is written as: f(x) = 4x^3 - 4x^2.",
        "gt_answers": "x ^ { 2 } - y ^ { 2 } - 4 x + 4 y = 0\n",
        "image_path": "./data/HME100K/test_images/test_3360.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula in the image is: 2x + 3y = 9.\n\nThis formula is a linear equation in two variables, x and y. It represents the line that passes through the point (3, 3) and is parallel to the line that passes through the points (0, 0) and (3, 6). The equation has a slope of 2 and a y-intercept of 3.",
        "gt_answers": "\\times 8 \\times \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3361.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is 2x - 2y + 10.",
        "gt_answers": "\\times \\frac { E C } { A B } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3363.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n&#x336; &#x2205; 3&#x22C5;3 &#x2205; 5&#x22C5;5&#x22C5;5&#x2205; 3\" role=\"presentation\">\u03c3 \u221d 3\u2071 3 \u221d 5\u2071 5\u2071 5\u221d 3\u03c3 \u221d 3\u2071 3 \u221d",
        "gt_answers": "0 . 3 3 m = 3 3 c m\n",
        "image_path": "./data/HME100K/test_images/test_3364.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is given by: $\\frac{1}{\\sqrt{16}} + \\frac{5}{\\sqrt{64}}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:",
        "gt_answers": "3 x - 2 = 1 2 x - 4\n",
        "image_path": "./data/HME100K/test_images/test_3367.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not clear from the given image. It appears to be a mathematical equation, but the variables and values are not specified. To write the formula in LaTeX format, you need to provide the equation, variables, and values.\n\nHowever, assuming the image represents a mathematical equation, the formula can be written as follows:\n\n$$ \\text{f}(x) = \\frac{1}{2}x^2 + 4x - 3 $$\nwhere $x$ is a variable representing the input to the function.",
        "gt_answers": "F G = M h\n",
        "image_path": "./data/HME100K/test_images/test_3368.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Can you please provide the image so that I can assist you in finding the formula?",
        "gt_answers": "y = \\frac { 2 x - 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3369.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b",
        "gt_answers": "3 6 \\times 5 = 1 8 0 c m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3370.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ y = \\frac{a\\*b}{c} $$\n\nwhere a, b, and c are the numbers indicated in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a geometric diagram of a triangle, with sides labeled ` a ',' b ', and 'c'. The length of side ` a'is 4 units, the length of side ` b'is 6 units, and the length of side ` c'is 8 units.\n\nIn LaTeX format, the expression for the area of the triangle would be:\n\n`A= (1/2)ab`\n\nwhere `a` is the length of side ` a'and `b` is the length of side ` b'in the triangle.\n\nSubstituting the given",
        "gt_answers": "k = 5 , b = - 2\n",
        "image_path": "./data/HME100K/test_images/test_3373.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: (5 + 2) \u00d7 4.\n\nHere's the LaTeX format:\n\n\\begin{align}\n(5 + 2) \\times 4\n\\end{align}\n\nThe expression is the product of the sum of 5 and 2, and 4.",
        "gt_answers": "\\frac { 5 } { 3 } x - 1 + \\frac { x } { 3 } = - 4\n",
        "image_path": "./data/HME100K/test_images/test_3376.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{2}{x^2 - 4}$. This is the formula for the quadratic function $y = 2x^2 - 4$. The image shows the graph of this function with its vertex at the origin and its minimum value at $x = -2$.",
        "gt_answers": "\\frac { 2 } { 5 } x = \\frac { 3 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3377.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you can use the following code:\n\n$$\\begin{aligned} \\frac{0.5\\cdot100}{0.8\\cdot0.2} &= 0.5 \\times 100 / (0.8 \\times 0.2) \\\n&= 0.5 \\times 50 / (0.8 \\times 0.04) \\\n&= 0.5 \\times 12.5 / (0.8 \\times 0.04) \\",
        "gt_answers": "9 0 + 9 0 x = 4 0 0\n",
        "image_path": "./data/HME100K/test_images/test_3378.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression of the formula in LaTeX format for the image:\n\n$$\\begin{aligned} \\text{Image Content} \\end{aligned}$$",
        "gt_answers": "9 : 1 2 ) ( 1 2 \\times 9 ) : ( 1 4 \\times 1 ) : ( 1 5 \\times 1 ) = 1 0 8 : 1 4 : 1 3\n",
        "image_path": "./data/HME100K/test_images/test_3379.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{5x^2 - 4xy + 3y^2 + 2xy^2}{x^2 - y^2}$.\n\nHere is the image:\n\n![Image of equation](https://i.imgur.com/KBFjcqK.png)",
        "gt_answers": "\\frac { 1 } { 2 a } = ( \\frac { 1 } { 2 } ) ^ { 2 } + \\frac { 1 } { 2 ^ { 2 } } + \\frac { 1 } { 2 ^ { 4 } } + \\cdots + \\frac { 1 } { 2 ^ { 1 0 0 } } + \\frac { 1 } { 2 ^ { 1 0 1 } }\n",
        "image_path": "./data/HME100K/test_images/test_3380.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the image:\n\n$$\\frac{1}{4} + \\frac{1}{4} + \\frac{1}{4} + \\frac{1}{4} = \\frac{1}{2}$$\n\nIn this formula, the four fractions on the left-hand side represent the four corners of a square, and the fraction on the right-hand side represents the sum of the four corners. The result is that the sum of the four corners is equal to half of a square.",
        "gt_answers": "= \\frac { 4 x - 4 k - 4 } { k + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_3381.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To calculate the probability that an image has a given content, we can use Bayes' formula. Bayes' formula is defined by:\n\nP(A|B) = P(B|A) \\* P(A) / P(B)\n\nwhere P(A) is the prior probability that the image has content A, P(B|A) is the likelihood of the content B given that the image has content A, and P(B) is the prior probability of the content B.\n\nFor this image, let A be the content \"a person standing on a chair\" and",
        "gt_answers": "b ^ { 2 } + c ^ { 2 } \\geq 2 b c\n",
        "image_path": "./data/HME100K/test_images/test_3382.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the formula in the image:\n\n$$\\text{f(x) = \\frac{1}{4}x^2 - \\frac{1}{2}x + 2}$$\n\nThe function $f(x)$ is a quadratic function with a constant term of $2$ and a leading coefficient of $\\frac{1}{4}$. The function has two turning points at $x=-\\frac{1}{2}$ and $x=\\frac{1}{2}$, where the concavity of the parabola changes. The minimum value of the function is",
        "gt_answers": "x \\in [ \\frac { \\pi } { 2 } , \\pi ]\n",
        "image_path": "./data/HME100K/test_images/test_3383.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n\\begin{align\\*}\nf(x) &= \\frac{x^2 - 4x + 3}{x - 1} \\\n&= \\frac{x^2 - 4x + 3}{x - 1} \\\n&= \\frac{x - 1}{x - 1} \\\n&= 1\n\\end{align\\*}",
        "gt_answers": "\\frac { 1 0 } { 1 2 } > \\frac { 9 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3386.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$ 2x + 5 = 14 $$\n\nTo solve the equation, we can substitute 2x with 7, since 2x + 5 = 7 + 5 = 12. Substituting this value in the equation, we get:\n\n$$ 2(7) + 5 = 14 $$\n\nSimplifying the equation, we get:\n\n$$ 14 = 14 $$\n\nThis equation is satisfied for any value of x, so the solution is x = 0",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the provided image does not contain any mathematical expression. Can you please provide a different image or specify what mathematical expression you want to write out in LaTeX format?",
        "gt_answers": "\\angle A B C = 9 0 ^ { \\circ } ,\n",
        "image_path": "./data/HME100K/test_images/test_3388.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of the triangle is given by the following LaTeX expression: $\\frac{1}{2}bh$.\n\nWhere $b$ is the base of the triangle and $h$ is the height of the triangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the given image is $\\text{ImageContent}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\frac{x^2 - 2x + 1}{x - 1}\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "$\\int\\_{-\\infty}^{\\infty}\\frac{\\delta(x)}{x}\\mathrm{dx}$\n\nThis is the indefinite integral of the delta function with respect to x, evaluated over the infinite interval [-\\infty, infinity]. The result is 0.",
        "gt_answers": "\\angle A O D = 9 0 ^ { \\circ } - a\n",
        "image_path": "./data/HME100K/test_images/test_3393.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{1}{2}x^2 + \\frac{1}{4}x - \\frac{1}{8}$$",
        "gt_answers": "\\therefore \\Delta B D E \\sim \\Delta E D O\n",
        "image_path": "./data/HME100K/test_images/test_3394.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is as follows:\n\n$$ \\text{x} + 2 = 12 $$",
        "gt_answers": "S = \\frac { ( 1 + 2 ) \\times 1 } { 2 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3395.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n$$\\frac{1}{4}x^2 + \\frac{3}{2}x - \\frac{1}{4}$$\n\nThis formula is derived from the given image by taking the difference between the sum of the squares of the x-coordinates and half the sum of the x-coordinates, and then dividing by 4.",
        "gt_answers": "x _ { 2 } = 9\n",
        "image_path": "./data/HME100K/test_images/test_3396.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is as follows:\n\n$$\\frac{12+28-36}{4\\times 4}$$\n\nThe expression is obtained by dividing the sum of the four numbers in the image by 4 times 4. The result is 24.",
        "gt_answers": "4 ^ { 3 } = 6 4 4 \\times 3 = 1 2 4 + 4 + 4 = 1 2\n",
        "image_path": "./data/HME100K/test_images/test_3397.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I don't see any image in the prompt. Can you please provide the image so I can assist you?",
        "gt_answers": "1 0 \\times \\frac { 1 } { 5 } x - 2 0 = \\frac { 8 } { 5 } x \\times 2 5 + \\frac { 3 } { 2 5 } \\times 2 5\n",
        "image_path": "./data/HME100K/test_images/test_3398.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by the following LaTeX code:\n\n\\begin{center} $\\frac{a^4 + 4b^2 - 4ab}{2a + 2b}$ \\end{center}\n\nwhere $a$ and $b$ are variables.",
        "gt_answers": "2 y = 4\n",
        "image_path": "./data/HME100K/test_images/test_3399.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The equation in the image can be written as follows using LaTeX format:\n\n$$\\begin{aligned} 10x^2 + 6x - 5 &= 0 \\end{aligned}$$\n\nIn this equation, the variable x is raised to the power of 2, and is multiplied by 10, with a constant term of 6x and a constant term of 5 on the left side. The equation is balanced, so the equation is satisfied when x = - 2, which is the only solution that satisfies the equation.\n\nAlternatively, we can",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3400.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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 + 4x - 4.\n\nIn LaTeX format, this is written as: $4x^2 + 4x - 4$",
        "gt_answers": "y = 4\n",
        "image_path": "./data/HME100K/test_images/test_3401.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n\\begin{center} 5 + 5i \\end{center}\n\nwhere i is the imaginary unit, defined as the square root of -1. The expression represents a complex number with real part 5 and imaginary part 5i.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is $\\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. For this triangle, we have $b = 5$ and $h = 7$, so the area is $\\frac{1}{2}5(7) = 12.5$.\n\nThe volume of the triangle is given by the formula $V = \\frac{1}{3}bh$, where $b$ is the base and $h$ is the height. For this triangle, we have $b = 5$ and",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by:\n\n$$\\begin{aligned}x + 3y &= 11\\text{,} \\\\ 2x + 5y &= 16\\text{.}\\end{aligned}$$\n\nThis system of equations can be solved by using the substitution method. We first solve for one variable in terms of the other, and then substitute the resulting expression into the other equation to solve for the remaining variable.\n\nStarting with the first equation, we can solve for x in terms of y:\n\n$$\\begin{aligned}x + 3y",
        "gt_answers": "2 x ^ { 2 } + x = 2 x ^ { 2 } + 4 x + 2\n",
        "image_path": "./data/HME100K/test_images/test_3404.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{mg} = \\frac{\\text{m}}{\\text{v^2}}$$\n\nwhere $m$ is the mass of the object and $v$ is its velocity.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression on the image is not visible as it is written in ascii text. It is not possible to write out the formula using LaTeX format as the expression is not visible.\n\nTo display the formula in LaTeX format, you need to have the expression written out in LaTeX code. If you can provide the LaTeX code for the expression, I can help you write it out in LaTeX format.",
        "gt_answers": "x < \\frac { 1 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_3406.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{x^2+y^2}{2}$.",
        "gt_answers": "\\frac { 3 } { x } = \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3407.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the equation of a circle, which is given by:\n\n(x - h)^2 + (y - k)^2 = r^2\n\nwhere x and y are the coordinates of a point on the circle, h and k are the coordinates of the center of the circle, and r is the radius of the circle.",
        "gt_answers": "x _ { 1 } = - \\frac { 1 } { 3 } x _ { 2 } =\n",
        "image_path": "./data/HME100K/test_images/test_3408.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the probability density function (pdf) of the Poisson distribution with parameter lambda, denoted by lambda. It is given by the equation:\n\nP(x) = (e^-lambda\\*lambda^x)/x!\n\nwhere x is the number of events and lambda is the average rate at which events occur.",
        "gt_answers": "\\cos B = \\frac { a ^ { 2 } + c ^ { 2 } - } { 2 a c }\n",
        "image_path": "./data/HME100K/test_images/test_3409.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\nx^2 + 3x - 4 &= 0 \\\n&= \\left(x - 2\\right)^2 + 3\\left(x - 2\\right) - 4 \\\n&= \\left(x - 2\\right)^2 + 3x - 6 - 4 \\\n&= \\left(x - 2\\right)^2 + 3x - 10 \\\n&= x^2 - 4x + 9 + 3x",
        "gt_answers": ": \\overline { x _ { 3 } } > \\overline { x _ { 2 } } > \\overline { x _ { 1 } }\n",
        "image_path": "./data/HME100K/test_images/test_3410.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with base b and height h is:\n\nA = bh\n\nThis formula can be derived from the concept of the formula for the area of a rectangle, which is:\n\nA = lw\n\nwhere l is the length of the rectangle and w is its width. The height of a rectangle is equal to its length, so we can substitute w for h in the formula for the area of a rectangle with base b and height h:\n\nA = bh\n= bl\n\nwhere b is the base of the rectangle and l is its length. Solving",
        "gt_answers": "( a + 2 ) ^ { 2 } + ( 1 - a ) ( 1 + a )\n",
        "image_path": "./data/HME100K/test_images/test_3411.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in the image using LaTeX format, we need to know the values of the variables and the mathematical operations involved in the formula.\n\nAssuming that the variables in the formula are x and y, we can write the formula as:\n\nx^(2 + 3y) - 4x^2y\n\nTo calculate the derivative of this formula with respect to y, we can use the chain rule as follows:\n\nd/dy (x^(2 + 3y) - 4x^2y) = (2x + 3y) \\* (",
        "gt_answers": "2 ( 2 + n ) + 3 n = 1 4\n",
        "image_path": "./data/HME100K/test_images/test_3412.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\text{Image Content} = \\frac{a}{b}\\text{+}\\frac{c}{d}\\text{+}\\frac{e}{f}$$\n\nwhere,\n\na = the number of black squares in the top row\nb = the number of white squares in the top row\nc = the number of black squares in the second row\nd = the number of white squares in the second row\ne = the number of black squares in the third row\nf = the number of white squares in the third row\n\nThe denominator is the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{center} $\\text{d} \\Omega \\text{d} x + \\text{d} \\Omega \\text{d} y = \\frac{\\partial E}{\\partial t} $ \\end{center}\n\nwhere $\\Omega$ is the solid angle subtended by the differential element $\\text{d} x \\text{d} y$ at the point $(x, y)$ on the surface of the sphere. The expression represents the flux of energy through the differential surface element.",
        "gt_answers": "D O = \\frac { 1 } { 2 } B D\n",
        "image_path": "./data/HME100K/test_images/test_3415.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: 8x + 6y + 6z = 42.\n\nIn LaTeX format, this expression can be written as:\n\n\\begin{align\\*} 8x + 6y + 6z &= 42 \\end{align\\*}\n\nNote: The above expression is only an approximation, as the image is not clear enough to read the numbers on it.",
        "gt_answers": "8 0 0 + 8 0 + 8 = 8 8 8\n",
        "image_path": "./data/HME100K/test_images/test_3416.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by the following LaTeX format:\n\n$$\\begin{aligned}x^2+y^2 &= r^2\\end{aligned}$$\n\nThis is a formula for a circle with center at the origin and radius $r$. The formula states that the sum of the squares of the x and y coordinates of any point on the circle is equal to the square of the radius of the circle.",
        "gt_answers": "w = - x ^ { 2 } + 7 x + 4 8\n",
        "image_path": "./data/HME100K/test_images/test_3417.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression written in LaTeX format.\n\nThe expression is the derivative of the function f(x) = x^4 with respect to x.\n\nThe derivative is written as:\n\nf'(x) = d/dx [x^4]\n= 4x^3\n\nTherefore, the derivative of f(x) = x^4 with respect to x is 4x^3.",
        "gt_answers": "\\Rightarrow y _ { 1 } ^ { 2 } = 3 x _ { 1 } ^ { 2 } - 3\n",
        "image_path": "./data/HME100K/test_images/test_3418.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:$$x^{2}+y^{2}=k\\text{ or }(x+y)^{2}=k$$where k is a constant.",
        "gt_answers": ", \\angle C = \\angle B A D = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3419.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image:\n\n\\begin{center}\n\\begin{align}\ny &= \\frac{3x^2}{2} \\\n\\end{align}\n\\end{center}\n\nThis is the same formula as the one written in the image, just in LaTeX format.",
        "gt_answers": "y _ { 2 } = - \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3420.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: $\\frac{4}{2} - \\frac{1}{3}$.",
        "gt_answers": "\\frac { 2 4 } { 2 } = 1 2 1 2 = 1 2\n",
        "image_path": "./data/HME100K/test_images/test_3421.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula is: \u2211i=1n ( xi - x\u0304 ) 2.\n\nHere, \u2211i=1n represents the sum of the elements from i = 1 to n. The expression inside the sum is ( xi - x\u0304 ) 2, which is the square of the difference between each element and the mean of the data set. This formula is used in the context of linear regression to calculate the sum of squared errors or residuals.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with base 9 and height 15 can be written as: A = 9h15. This formula is derived from the formula for the area of a rectangle, which is A = l x w, where l is the length and w is the width. The base of a rectangle is the length, and the height is the width. Therefore, to find the area of the rectangle in the image, we can substitute 9 for l and 15 for w in the formula for the area of a rectangle. This gives us A = 9h15.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\\frac{m}{v} \\cdot \\frac{n}{v} = \\frac{m \\cdot n}{v^2} \\cdot \\frac{v}{2} \\cdot \\frac{n}{v} = \\frac{m \\cdot n}{2v} \\cdot \\frac{v}{2} = \\frac{m \\cdot n}{v} \\cdot \\frac{1}{2} = \\frac{m \\cdot n}{v \\cdot 1/2} = \\frac{m \\cdot n}{v/2} = \\frac{m}{v} \\cdot",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length 10cm and width 5cm is: A = l \\* w, where l is the length and w is the width. The area of the rectangle is 10 cm \\* 5 cm = 50 cm^2.\n\nThe formula for the area of a circle with radius 5cm is: A = (pi) \\* r^2, where r is the radius. The area of the circle is (3.14159) \\* (5 cm)^2 = 78 53.98",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: x + 1 = 2y + 4z + 2.",
        "gt_answers": "2 \\times 7 = 1 4\n",
        "image_path": "./data/HME100K/test_images/test_3426.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 2x + 3y = 12xy.\n\nThe variable x represents the horizontal distance from the point where the line intersects the x-axis to the point where the line intersects the y-axis. The variable y represents the vertical distance from the point where the line intersects the y-axis to the point where the line intersects the x-axis.\n\nThe equation 2x + 3y = 12xy represents the equation of a line that passes through the points (2,0) and (1,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a parabolic arch is given by the equation y = x^2 + (2x - 4)y^2, where x and y are the variables in the formula. The equation represents a parabolic arch, with the vertex at the origin and the axis of symmetry passing through the vertex and the origin. The formula can be used to determine the equation of the parabolic arch.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: f(x) = 2x3 + 4x2 - 8x + 12.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write out the expression for the formula in the image using LaTeX format.\n\nThe formula is given as:\n\nf(x) = \u222b\u222b p(x - h) \\* \u221a[2(x^2 + h^2)] \\* sin(h/2) dx\n\nwhere p(x) is the probability density function of a normal distribution with mean \u03bc = 1 and standard deviation \u03c3 = 1.\n\nTo evaluate this integral, we can use the substitution rule for the integral sign, which states that if u = f(x),",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: 504.632 + 321.283 + 500.115 + 63.215 = 1281.002 kg/m\u00b2\n\nThe units of the formula are:\n\n* g (grams)\n* m\u00b2 (square meters)\n\nNote that the units of the formula are given in terms of the base units of the International System of Units (SI), which are the meter for length, the kilogram for mass, and the second for time. The formula can",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written in LaTeX format is: $\\frac{1}{3}x^2 + \\frac{2}{5}x + \\frac{1}{6}$\n\nThis is a quadratic equation in the form of a sum of powers, with the variable x raised to the power of 2, and constants 1/3, 2/5, and 1/6.",
        "gt_answers": "x _ { 2 } = \\frac { 7 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3434.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the expression of the formula in the image using LaTeX format:\n\n$$\\text{Image content}=\\frac{500}{150}\\left(\\frac{500}{150}\\right)^3+\\frac{100}{150}\\left(\\frac{100}{150}\\right)^3$$\n\nThis equation is based on the formula for the area of a rectangle, which is given by the formula:\n\n$$A=l\\cdot w$$\n\nwhere A is the area, l is the length and w is the width. In",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is not displayed in the image.",
        "gt_answers": "y _ { 3 } = - \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3437.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we need to identify the equation and its variables. The equation is: 2x + 6y = 12.\n\nThe variables are x and y. To write the equation in LaTeX format, we can use the following code:\n\n$$2x + 6y = 12$$\n\nIn LaTeX, the operator $\\$ is used to denote mathematical expressions. The equals sign (=) is used to indicate equality. The variable x is represented by the letter x, and the variable y is represented by the letter y. The equation",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle with vertices at the points (1, 1), (1, 3), and (3, 1) is:$\\text{Area of } $\\triangle ABC = \\frac{1}{2}(bh + ch)$, where $b$ and $c$ are the lengths of the base and height of the triangle, respectively. Using the given coordinates, we have:b = 1c = 3The area of the triangle is therefore:$\\text{Area of } $\\triangle ABC = \\frac{1}{2}(1 \\* 3 + 3 \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{center}\n\\frac{2\\pi r}{L} = \\frac{1}{2} \\left(\\frac{h^2 + k^2}{r^2}\\right)\n\\end{center}\n\nwhere $r$ is the radius of the circular antenna pattern, $L$ is the wavelength, $h$ and $k$ are the coordinates of the point on the antenna pattern at which the reflected signal is received.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by:\n\n$$x^2+y^2=r^2$$\nwhere $x$ and $y$ are the Cartesian coordinates of a point on the circle, and $r$ is the radius of the circle. The equation represents the standard form of a circle equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x+3}{2}$.",
        "gt_answers": "- 3 x - 2 x = - 8 - a\n",
        "image_path": "./data/HME100K/test_images/test_3442.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{m}{t} = \\frac{k}{t}$$\n\nwhere $m$ is the mass of the object being dropped and $k$ is the acceleration due to gravity, both in units of kg/s.\n\nThe variable $t$ represents the time in seconds it takes for the object to fall from rest to the ground, assuming no air resistance.\n\nThis equation shows that the acceleration of the object is directly proportional to the force acting on it, which is equal to its mass multiplied by the acceleration due to",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: a + b + c = d.",
        "gt_answers": "a ^ { 2 } + b ^ { 2 } = 2 \\geq 2 a b\n",
        "image_path": "./data/HME100K/test_images/test_3444.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\text{Average depth} = \\frac{1}{N}\\text{sum of depths of all objects}$$where N is the total number of objects in the image. This formula calculates the average depth of all objects in the image by taking the sum of their depths and dividing it by the total number of objects.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a mathematical expression that describes a geometric shape, but it cannot be written in LaTeX format as it is not a mathematical expression. It appears to be a geometric diagram that shows a circular shape with a radius of 3cm and an arc length of 6cm.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: (x - 1) + 3 = 2(x + 1) - 1.",
        "gt_answers": "\\frac { 5 } { x } = \\frac { 2 } { 5 } - \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3447.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\begin{aligned} f(x) &= \\frac{2x^2}{x+3} \\end{aligned} $$",
        "gt_answers": "O P = \\sqrt { 4 + 1 } = \\sqrt { 5 } < 4\n",
        "image_path": "./data/HME100K/test_images/test_3448.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is $\\frac{x^2 + y^2}{2}$.",
        "gt_answers": "x = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3449.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is pi*r^2, where r is the radius of the circle. In this image, the radius is 3 inches, so the formula would be 3.14\\*3^2, which equals 31.4 in^2.",
        "gt_answers": "f ^ { \\prime } _ { ( x ) } = e x - 2 x - a\n",
        "image_path": "./data/HME100K/test_images/test_3450.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I can't see the image you've provided. Can you please provide the image so I can help you with your question?",
        "gt_answers": "4 x ^ { 2 } + ( 4 b - 9 ) x + b ^ { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_3451.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the expression in the image:\n\n\\begin{equation}\ny = \\frac{x^2 + 4x - 6}{x^2 - 6}\n\\end{equation}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2x + 3y = 14.",
        "gt_answers": "\\frac { - 1 + x } { 2 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_3453.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n\\frac{1}{2} (4x + 6y) + 3z = 12",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by: 2x^2 + 2x - 8 = 0.",
        "gt_answers": "\\angle A F C = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3455.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$\\frac{a}{b} = \\frac{1000}{10000}$\n\\end{center}\n\nwhere a and b are the coefficients of the formula.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{a}{b} + \\frac{c}{d} = \\frac{ad+bc}{bd+ac} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$50+20\\cdot3+4\\cdot5+1\\cdot6+3\\cdot7+2\\cdot8+5\\cdot9+4\\cdot10+1\\cdot11+3\\cdot12$$This expression represents the total number of people in the image.",
        "gt_answers": "4 2 \\textcircled { < } 5 0 5 9 \\textcircled { < } 6 3\n",
        "image_path": "./data/HME100K/test_images/test_3458.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not shown. Can you please provide the image?",
        "gt_answers": "O _ { 2 } + 4 e ^ { - } + 4 H ^ { + } = 2 H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_3459.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$latex\n\\frac{\\Delta t}{\\Delta x} = \\frac{\\Delta E}{\\Delta t}\n$$\n\nwhere $\\Delta t$ is the time interval and $\\Delta x$ is the distance traveled. The left-hand side of the equation represents the speed of the object, while the right-hand side represents the acceleration of the object.\n\nIn this equation, the time interval is divided by the distance traveled to give the speed of the object. The energy required to accelerate the object is then divided by the time interval to give the acceleration of the object.",
        "gt_answers": "\\angle A B O = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3461.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$ x\\_1 = 0 $\n$ x\\_2 = 1 $\n$ x\\_3 = 2 $\n$ x\\_4 = 3 $\n\nNote that the domain of the function is the set of all real numbers from 0 to 3, which includes the four values of x\\_1, x\\_2, x\\_3, and x\\_4. The range of the function is the set of all real numbers from 0 to 2, which includes the values of f(x\\_1), f(x",
        "gt_answers": "\\angle C O B = 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3462.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent}$$",
        "gt_answers": "2 n + \\frac { 4 } { 3 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3463.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\frac{1}{2}(x + 3y) - 4z",
        "gt_answers": "7 x = 4 2 x = 6\n",
        "image_path": "./data/HME100K/test_images/test_3464.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n\\frac{a^2+b^2}{2ab} \\\n\nThis is the formula for the dot product of two vectors a and b.",
        "gt_answers": "T _ { A } : T _ { B } : T _ { c } = 3 : 4 : 3\n",
        "image_path": "./data/HME100K/test_images/test_3465.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$\\frac{100 - 25}{50 + 25} = \\frac{100 - 25}{75} = \\boxed{\\frac{75}{75} = 1}$$",
        "gt_answers": "\\frac { 4 } { x } + \\frac { x + 2 } { y } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3466.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given formula:\n\n\\begin{align}\ny &= \\frac{2x^2 - 9x - 4}{x + 2} \\notag \\\\\n&= \\frac{2x^2 - 9x - 4}{x + 2} \\notag \\\\\n&= \\frac{2x(x + 2) - 9x - 4}{x + 2} \\notag \\\\\n&= 2x - 9 + \\frac{4}{x + 2} \\notag \\\\\n&=",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\text{Number of pairs with values less than or equal to x:}\\ 4$$",
        "gt_answers": "x = 5 \\div \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3468.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\begin{aligned}\nf(x) = \\frac{1}{x^2 - 4}\n\\end{aligned}\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle can be expressed as follows:\n\narea = length \u00d7 width\n\nwhere length and width are the dimensions of the rectangle. The formula can be written in LaTeX format as:\n\n\\[ A = L \\times W \\]\n\nwhere A is the area of the rectangle, L is the length of the rectangle, and W is the width of the rectangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\ny & = \\frac{x^2 - 4x + 4}{x - 2} \\\n&= \\frac{(x - 2)(x + 2)}{(x - 2)} \\\n&= (x + 2) \\\n&= x + 2\n\\end{align\\*}",
        "gt_answers": "x = \\frac { 1 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_3472.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by A = \u03c0r^2, where r is the radius of the circle. In this image, the radius of the circle is given by the length of the radius vector, which is shown in blue. Therefore, the area of the circle is given by A = \u03c0(3^2) = 9\u03c0.\n\nThe formula for the volume of a cylinder is given by V = \u03c0r^2h, where r is the radius of the cylinder and h is its height. In this image, the radius of the cylinder is given by",
        "gt_answers": "1 x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3473.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that!\n\nThe expression for the formula in the image can be written as:\n\n$\\frac{x^{3}}{x+2}$\n\nThis is a fraction, where the numerator is $x^{3}$, and the denominator is $x+2$.",
        "gt_answers": "\\sqrt { 5 } - 2\n",
        "image_path": "./data/HME100K/test_images/test_3475.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the formula in the image:\n\n\\begin{center}\n$x^2 + 5x + 6 = 0$\n\\end{center}\n\nThe formula is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 1$, $b = 5$, and $c = 6$. The solution to this equation is given by the quadratic formula:\n\n\\begin{center}\n$x = \\frac{-b \u00b1 \u221a(b^2 - 4ac",
        "gt_answers": "( 2 ) f _ { A } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3476.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given formula:$$\\frac{4n^2 - 9n + 3}{n^2 - 5n + 3}$$Note that the numerator is a binomial and the denominator is a difference of two binomials. The numerator is a binomial that is not fully factored, so we need to use the distributive property to factor it. The denominator is a difference of two binomials that is fully factored, so we do not need to use any factoring techniques on it.\n\nThe binomials in the numer",
        "gt_answers": "3 6 \\div 4 = 9\n",
        "image_path": "./data/HME100K/test_images/test_3477.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To represent the formula for finding the derivative of a function f(x) = 3x^2 - 5x + 2, we can write:",
        "gt_answers": "x _ { 3 } = - 2 + 2 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3478.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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\u222b(x) dx = \u222b(x^2 + 2x + 1) dx\n\nThe antiderivative of x^2 + 2x + 1 is x^3/3 + x^2/2 + x, so we have:\n\n\u222b(x) dx = \u222b(x^3/3 + x^2/2 + x) dx\n= [x^3/3 + x^2/2 + x] + C\n\nSubstituting x = 3, we get",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the expression can be written as follows:\n\n$$g\\_3 = \\frac{3 \\times 4 + 5 \\times 7}{2 \\times 3 + 7 \\times 4} = \\frac{3(10) + 5(14)}{2(6) + 7(18)} = \\frac{30 + 70}{12 + 28} = \\frac{130}{150} = \\boxed{0.8666667}$$",
        "gt_answers": "( 2 a - 3 ) + ( a + 1 ) > 7\n",
        "image_path": "./data/HME100K/test_images/test_3480.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\text{Image Content}$$",
        "gt_answers": ". \\angle O A E = \\angle G A E\n",
        "image_path": "./data/HME100K/test_images/test_3481.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$a = \\frac{b}{c}$\n\\end{center}\n\nIn this formula, `a` is the result, `b` is the numerator, and `c` is the denominator. The fraction bar (`/`) is used to denote division.",
        "gt_answers": "A M = \\sqrt { 5 ^ { 2 } - 3 ^ { 2 } } = 4\n",
        "image_path": "./data/HME100K/test_images/test_3482.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:6x^2+2x-8.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a mathematical expression written in LaTeX format:\n\n$$\\begin{aligned} \\frac{\\text{c}}{\\text{d}} \\cdot \\frac{\\text{b}}{\\text{a}} \\cdot \\frac{\\text{x}^{2}}{\\text{x}+1} \\cdot \\frac{\\text{y}-\\text{a}}{\\text{y}+\\text{b}} \\cdot \\frac{\\text{z}^{3}}{\\text{z}+2} \\cdot \\frac{\\text{r}}{\\text{s}} \\cdot \\frac{\\text{t}}{\\text{u}} \\cdot \\frac{\\",
        "gt_answers": "( 4 a ^ { 3 } b - 2 a ^ { 2 } + a ) \\div 2 a = 2 a ^ { 2 } b - a + \\frac { 1 } { 2 \u3002 }\n",
        "image_path": "./data/HME100K/test_images/test_3484.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the image:\n\n\\begin{align\\*}\n\\frac{5}{7}+\\frac{6}{9} = \\frac{11}{15}\n\\end{align\\*}\n\nThis formula is an example of how to add fractions with unlike denominators and simplify the result to a fraction with a common denominator. The fraction $\\frac{5}{7}+\\frac{6}{9}$ is the sum of two fractions with unlike denominators, so we need to simplify it before we can add it. To do this, we can add the fractions",
        "gt_answers": "\\frac { x } { 6 0 } - \\frac { x } { 7 2 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3485.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:$$f(x) = \\frac{x^2 + 4x - 12}{x - 2}$$This can be written in LaTeX format as:$$f(x) = \\frac{x^2 + 4x - 12}{x - 2}$$",
        "gt_answers": "x - \\frac { y - 2 } { 2 } = 1 - \\frac { x - 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3487.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The expression for the given formula can be written as:\n\n$$ \\text{x} = \\frac{3\\text{y} + 4}{5} $$\n\nwhere x and y are variables representing the given numbers. To represent this equation in LaTeX format, you can use the following code:\n\n$$ x = \\frac{3y + 4}{5} $$\nThis code will produce the equation in a monospace font and in the proper mathematical notation.",
        "gt_answers": "3 x ^ { 2 } + 2 x y = 0\n",
        "image_path": "./data/HME100K/test_images/test_3488.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 4x\u00b2 - 9x + 10.",
        "gt_answers": "b = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3489.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "y = k x + b ( k = l 0 )\n",
        "image_path": "./data/HME100K/test_images/test_3490.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: x^4 + x^3 + x^2 + x + 1.",
        "gt_answers": "x + 1 = 1 + x - 2 \\sqrt { x }\n",
        "image_path": "./data/HME100K/test_images/test_3491.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{x}{y}$\n\nwhere $x$ and $y$ are variables.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot provide the image you requested as it violates copyright laws. However, I can help you with the formula in LaTeX format.\n\nThe formula for the area of a rectangle is A = l \u00d7 w, where l is the length and w is the width.\n\nIn LaTeX format, the formula would be written as:\n\n$ A = l \\times w $\n\nWhere l and w are variables representing the length and width of the rectangle, respectively.",
        "gt_answers": "a = 1 b = 1\n",
        "image_path": "./data/HME100K/test_images/test_3493.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the rectangle with a width of 6 cm and a height of 9 cm is $\\frac{9 \\times 6}{2}$. This can be written in LaTeX format as $\\frac{9 \\times 6}{2}$.",
        "gt_answers": "x = \\frac { - 1 + 1 . 4 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3495.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as:A=\u03c0r^2where r is the radius of the circle. The radius of the circle is half the diameter, which is also equal to \u03c0. Therefore, we can write the formula as:A=\u03c0r^2\u03c0r=d\u03c0d=2rA = \\frac{\\pi}{r^2} \\pi r = \\frac{d}{\\pi} d = 2rA=\u03c0r2\u200bd\u03c0d\u200b=2rA = \\frac{\\pi}{r^2} \\pi r = \\frac{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n`((166293527842867895313955492309467893237400567757176846739682731875517423587429176063517282911737682791312823591282735",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be expressed as follows:\n\n![](https://example.com/image.png)\n\nwhere $\"ImageContent\" is the content of the image. The LaTeX code for the above expression is:\n\n\\begin{center}\n\\includegraphics[width=0.5\\textwidth]{https://example.com/image.png}\n\\end{center}\n\nNote that the above LaTeX code assumes that the image file is hosted on a website and accessible via a URL. If the image file is not hosted online, you will need to provide the file path to the image",
        "gt_answers": "1 2 - 4 k > 0\n",
        "image_path": "./data/HME100K/test_images/test_3499.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nx + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x + 3y = 9x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression in the image:\n\n\\begin{center}\n\\begin{equation}\nE = mc^2\n\\end{equation}\n\\end{center}\n\nThis equation states that the energy (E) of an object is equal to the mass (m) of that object multiplied by the speed of light (c) squared.",
        "gt_answers": "E F = \\frac { 1 } { 2 } A B\n",
        "image_path": "./data/HME100K/test_images/test_3505.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for a line in the given image is given by:\n\ny = 3x + 5",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image in LaTeX format is given below.\n\n$$\\frac{a+b}{2}=\\sqrt{2(a-b)}$$\n\nIn this formula, the variables a and b represent the coordinates of the midpoint of the line segment connecting the two points. The denominator 2(a-b) represents the length of the line segment. The numerator a+b represents the distance from the midpoint to the second point. The radical symbol represents the midpoint of the line segment.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = l \u00d7 w\n\nWhere l is the length of the rectangle and w is the width of the rectangle. In this image, the rectangle has length 5 and width 4, so the area is:\n\nA = 5 \u00d7 4 = 20 cm\u00b2",
        "gt_answers": "B D = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3511.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{align\\*}\nx & = \\frac{2(x+2)}{x+4} \\\ny & = \\frac{x+4}{2(x+2)}\n\\end{align\\*}\n\nThis is a system of linear equations in two variables, where x is the first variable and y is the second variable. The solutions to this system are the values of x and y that make both equations true.",
        "gt_answers": "x = \\frac { - b \\pm \\sqrt { 0 } } { 2 a }\n",
        "image_path": "./data/HME100K/test_images/test_3512.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: ( a + b ) \\* ( c - d ).",
        "gt_answers": "A M ^ { 2 } + B N ^ { 2 } = M N ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3513.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![Image](https://www.quickchart.com/chart?bkg=white&c=%7B%0A%20%20type%20%20%22text%22%20%7D)\n\n![Image](https://www.quickchart.com/chart?bkg=white&c=%7B%0A%20%20width%20%22300px%22%20%7D)\n\n![Image](https://www",
        "gt_answers": "\\angle A D C = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3514.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{equation}\ne^{-t/3}\\left(\\sin\\left(\\frac{t}{3}\\right)+3\\right)\\left(e^{-2t/3}+e^{-t/3}\\right)\n\\end{equation}",
        "gt_answers": "E ( 0 , \\frac { 4 } { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_3515.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX formula for the image:\n\n$$\\frac{a+b}{c+d} = \\frac{a}{c} + \\frac{b}{d}$$\n\nThe formula is derived from the distributive property of multiplication over addition, which states that:\n\n$$(a + b) \\times (c + d) = a \\times c + b \\times d$$\n\nExpanding the distributive property and simplifying, we get:\n\n$$\\frac{a+b}{c+d} = \\frac{a}{c} + \\frac",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n![](image.png)\n\nIn this formula, the value of 'a' is given as 3, and the value of 'b' is given as 4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is $\\frac{a}{b}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ f(x) = \\frac{3x^2 - 5x + 1}{x - 1}$$This is a quadratic formula with a leading coefficient of 3 and a constant term of 1.",
        "gt_answers": "a ^ { 2 } + b ^ { 2 } - a b - 3 = 0\n",
        "image_path": "./data/HME100K/test_images/test_3519.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX formula for the expression in the image:\n\n$$\\frac{a+b}{c}$$\n\nwhere a, b, and c are constants.",
        "gt_answers": "( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3520.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression in the image:\n\n\\begin{equation}\n2x + 5 = 10\n\\end{equation}\n\nThis is a simple linear equation with two variables, x and y. The left side of the equation represents the value of x when added to 5. The right side of the equation represents the value of 10.",
        "gt_answers": "\\therefore B D = C E\n",
        "image_path": "./data/HME100K/test_images/test_3521.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{1}{2}\\left(\\frac{5+4}{3}+\\frac{9-5}{3}\\right)$$\n\nwhich simplifies to:\n\n$$\\frac{1}{2}(5+4)+\\frac{1}{2}(9-5)$$\n\n$$\\frac{7}{2}$$\n\nSo the image represents the fraction $\\frac{7}{2}$.",
        "gt_answers": "b = \\frac { 1 0 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3522.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\nx &= \\frac{1}{2} \\times 10 \\\\\ny &= \\frac{1}{4} \\times 9 \\\\\nz &= \\frac{1}{6} \\times 8\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression in the image:\n\n\\begin{equation} c\\_af\\_co = \\frac{a\\_f\\_{co}}{c\\_af\\_c} \\end{equation}\n\nThis formula is derived from the principle of conservation of energy and conservation of momentum, which state that the total energy and total momentum of a closed system must remain constant. The formula is used to determine the velocity of a gas in a piston engine and is given by the ratio of specific heats of the gas at constant pressure and constant volume, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent} = \\frac{a\\cdot b}{c}$$\n\nwhere $a, b, c$ are the coefficients in the formula.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{x - \\frac{1}{4}}{\\frac{1}{2} + \\frac{1}{4}} = \\frac{x}{1 + \\frac{1}{2}} = \\frac{x}{1 + \\frac{1}{4}} = \\frac{2x}{5}$$\n\nThe expression can be simplified further using the distributive property of multiplication over addition:\n\n$$\\frac{x - \\frac{1}{4}}{\\frac{1}{2} + \\frac{1}{4}} = \\frac",
        "gt_answers": "2 x + 1 = \\frac { 1 } { 2 } x + 4\n",
        "image_path": "./data/HME100K/test_images/test_3526.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\\begin{align}\n\n\\frac{1}{2}\\frac{1}{3}\\frac{1}{4}\\frac{1}{5} &= \\frac{1}{2}\\frac{1}{3}\\frac{1}{4}\\frac{1}{5} \\\\\n&= \\frac{1}{4}\\frac{1}{5}\\frac{1}{6} \\\\\n&= \\frac{1}{5}\\frac{1}{6} \\\\\n&= \\frac{1}{6}\n\\end{align}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 56 - 50 / 4 = 11.25.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is not visible in the provided image. Please provide a valid image for me to write the formula in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is pi*r^2, where pi is a mathematical constant approximately equal to 3.14 and r is the radius of the circle.\n\nThe area of the circle in the image is pi*r^2, where pi is approximately equal to 3.14 and r is approximately equal to 0.72 meters.\n\nThe formula for the circumference of a circle is 2*pi*r, where pi is a mathematical constant approximately equal to 3.14 and r is the radius of the circle.\n\nThe circumference of the",
        "gt_answers": "a = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3530.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{n^2+5n+4}{n^2-3n+2} $$\n\nNote: The variables in the formula are n and the numerator is $n^2+5n+4$ and the denominator is $n^2-3n+2$.",
        "gt_answers": "\\angle B O D = 2 \\angle B A D = 6 0 ^ { \\circ } .\n",
        "image_path": "./data/HME100K/test_images/test_3531.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\nx + 3x + 5 = 15\n\\end{align\\*}\n\nThis equation represents a system of linear equations, where the first equation is x + 3x = 9, and the second equation is x + 5 = 15. By adding the two equations together, we get 2x + 8 = 24, which simplifies to x + 4 = 15. Therefore, the solution to the system is x = 11",
        "gt_answers": "x = \\frac { 1 6 } { 2 0 } - \\frac { 5 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3532.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$x = \\frac{2}{y + \\frac{5}{y - 2}}$$\n\nNote that this formula assumes that $x$ and $y$ are real numbers.",
        "gt_answers": "\\arcsin x = \\frac { 1 - y } { 2 } x = \\sin \\frac { 1 - y } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3533.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given as:\n\n$$\\text{k} = \\frac{1}{4} + \\frac{1}{2}i + \\frac{1}{4} - \\frac{1}{8}i^2$$\n\nThis formula represents the sum of the terms in the geometric sequence with first term 1/4 and common ratio 1/2.",
        "gt_answers": "k = - \\frac { 8 } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3534.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with width w and length l is given by: A = wlThe formula for the perimeter of a rectangle with width w and length l is given by: P = 2(w + l)The formula for the volume of a rectangular prism with length l, width w, and height h is given by: V = whlThe formula for the surface area of a rectangular prism with length l, width w, and height h is given by: S = 2(l + w) + 2(w + h)The formula for the circumference",
        "gt_answers": "a _ { 1 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3536.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula with two variables and one constant. The formula can be written as follows:\n\nf(x) = b \u00d7 pf - pf \u00d7 d\n\nwhere pf and d are constants, and x is the variable. The constant b represents the slope of the line and can be calculated by dividing the difference between the y-values of the two points by the difference between their x-values. The constant d represents the y-intercept of the line and can be calculated by subtracting the y-value of the second point from the y-value of the first point.",
        "gt_answers": "\\frac { B E } { D F } = \\frac { B C } { D C }\n",
        "image_path": "./data/HME100K/test_images/test_3537.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nP = (b / (b + \u221a(c/d)))",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot write out the expression of the formula in the image using LaTeX format as there is no image provided. Can you please provide the image so I can assist you with the LaTeX format?",
        "gt_answers": "\\overline { B D } = \\overline { D C }\n",
        "image_path": "./data/HME100K/test_images/test_3541.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ \\frac{m \\times r \\times t}{4}$$ where $m$ is the mass of the object being thrown, $r$ is the radius of the circle on which the object is thrown, and $t$ is the time it takes for the object to fall to the ground. This formula can be used to determine the acceleration of an object thrown from rest at a height $h$ above the ground.\n\nThe formula can be derived using the following steps:\n\n1. The force acting on the object is the force of gravity, which",
        "gt_answers": "y = \\frac { 9 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3542.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not specified, so I cannot provide an answer. Can you please provide more information or context for the equation?",
        "gt_answers": "A E = A Q + E Q = 4 0 + 3 0 \\sqrt { 3 } \\approx 6 1 . 9 c m\n",
        "image_path": "./data/HME100K/test_images/test_3543.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$\\frac{1}{x^2+2x+1}$.\n\nTo write out the expression in LaTeX format, you can use the following code:\n\n$$\\frac{1}{x^2+2x+1}$$\n\nIn this expression, the variable x is raised to the power of 2 and added to 2x and 1, resulting in $\\frac{1}{x^2+2x+1}$.",
        "gt_answers": "x = 1 , x = 2\n",
        "image_path": "./data/HME100K/test_images/test_3544.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression for the formula in the image using LaTeX format:\n\n$$ \\frac{3}{4} \\times \\frac{9}{12} \\times \\frac{20}{25} = \\frac{3 \\times 9 \\times 20}{4 \\times 12 \\times 25} = \\frac{270}{1000} = 0\\_{2} $$\n\nIn this formula, we have used the multiplication symbols $\\times$ to represent the multiplication of the three fractions, and the subscript notation $x$",
        "gt_answers": "1 5 n ^ { 2 } + 2 n - 1 = 0\n",
        "image_path": "./data/HME100K/test_images/test_3545.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is given by:2x+1x2\u2212x3=\u22125x+3x23x+1x2=\u2212x3\u22125x+3x22x+1x2=\u2212x3+5x\u22123x22x+1x2=\u2212x3+5x+3x22x+1x2=\u2212x3\u22125x+3x22x+1x2=\u2212x3+5x\u22123x22x+1x2=\u2212x3+5x+3x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by the following LaTeX code:\n\n\\begin{center}\n\\begin{align}\n\\frac{3000 - 2000}{400} &= \\frac{1000}{400} \\\n&= 2.5 \\\n&= 2.5 - 1 \\\n&= 1.5 \\\n&= 1.5 / 2 \\\n&= 0.75 \\\n&= 0.75 x 2 \\\n&= 1.5\n\\end{align}\n\\end{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of r is given by:\n\nA = \u03c0r\u00b2\n\nThis formula can be derived using the formula for the area of a rectangle, which is:\n\nA = l \u00d7 w\n\nwhere l is the circumference of the circle (which is equal to 2\u03c0r) and w is the width of the rectangle. The height of the rectangle is equal to the radius of the circle.\n\nSo, we can substitute the values for l and w into the formula for the area of a rectangle to get:\n\nA = 2\u03c0",
        "gt_answers": "y = \\frac { - 1 \\pm \\sqrt { 1 7 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3548.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{L + a\\_0 + b\\_0 + c\\_0 + d\\_0 = A + B + C + D}$$\nwhere $\\text{L}$ is the Laplacian matrix, $\\text{a\\_0}$, $\\text{b\\_0}$, $\\text{c\\_0}$, and $\\text{d\\_0}$ are the constants, and $\\text{A}$, $\\text{B}$, $\\text{C}$, and $\\text{D}$ are the Laplacian coefficients.",
        "gt_answers": "\\angle A O C : \\angle A O B = 2 k = 9 k\n",
        "image_path": "./data/HME100K/test_images/test_3549.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\begin{center}\n\\frac{x^2+y^2}{x^2-y^2}=\\frac{a^2+b^2}{a^2-b^2}\n\\end{center}\n```",
        "gt_answers": "1 5 0 \\div 3 0 0 = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3550.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by: $x^2 - 3x + 4 = 0$",
        "gt_answers": "y _ { 1 } = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3551.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX formula for the expression in the image:\n\n$$\\frac{1}{2}(3x + 4y) = \\frac{1}{2}(2x + 3y)$$\n\nThis equation states that the sum of $3x$ and $4y$ is equal to the sum of $2x$ and $3y$.",
        "gt_answers": "C _ { 7 } = 9 0 0 N\n",
        "image_path": "./data/HME100K/test_images/test_3553.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the cost of caring for the patient with a traumatic brain injury is given as:\n\nC = $10,000 \\* (100/125)^2 \\* (100/125)^4 \\* 120/365$\n\nwhere $C$ represents the cost of caring for the patient for one year, and the values within the parentheses are estimated probability of survival, length of hospital stay, and length of rehabilitation, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is $\\frac{1}{4}x^2 + \\frac{1}{2}x + \\frac{1}{4}$.",
        "gt_answers": "\\frac { n } { 2 } ( n + 1 )\n",
        "image_path": "./data/HME100K/test_images/test_3555.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is shown below:\n\n![](https://cdn.pixabay.com/photo/2016/08/26/22/26/woman-570883\\_1280.jpg)\n\n![](https://cdn.pixabay.com/photo/2016/08/26/22/26/woman-570883\\_1280.jpg)spoa-sone=a+bspoa-sone=a+b\\frac",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a calculation for the probability of an event occurring based on the number of outcomes and the number of successful outcomes. The formula is: P(A) = (n/s) x (s/n) where n is the number of successful outcomes and s is the number of total outcomes. In this case, n = 90 and s = 150, so P(A) = (90/150) x (150/90) = 0.3928.",
        "gt_answers": "\\frac { 9 0 } { x } = \\frac { 1 3 5 } { x + 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3557.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{align} 2x - 3 &= 6 \\\n\\end{align}\n\nThis is a linear equation in one variable, with a constant term of 6 on the left-hand side and a variable term of 2x on the right-hand side. The solution to this equation is x = 4, which can be found by substituting this value into the equation and solving for x.",
        "gt_answers": "x ^ { 2 } - k _ { 1 } x - b _ { 1 } = 0 \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_3558.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$$ \\frac{4+5}{9} = \\frac{9}{9} = 4$$The fraction in the image is $\\frac{4+5}{9}$. The numerator is $4+5$, and the denominator is $9$. When we simplify the fraction, we get $\\frac{9}{9}$, which is equal to $4$. Therefore, the answer to the image is $4$.",
        "gt_answers": "\\frac { 4 } { 5 } x = \\frac { 3 } { 1 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3560.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\u222f\ufffd",
        "gt_answers": "S _ { \\Delta } A P B = \\frac { 1 } { 2 } A B \\times P H = \\frac { 1 } { 2 } \\times 3 \\times 1 = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3561.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{\\frac{2\\times3\\times4\\times5\\times6\\times7\\times8\\times9}{12\\times3\\times5\\times7\\times9}}{\\frac{10}{12}\\times\\frac{9}{10}\\times\\frac{8}{9}\\times\\frac{7}{8}\\times\\frac{6}{7}\\times\\frac{5}{6}\\times\\frac{4}{5}\\times\\frac{3}{4}}}$$",
        "gt_answers": "- \\frac { 1 6 } { 3 } < b < - \\frac { 8 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3563.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image is:$$r^2 + (b^2 - a^2) = (a + b)^2$$This is the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The variable a represents the length of the base of the triangle, b represents the length of the hypotenuse, and r represents the length of the altitude drawn from the right angle to the base.",
        "gt_answers": "k = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3565.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the slope of a line is given by the formula:\n\ny = mx + b\n\nwhere m is the slope of the line and b is the y-intercept. The equation for a vertical line with a slope of m is given by:\n\ny = mx\n\nwhere m is the slope of the line. The equation for a horizontal line with a y-intercept of b is given by:\n\nx = b\n\nwhere b is the y-intercept.",
        "gt_answers": ": y = \\frac { 1 } { 2 } x ^ { 2 } - 2 x - 6\n",
        "image_path": "./data/HME100K/test_images/test_3566.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$\\text{1 + 1} = \\frac{3}{2}$$\n\nIn this formula, the symbol $\\frac{3}{2}$ represents the sum of two numbers, $1$ and $1$, as $1 + 1 = \\frac{3}{2}$. The formula is written in LaTeX as $\\frac{3}{2}$, with the $\\frac$ symbol indicating that we are taking the sum of the two numbers.",
        "gt_answers": "1 3 b - 1 1 = 0\n",
        "image_path": "./data/HME100K/test_images/test_3567.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{c^2}{a^2 + b^2}$$\n\nThis formula is known as the Pythagorean theorem, which is used to calculate the length of the hypotenuse of a right triangle. The variables a, b, and c represent the lengths of the triangle's legs and hypotenuse, respectively.",
        "gt_answers": "\\therefore S _ { \\Delta B E D } = \\frac { 1 } { 2 } E H \\cdot B D = 2\n",
        "image_path": "./data/HME100K/test_images/test_3569.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{x}\\sin{\\left(\\frac{\\pi}{2}\\right)} = \\frac{1}{2}$$",
        "gt_answers": "y - \\frac { 6 } { y } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3571.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$\\text{f(x) = 2x^3 + 6x^2 - 4x + 1}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following code:\n\n\\begin{center}\n$\\frac{a+b}{c-d}$\n\\end{center}\n\nHere, a, b, c, and d represent the values in the image. For example, a could represent 2, b could represent 3, c could represent 5, and d could represent 7.\n\nThis formula is a fraction, with the numerator being a sum of two terms and the denominator being the difference of two terms. The values a and b are",
        "gt_answers": "x = 7 \\div \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3573.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n\\begin{align\\*}\nx = \\frac{a^2 - b^2}{2ab}\n\\end{align\\*}\n\nThis formula represents the intersection point of two circles with centers at $(a, 0)$ and $(b, 0)$ and radii $a$ and $b$, respectively. The denominator is simply the sum of the two circles'radii. The numerator is the difference between the squares of the two circles'centers, which",
        "gt_answers": "x - 1 = \\frac { 2 } { 3 } x + \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3574.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 1/2 x 0.125 + 0.08 x 0.5 + 1.1 x 0.25 + 0.05 x 0.5 = 0.043. This formula calculates the result of an experiment involving four variables: two independent variables and two dependent variables. The independent variables are the concentrations of two different types of acid, and the dependent variables are the pH values of the resulting solutions. The formula uses the laws of dilution and combination to calculate the pH values of",
        "gt_answers": "1 - y = 0\n",
        "image_path": "./data/HME100K/test_images/test_3575.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}x &= \\frac{1}{2}y^2 - \\frac{1}{4}y - \\frac{1}{4}\\\n\\end{aligned}$$\nThis formula can be used to find the x-coordinate of the vertex of the parabola given in the image, assuming that the origin is at the bottom left corner of the coordinate plane.",
        "gt_answers": "\\lambda + m = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3576.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we need to first identify the formula and its components. The formula appears to be an equation for the area of a circle.\n\nThe formula is given by the equation:\n\n(\u03c0r^2) / 4\n\nwhere r is the radius of the circle. The constant value of 4 is used to simplify the formula.\n\nTherefore, the LaTeX expression for the formula would be:\n\n$\\frac{\\pi r^2}{4}$\n\nwhere r is the radius of the circle.\n\nNote: The LaTeX",
        "gt_answers": "C a ( O H ) _ { 2 } + C O _ { 2 } = C a C O _ { 3 } \\downarrow + H _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3578.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To represent the image as an equation in LaTeX format, we can use the following LaTeX code:\n\n$$ \\frac{c}{a + b} = 1 $$\n\nwhere $a$ and $b$ are the coordinates of the image, and $c$ is the area of the image.\n\nTo find the equation for the image given, we can use the following steps:\n\n1. Identify the coordinates of the image:\n\nThe image is a rectangle with width $2$ and height $3$, so its coordinates are $(0, 0), (2, 0), (2",
        "gt_answers": "\\frac { b c } { a ^ { 2 } } \\cdot \\frac { 2 a } { b ^ { 2 } c }\n",
        "image_path": "./data/HME100K/test_images/test_3579.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is 5x - 4y + 10.",
        "gt_answers": "5 \\frac { 3 } { 8 } x = 4 7 . 5\n",
        "image_path": "./data/HME100K/test_images/test_3581.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: m/s^2 = (2*v*v)/r.",
        "gt_answers": "M _ { 3 } ( \\frac { \\sqrt { 3 } } { 3 } , 0 ) M _ { 4 } ( \\sqrt { 3 } + 2 , 0 )\n",
        "image_path": "./data/HME100K/test_images/test_3582.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n\\begin{align}\ny & = \\frac{500}{x^2 + 4x + 5}\n\\end{align}\n\nwhere $x$ is the number of days and $y$ is the number of people.",
        "gt_answers": "4 . 5 0 6 < 4 . 5 6 < 4 . 5 6 5 < 5 . 6 5\n",
        "image_path": "./data/HME100K/test_images/test_3583.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression 5\\* 3 + 2 can be written as:$\\ $5\\*3 + 2$$$5 \\* 3 + 2$$$5\\*3 + 2$$$5\\*3 + 2$$$5\\*3 + 2$$$5\\*3 + 2$$$5\\*3 + 2$$$5\\*3 + 2$$$5\\*3 + 2$$$5\\*3 + 2$$$5\\*3 + 2$$$5\\*3 + 2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \\frac{x}{y}.",
        "gt_answers": "x = \\frac { 2 8 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_3586.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:$$ 2 \\cdot 4 \\cdot 5 \\cdot 6 \\cdot 7 \\cdot 8 \\cdot 9 \\cdot 10 = 3625$$This can be written using LaTeX format as follows:$$2 \\cdot 4 \\cdot 5 \\cdot 6 \\cdot 7 \\cdot 8 \\cdot 9 \\cdot 10 = 3625$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n$$ 10\\_{5} - 3\\_{6} = 13 $$\n\nwhere $10\\_5$ represents the number of 10 in base 5 and $-3\\_6$ represents the number of $-3$ in base 6. The expression can be simplified to:\n\n$$ 10 - 3 = 13 $$\n\nwhere $-3$ is the result of subtracting 3 from 10 in the decimal system. The image is shown below:\n\n![Image of the",
        "gt_answers": "O ^ { \\prime \\prime } B = O B = 1\n",
        "image_path": "./data/HME100K/test_images/test_3588.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format of the expression in the image:\n\n\\begin{center}\n$ \\frac{3(x+2y)}{5} - \\frac{x}{3} - \\frac{y}{2} = 1$\n\\end{center}\n\nThis is a linear equation in two variables with a coefficient of 3 in the numerator and a constant term of 1 in the denominator. The solutions to the equation are the values of x and y that make the equation true.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\n$$I = \\frac{1}{2}\\left(\\frac{1}{4} + \\frac{1}{4}\\right) = \\frac{1}{4}$$\n\nIn words, the image shows the average of two pieces of cake, each cut into four equal pieces, which results in one quarter of a cake.",
        "gt_answers": "A M = \\frac { 1 } { 2 } B C = 5\n",
        "image_path": "./data/HME100K/test_images/test_3593.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{100}{160}+\\frac{30}{40}=\\frac{100+30}{160+40}=0.8125$$This expression represents the proportion of the total number of apples that have been sold.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$ \\frac{P\\_t}{P\\_0}=\\left(\\frac{d}{d+1}\\right)^t $$\n\nThis formula is derived using the binomial series expansion of the exponential function and is used to calculate the present value of a sequence of future cash flows.",
        "gt_answers": "- 2 x = 7\n",
        "image_path": "./data/HME100K/test_images/test_3595.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n3x + 4y = 14\n\nThis is a linear equation with two variables, x and y. The constant term is 14, and the coefficients are 3 for x and 4 for y.",
        "gt_answers": "x = 3 . 3 7 5\n",
        "image_path": "./data/HME100K/test_images/test_3596.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image given is:\n\n$$\\frac{4-5\\sqrt{2}}{9}$$",
        "gt_answers": "+ \\frac { \\sqrt { 5 } } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3597.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the sum of two binomials is given by:$$\\sum\\_{i=1}^{n} (x\\_i + y\\_i)$$where $x\\_i$ and $y\\_i$ are the values of the independent variables in the $i$-th binomial. The sum is calculated by adding the values of each binomial. For example, if we have two binomials with $x\\_1 = 3$ and $y\\_1 = 5$, and $x\\_2 = 6$ and $y\\_2 = 8$, then the sum would be:$$",
        "gt_answers": "( x ^ { 2 } + 2 x ) ^ { 2 } - ( x ^ { 2 } + 2 \\times ) - 6 = 0\n",
        "image_path": "./data/HME100K/test_images/test_3598.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{2x + 3y - 5}{x - y + 2}$.\n\nThe image shows a rectangle with two parallel sides and two parallel sides that intersect at a right angle. The length of the rectangle is 5 units and the width is 3 units. The image also shows a circle with a center at the intersection of the two parallel sides and a radius of 2 units.\n\nThe formula for the area of the rectangle is given by: $A = lw$, where $l$ is the length and $w$",
        "gt_answers": "x = \\frac { 1 } { 5 } \\div \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3599.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n<img>sin(45)+2sin(30)</img>\n\nTo express this formula using LaTeX format, you would write:\n\n$$\\sin(45) + 2\\sin(30)$$\n\nThis formula calculates the sum of the sine of two angles: 45 degrees and 30 degrees.",
        "gt_answers": "\\sin ( - 4 \\pi + \\frac { \\pi } { 2 } ) + \\tan \\pi - 2 \\cos O\n",
        "image_path": "./data/HME100K/test_images/test_3601.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To calculate the area of a rectangle, we can use the formula:A=l\u00d7wwhere l is the length and w is the width. For this image, the length is 4 cm and the width is 6 cm. So the area of the rectangle is 4 cm \u00d7 6 cm = 24 cm2.",
        "gt_answers": "A M = M Q\n",
        "image_path": "./data/HME100K/test_images/test_3602.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format.\n\nThe formula in the image is a mathematical expression that relates the pressure of a gas to its volume and temperature. The formula is written in Japanese kanji characters, which can be translated into the following LaTeX code:\n\n\\begin{center}\nPV = nRT\n\\end{center}\n\nHere, P is the pressure of the gas, V is its volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature of the gas in Kelvin.",
        "gt_answers": "4 ( y + 1 ) ^ { 2 } - y ^ { 2 } = 4\n",
        "image_path": "./data/HME100K/test_images/test_3604.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format:\n\n$$\\begin{aligned} x^2 + 2x + 1 &= 0 \\Rightarrow (x - \\frac{1}{2})^2 = \\frac{1}{4} \\Rightarrow (x - \\frac{1}{2})^2 = \\frac{1}{4} \\Rightarrow (x - \\frac{1}{2})^2 = \\frac{1}{4} \\Rightarrow (x - \\frac{1}{2})^2 = \\frac{1}{4} \\Rightarrow (x -",
        "gt_answers": "\\vert x - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3605.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the sum of two numbers, x and y. The formula is written as x + y.",
        "gt_answers": "\\vert x \\vert = 5\n",
        "image_path": "./data/HME100K/test_images/test_3606.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$ 2x^2 + 4x - 5 $",
        "gt_answers": "s = v t = 1 8 0 k m / h \\cdot / \\min = 1 8 0 k m / h \\cdot \\frac { 1 } { 6 0 } h = 3 k m\n",
        "image_path": "./data/HME100K/test_images/test_3607.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is:<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mi mathvariant=\"normal\">a</mi><mspace width=\"1em\"></mspace></mrow><mi mathvariant=\"normal\">b</mi></mrow></mfrac></mrow><annotation encoding=\"application/x-tex\">\\frac a b</annotation></semantics></math>This formula can be written in LaTeX format as:$\\frac{a}{b}$This formula",
        "gt_answers": "\\angle K H D = A K F\n",
        "image_path": "./data/HME100K/test_images/test_3609.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can follow these steps:\n\n1. Select the text in the image and copy it to the clipboard.\n2. Open a LaTeX editor, such as TeXstudio or overleaf.\n3. Create a new document and paste the copied text into it.\n4. Use LaTeX commands to write out the formula in the image. Here's how the formula would look in LaTeX format:\n\n$$ \\begin{aligned} \\text{sin} \\left( \\frac{\\pi}{4} \\right) + \\text{",
        "gt_answers": "3 , x = - 1\n",
        "image_path": "./data/HME100K/test_images/test_3610.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression given in the image is not shown in LaTeX format. However, the equation is written in the following way:$$\\frac{\\frac{1}{2}(x+y)}{\\frac{1}{4}x^2 + \\frac{1}{4}y^2} = \\frac{1}{2}\\sqrt{x^2 + y^2}$$This equation can be read as: The ratio of the sum of x and y to the sum of x squared and y squared is equal to the square root of the sum of x squared and y squared.",
        "gt_answers": "y 2 = k 1 \\times ( k \\neq 0 )\n",
        "image_path": "./data/HME100K/test_images/test_3611.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image provided. Please provide a clear and legible image so that I can assist you with your request.",
        "gt_answers": "y = - 1\n",
        "image_path": "./data/HME100K/test_images/test_3612.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a LaTeX formula expression in LaTeX format:\n\n$$s^2 + 4s - 3 = 0$$\n\nwhere $s$ is a variable representing the independent variable.",
        "gt_answers": "S _ { 9 } = 4 \\times 9 + 3 6 d = 0\n",
        "image_path": "./data/HME100K/test_images/test_3613.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression of the formula in the image using LaTeX format:\n\n$$\\frac{8\\times \\left(\\frac{3\\times 10+2\\times 9}{5}\\right)+3\\times 4\\times 2+4\\times 10\\times 3+1\\times 10\\times 3}{3\\times 6+4\\times 8+5\\times 9+6\\times 8}$$\n\nThe image is a formula that evaluates to: 348.",
        "gt_answers": "\\angle D O E = \\angle A O B = 9 0 ^ { \\circ } - 1 5 ^ { \\circ } = 7 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3614.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{equation} x = \\frac{45}{3} \\times 5 - 7\\end{equation}",
        "gt_answers": "x = 6 . 3 \\div 7\n",
        "image_path": "./data/HME100K/test_images/test_3615.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as:$$\\frac{x+4y}{x+2y}=\\frac{3x+4y}{3x+2y}=4$$In LaTeX format, this can be written as:$$\\frac{x+4y}{x+2y}=\\frac{3x+4y}{3x+2y}=4$$Note that the denominator in the first fraction is x+2y, and the denominator in the second fraction is x+2y. This cancels out the x+2y term in both fractions, leaving only the x and y",
        "gt_answers": "\\frac { 3 k } { 5 k } = \\frac { C H } { 2 } = \\frac { O H } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3616.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image is:$$x + 2y = 10$$The formula is a system of linear equations with two variables, x and y, and a constant value of 10. To solve for the values of x and y, we can use the substitution method, which involves solving one equation for one variable and substituting the result into the other equation to solve for the other variable. For example, we can start by solving the equation 2x + 4y = 10 for x:$$2x = 10 - 4y$$Subst",
        "gt_answers": "1 2 \\div \\frac { 6 } { 3 5 } = 7 0\n",
        "image_path": "./data/HME100K/test_images/test_3617.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{4}(x+y)(x-y)=-\\frac{1}{4}xy$.",
        "gt_answers": "S _ { \\Delta } A O D \\Rightarrow A\n",
        "image_path": "./data/HME100K/test_images/test_3618.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}(x + 2y)$.",
        "gt_answers": "x + \\frac { 3 } { 5 } x = 6 4 0\n",
        "image_path": "./data/HME100K/test_images/test_3619.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you can use the following code:\n\n\\begin{center}\n\\begin{tabular}{|c|c|}\n\\hline\n$x$ & $2x^2 + 3x - 4$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nThis code will display the formula in the same format as the image. Note that the formula is in the format of an arithmetic expression, and not a LaTeX equation, as the original image did not contain any LaTeX equations.",
        "gt_answers": "1 8 0 \\div 1 6 0 = \\frac { 9 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_3620.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{1}{2}\\left( x\\_{max} - x\\_{min}\\right) $$\nwhere xmax and xmin are the maximum and minimum x-values of the image, respectively.",
        "gt_answers": "a _ { 1 } = - 1 5 2\n",
        "image_path": "./data/HME100K/test_images/test_3621.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is:$$\\frac{a^2}{b^2}+\\frac{c^2}{d^2}=\\frac{a^2+b^2}{c^2+d^2}$$This formula represents the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.",
        "gt_answers": "y = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3622.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$ $\\frac{x\\_{n+1}}{x\\_n}=\\frac{k\\left(\\frac{x\\_{n+1}}{x\\_n}\\right)+h\\left(\\frac{x\\_{n+1}}{x\\_n}\\right)}{k\\left(\\frac{x\\_n}{x\\_{n-1}}\\right)+h\\left(\\frac{x\\_n}{x\\_{n-1}}\\right)$",
        "gt_answers": "4 7 ^ { \\circ } S - 3 0 ^ { \\circ } N\n",
        "image_path": "./data/HME100K/test_images/test_3623.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:$$x^2+y^2=r^2$$where x, y and r are variables. The image shows a right triangle with sides x, y and r and the equation represents the Pythagorean theorem that states the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side.\n\nThe equation is a quadratic equation in x and y, with the variable r raised to the power of 2. The solution to the equation involves finding the values of x and y that satisfy the",
        "gt_answers": "a _ { 2 } = \\frac { 3 } { 4 } , 9 = - \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3624.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the derivative of f(x) with respect to x, denoted by f'(x). The formula is given by: f'(x) = lim (h \u2192 0) (f(x + h) - f(x))/h.\\nThe derivative measures the rate of change of a function at a given point.",
        "gt_answers": "\\therefore x ^ { 2 } - y ^ { 2 } = ( x + y ) ( x - y\n",
        "image_path": "./data/HME100K/test_images/test_3625.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\frac{1}{2}\\left(\\frac{2x + 3y - 4z}{x + y - 2z}\\right) = \\frac{1}{2}\\left(\\frac{2(x + 2) + 3y - 4z}{x + 2y - 2z}\\right) = \\frac{1}{2}\\left(\\frac{2x + 5 + 3y - 4z}{x + y - 2z}\\right) = \\frac{1}{",
        "gt_answers": "\\frac { C H } { A H } = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3626.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the triangle with vertices at the points (3, 4), (0, 1) and (0, 1) can be found using Heron's formula. The formula is as follows:\n\nA = 1/2 x (b x h) + (sqrt x (c x h))\n\nWhere b is the base of the triangle, c is the height, and h is the altitude. Plugging in the values for the base, height, and altitude, we get:\n\nA = 1/2 x (4 x 4)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: 3x - 8y + 4z = 9.",
        "gt_answers": "x _ { 3 } = - \\frac { 8 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3629.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe expression in the image is: $1 - \\frac{4}{5} \\cdot \\frac{3}{4}$\n```",
        "gt_answers": "x _ { 1 } = 4\n",
        "image_path": "./data/HME100K/test_images/test_3630.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: $ 2^{5\\ 2} \\cdot 4\\ 5 $\n\nHere, we are taking the base 2 power of 5, which is 2 to the power of 5. Then we multiply this by 4 and 5, which gives us the final answer of $ 2^{5\\ 2} \\cdot 4\\ 5 = 2^{5\\ 2} \\cdot 20 = 32,766 $.\n\nIn LaTeX format, the formula would be written as: $ 2^{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\textstyle a = \\frac{4}{5}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image provided doesn't have a clear formula. It appears to be a piece of paper with some mathematical expressions written on it, but without any context or information about what the problem is asking for, it's difficult to provide a clear answer. If you could provide more context or information about the problem, I would be happy to help you with your math question.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$x^2 + 2x + 1 = 0$",
        "gt_answers": "x ^ { 4 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3637.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=1]\n\\draw[fill=black] (0,0) rectangle (1,1);\n\\node[right,above] at (1,0.5) {b c d};\n\\end{tikzpicture}\n\\end{center}\n\nThis LaTeX code creates a rectangle with the letters `b`, `c`, and `d` written inside it. The node is placed above the rectangle, with the letters `b`, `c`, and `d` written",
        "gt_answers": "B D = C D\n",
        "image_path": "./data/HME100K/test_images/test_3638.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![](https://www.mathworks.com/help/symbolic/ug/ug0004589.gif)\n\nwhere a, b, and c are constants and x and y are variables.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n&#x2211;x\" role=\"presentation\" style=\"position: relative;\">ddd xxxddx\\frac{ddd}{x}ddx\\frac{x^2}{a^2}+b^2=c^2\" role=\"presentation\" style=\"position: relative;\">ddd xxxddx\\frac{ddd}{x}ddx\\frac{x^2}{a^2}+b^2=c^2ddd xxxddx\\frac{ddd}{x}dd",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "In LaTeX, the expression for the formula in the image is:$$\\frac{x^2 + y^2}{a^2 + b^2} = \\frac{a^2 + b^2}{x^2 + y^2}.$$ This formula represents the distance between two points in a two-dimensional space.\n\nTo derive this formula, we start with the distance formula for the Pythagorean theorem, which states that the distance between two points in a two-dimensional space is given by the square root of the sum of the squares of the differences in the x and y coordinates:$$",
        "gt_answers": "\\frac { 1 } { a } + \\frac { 3 } { b } = 6\n",
        "image_path": "./data/HME100K/test_images/test_3643.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of the circle is A = \u03c0r^2, where r is the radius of the circle. Using the given measurements, the radius of the circle is 4 cm and the area is 50 cm^2. The volume of the sphere is then 4/3\u03c0r^3, which is 50/3\u03c0 cm^3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows:\n\n\\begin{align\\*}\n(x + y + 2) \\* (2x - 3y) &= x^2 + y^2 - xy - 2xy + 2y^2 - 3y^2 \\\n&= x^2 + y^2 - xy - 3xy + 3y^2 \\\n&= (x - y)^2 + 2y^2 \\\n&= (x - y)^2 + 2 \\\n&= (x - y)^2 \\\n&= x",
        "gt_answers": "\\frac { U _ { v } } { U } = \\frac { n } { 1 }\n",
        "image_path": "./data/HME100K/test_images/test_3645.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n$$\\frac{x^2+y^2}{r^2}=1$$\nwhere $x$ is the horizontal coordinate, $y$ is the vertical coordinate, and $r$ is the radius of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x + 4y - 3z}{x + 3y - z}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula:\n\n$$\\frac{1}{x^2 + 4x + 4} = \\frac{1}{2(x + 2)^2}$$\n\nIn the denominator, we have a sum of squares and a constant term of 4, which can be factored as $2(x + 2)$. In the numerator, we have a polynomial of degree 2, which can be factored as $x^2 + 4x$.\n\nWhen we cancel out the common factors of 2, we get:\n\n$$",
        "gt_answers": "x = \\pm \\sqrt [ 4 ] { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3649.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by the formula A = \u03c0r^2, where A is the area, \u03c0 is the pi constant, and r is the radius of the circle.\n\nIn LaTeX format, the formula can be written as:\n\n\\[ A = \\pi r^2 \\]\n\nwhere A, \u03c0, and r are typeset in math mode. The pi constant can be represented using the pi symbol, which is often written as \\pi.",
        "gt_answers": "C E + E D _ { \\min } = \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3650.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize, but I cannot see the image you provided. Please ensure that the image is visible and can be accessed by others.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the area of a circle.\n\nThe formula is given by:\n\nA = \u03c0r^2\n\nWhere A is the area of the circle and r is its radius.\n\nIn LaTeX format, this equation would be written as:\n\n$A = \\pi r^2$\n\nWhere the letter pi (\u03c0) is used to represent the mathematical constant 3.14159265358979323846, and the letter r is used to represent the radius of the circle.",
        "gt_answers": "\\angle 1 = \\frac { 1 } { 2 } \\angle E A C\n",
        "image_path": "./data/HME100K/test_images/test_3653.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = l \\* w\n\nwhere l is the length and w is the width.\n\nIn the given image, we have:\n\nl = 3.14 meters\nw = 1.41 meters\n\nSo, the area of the rectangle is:\n\nA = 3.14 \\* 1.41 = 4.29 square meters\n\nTherefore, the value of the area of the rectangle is 4.29 square meters.",
        "gt_answers": "u _ { 3 } = u - ( u _ { 1 } + u _ { 2 } ) = 4 v\n",
        "image_path": "./data/HME100K/test_images/test_3654.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we need to use mathematical symbols and variables to represent the given quantities.\n\nThe given image represents a geometric problem where the area of a circle is to be found by dividing the circumference by pi. We can write the expression for the formula in the image as follows:\n\n$$A = \\frac{C}{\\pi}$$\n\nIn the given image, the circumference of the circle is represented by the expression 2r, and the area of the circle is represented by the expression pi r^2. Therefore, we can substitute these expressions",
        "gt_answers": "\\angle B E F = \\angle C + \\angle 1\n",
        "image_path": "./data/HME100K/test_images/test_3655.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the LaTeX format for the expression:$$\\frac{a+b}{c+d}=\\frac{a+b}{c+d}$$In words, it means that if the sum of a and b is equal to the sum of c and d, then the sum of a and b divided by the sum of c and d is also equal to the sum of c and d divided by the sum of a and b.",
        "gt_answers": "( 2 ) \\frac { 5 x } { 2 4 } = \\frac { 3 x - 4 } { 8 } - 2\n",
        "image_path": "./data/HME100K/test_images/test_3656.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{mgh}{2}$. This formula represents the work done by the force of gravity on an object, which is equal to the mass of the object multiplied by the acceleration due to gravity (9.8 m/s^2) multiplied by the height of the object. The force of gravity is given by the equation F = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.\n\nWhen the force of gravity acts on an object, it causes the object to accelerate",
        "gt_answers": "x \\in ( a _ { 0 } , + \\infty ) - g ( a ) < 0 . 9 0\n",
        "image_path": "./data/HME100K/test_images/test_3658.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Average of } 5 \\text{ numbers } = \\frac{5}{5} \\times \\frac{10}{10} + \\frac{6}{6} \\times \\frac{8}{8} + \\frac{8}{8} \\times \\frac{7}{7} + \\frac{9}{9} \\times \\frac{5}{5} + \\frac{4}{4} \\times \\frac{3}{3}$$\n\nThe average of the 5 numbers is $\\",
        "gt_answers": "2 x - 4 x = - 2 + m + m .\n",
        "image_path": "./data/HME100K/test_images/test_3659.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the formula in the image is: (3x + 2) / (x + 4) = 1.5x + 2.\n\nTo write out the equation in LaTeX format, use the following code:\n\n\\frac{3x + 2}{x + 4} = \\frac{1}{2}x + 2\n\nIn this equation, the fraction is written as \\frac{a}{b}, where a and b are the numerator and denominator, respectively. The multiplication symbol is written as the fraction bar, and the division symbol is written as a",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nx = (64 \\* 10^6 \\* t) / (0.994 \\* 10^6 \\* t) - 1.5 \\* 10^5",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:\n\n\\begin{align}\na &= \\frac{1}{b} \\times \\frac{1}{c} \\times \\frac{1}{d} \\times \\frac{1}{e} \\times \\frac{1}{f} \\times \\frac{1}{g} \\times \\frac{1}{h} \\times \\frac{1}{i} \\times \\frac{1}{j} \\times \\frac{1}{k} \\times \\frac{1}{l} \\times \\frac{1}{m} \\",
        "gt_answers": "x _ { 2 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3662.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX expression for the given formula:\n\n\\begin{align\\*}\nx &= \\frac{b}{2a} \\cdot \\frac{a+b}{a-b} \\cdot \\sqrt{\\frac{a^2+b^2}{2ab}} \\cdot \\sin \\left(\\frac{\\pi}{4}\\right) \\cdot \\left(\\frac{1}{2}+\\frac{1}{4}\\right) \\cdot \\frac{1}{\\sqrt{2}} \\cdot \\frac{1}{2} \\\\\n&= \\",
        "gt_answers": "x _ { 1 } = - \\frac { 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3663.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression: $\\frac{x}{2}$ $\\cdot$ $\\frac{3x+6}{4}$ $\\cdot$ $\\frac{4x+10}{5}$",
        "gt_answers": "\\frac { 1 } { 6 } : \\frac { 1 } { 1 8 } = 3 : 1\n",
        "image_path": "./data/HME100K/test_images/test_3664.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of the circle can be written as:\n\nA = \u03c0r^2\n\nwhere A is the area of the circle, r is the radius of the circle, and \u03c0 is the mathematical constant that is approximately equal to 3.14.\n\nSo, using the given values:\n\nr = 4\nA = \u03c0r^2 = \u03c0(4)^2 = 16\u03c0\n\nTherefore, the area of the circle is 16\u03c0 square units.",
        "gt_answers": "M G \\bot E F\n",
        "image_path": "./data/HME100K/test_images/test_3665.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: $\\frac{1}{2} \\cdot \\frac{3}{4} + \\frac{1}{3} \\cdot \\frac{5}{6} = \\frac{3}{8} + \\frac{5}{12} = \\frac{35}{48}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given as: $ $ $\\frac{2x}{3}+\\frac{5y}{3}=\\frac{9}{3}$$. This formula represents the equation of a line in the x-y plane with a slope of $\\frac{2}{3}$ and an intercept of $\\frac{5}{3}$. The equation of the line is given as $y = \\frac{2}{3}x + \\frac{5}{3}$.",
        "gt_answers": "y _ { 2 } = \\frac { - 1 - \\sqrt { 5 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3667.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{\\frac{1}{2}}{\\frac{1}{4}}=\\frac{1}{2}$\n\nThis formula is derived by dividing the numerator by the denominator, resulting in a quotient of 2. The fraction is then simplified by canceling the common denominator of 4.",
        "gt_answers": "= 2 \\sqrt { 3 } + \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3668.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is \\frac{a^2 + b^2}{2a}.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n&#x2208;&#x2206;&#x2202;&#x2208;&#x2206;&#x2202;&#x2208;&#x2212;&#x2202;&#x2208;&#x2206;&#x2202;&#x2208;&#x2212;&#x2202;&#x2208;&#x2206;",
        "gt_answers": "\\Delta A N D \\sim \\Delta A C M\n",
        "image_path": "./data/HME100K/test_images/test_3671.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:c + 3b = 11b.",
        "gt_answers": "c = b : d\n",
        "image_path": "./data/HME100K/test_images/test_3672.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The expression for the formula in the image using LaTeX format is given below. Please note that the formula is written in LaTeX format and may not display correctly in this chat window.\n\nThe formula is: $\\frac{x}{y} = \\frac{400}{1200}$.\n\nHere, $x$ is the number of days taken to complete a work, and $y$ is the number of days taken to complete another work. The formula gives the ratio of the number of days taken to complete the first work to the number of days taken to complete the",
        "gt_answers": "\\frac { 1 } { 2 } \\div \\frac { 1 } { 3 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3673.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a quadratic equation with a constant term of -1 and a leading coefficient of 3. The solutions to the equation are x = -2 and x = -1, which correspond to the x-intercepts of the parabola. The solutions are not real, as they do not satisfy the condition of being a real number.\n\nThe discriminant of the equation is given by b^2 - 4ac, which is calculated as follows:\n\n(-1)^2 - 4(3)(-1) = -1 - 4(-1) = 10\n\nThere",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is as follows:\n\n$$ \\frac{3}{2} \\times \\frac{5}{4} \\times 2 + 4 = \\frac{3}{2} \\times \\frac{5}{4} \\times 4 + 4 = \\frac{15}{4} + 4 = \\frac{19}{4} $$\n\nwhere the first step is to find the product of the fractions $\\frac{3}{2}$ and $\\frac{5}{4}$ and multiply it by 2, the second step is to add 4 to",
        "gt_answers": "\\because \\angle D C F = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3677.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$\\frac{a}{b}$\n\\end{center}\n\nWhere $a$ and $b$ are the coefficients of the equation, which are given by the values of the variables in the equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Can you please provide the image?",
        "gt_answers": "x = \\frac { 1 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3681.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written in LaTeX as follows: $\\frac{x^2 - 10x + 8}{x - 2}$. The fraction is $\\frac{x^2 - 10x + 8}{x - 2}$, which can be simplified using the distributive property of multiplication over addition as $\\frac{x^2 - 10x}{x - 2}$. The resulting equation is $\\frac{x - 2}{x - 2}$, which simplifies to $1$.",
        "gt_answers": "x = \\frac { 1 1 } { 4 8 }\n",
        "image_path": "./data/HME100K/test_images/test_3682.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2} x^2 - \\frac{1}{2} x - 5$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a circular disc with radius r is given by:\n\nr2 = (h + r)2 - (r - h)2\n\nwhere h is the height of the disc and r is the radius. The height of the disc can be found by subtracting the radius from the diameter, which is given by:\n\ndiameter = 2r\n\nThus, the height of the disc is given by:\n\nh = diameter - r\n\nSubstituting this expression for h in the formula for r2, we get:\n\nr2 = (diameter",
        "gt_answers": "u > v\n",
        "image_path": "./data/HME100K/test_images/test_3684.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:",
        "gt_answers": "\\therefore \\angle A H C = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3685.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 2x^2 - 3x - 4.\n\nExplanation:\n\nThe expression given in the image is a quadratic equation, which is represented by the formula ax^2 + bx + c = 0, where a, b, and c are constants. To write the expression in LaTeX format, we can use the following syntax:\n\n2x^2 - 3x - 4\n\nThe first term, 2x^2, represents the coefficient of the squared term in the polynomial. The second term",
        "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",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$ \\frac{2}{1} = 2 $$\n\nThis formula states that the numerator (2) is equal to the denominator (1), resulting in an equality.",
        "gt_answers": "B H = C H = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3687.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the product of the sum of the first $n$ terms of an arithmetic sequence and the sum of the first $n$ terms of an arithmetic sequence, with the index of the second sequence starting at $n+1$. This is expressed mathematically as: $\\prod\\_{i=1}^{n+1} \\sum\\_{j=1}^{n} a\\_j = \\prod\\_{i=1}^{n} \\sum\\_{j=1}^{n+1} a\\_j$",
        "gt_answers": "\\{ x \\vert - b \\leq x \\leq 3 \\}\n",
        "image_path": "./data/HME100K/test_images/test_3688.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\n$$\\frac{1}{16}$$\nwhere x is the length of the rectangle and y is the width.",
        "gt_answers": "f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x\n",
        "image_path": "./data/HME100K/test_images/test_3689.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a mathematical expression representing the result of dividing two numbers by three. The expression is:\n\n(x/3) + 1 = 3(x/3)\n\nSimplifying the equation:\n\nx = 9",
        "gt_answers": "\\frac { a } { c } = \\frac { 2 } { 3 } .\n",
        "image_path": "./data/HME100K/test_images/test_3690.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} 2(x + 2) - 3 &= 2x + 4 \\qquad \\text{(1)}$$\n$$\\begin{aligned} 2x + 4 &= 2(x + 2) - 3 \\qquad \\text{(2)}$$\n$$\\begin{aligned} 2x + 4 &= 2x + 2 \\qquad \\text{(3)}$$\n$$\\begin{aligned} 2x + 2 &= 2x + 4",
        "gt_answers": "( 1 - \\frac { 1 } { 3 } - \\frac { 1 } { 4 } - \\frac { 1 } { 8 } ) x < 1 5\n",
        "image_path": "./data/HME100K/test_images/test_3691.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "x ^ { 2 } + 2 x + 1 = \\frac { 2 } { x ^ { 2 } + 2 x }\n",
        "image_path": "./data/HME100K/test_images/test_3692.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $\\sqrt 3 - 1$.",
        "gt_answers": ": y = - \\frac { \\sqrt { 3 } } { 3 } x + 1\n",
        "image_path": "./data/HME100K/test_images/test_3693.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\ce{H2CO2 + 2H+ -> CO2 + 2H2O}$$This reaction represents the dissociation of carbon dioxide in water to form carbon dioxide and water. The chemical equation shows that two hydrogen ions (H+) are added to carbon dioxide (CO2) to produce carbon dioxide and two water molecules (H2O).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: xy = yx.",
        "gt_answers": "y = k _ { 2 } x + b\n",
        "image_path": "./data/HME100K/test_images/test_3695.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n![](https://i.imgur.com/5l8QYKx.png)\n\nIn LaTeX format, this expression is:\n\n\\begin{align\\*}\n\\frac{3x^2+6x-8}{x+3}\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\nx 3x 2x + 3x + 4\n\nTo obtain this expression, we can substitute the given values into the formula:\n\nx 3x 2x + 3x + 4 = x 3x 2x + 3x + 4\n\nThe formula is simply the sum of the powers of x raised to the indicated exponents.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\nf(x) = \\frac{1}{4}(2x^2 - 4x + 1) + \\frac{1}{4}(x - 2)\n= \\frac{1}{2}x^2 - \\frac{3}{2}x + \\frac{1}{2}\n= \\frac{1}{2}(2x - 3) + \\frac{1}{2}(x - 1)\n= x - \\frac{1}{2} +",
        "gt_answers": "\\frac { 2 } { 2 } x - \\frac { 1 } { 2 } x = ( - 2 )\n",
        "image_path": "./data/HME100K/test_images/test_3698.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following code:\n\n\\begin{align\\*}\n2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 &= 16 \\\n&= 2x^2 + 3x^3 + 4x^4 + 5x^5 + 6x^6 \\\n&= 2x^2 + 3x^3 + 4x^4 + 5x^5 + 6x^6 \\\n&=",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format. It is written in a different format, which is not readable.",
        "gt_answers": "( 3 \\times 4 ) ^ { 2 } ( 2 ) = ( 3 ) ( a b ) ^ { n }\n",
        "image_path": "./data/HME100K/test_images/test_3703.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$ \\frac{a^2+b^2}{c^2}=\\frac{1}{2}(a+b)^2-\\frac{1}{2}(a-b)^2 $$\n\nwhere a, b, and c are constants.",
        "gt_answers": "\\pm \\sqrt { \\frac { x } { y } } = \\pm \\sqrt { 4 } = \\pm 2\n",
        "image_path": "./data/HME100K/test_images/test_3704.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2x+1}$.",
        "gt_answers": "- \\frac { 1 } { 1 0 } x ^ { 2 } + 1 0 x = 2 1 0\n",
        "image_path": "./data/HME100K/test_images/test_3705.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$ 5 + 6i $$\n\nwhere the imaginary unit 'i' is used to represent the square root of -1. This is a complex number, as it contains both a real and imaginary part. The real part is 5, and the imaginary part is 6.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{m\\_a}{m\\_a + m\\_b - n}$.\n\nThe subscript `m\\_a` and `m\\_b` refer to the mass of the two particles involved in the reaction. The subscript `n` refers to the number of moles of the product. The numerator is the mass of the reactant particle `a`, and the denominator is the sum of the mass of the reactant particle `a` and the product particle `b` minus the number of moles of the product.\n\nThe formula is using",
        "gt_answers": "\\sqrt { h B ^ { 2 } } = \\sqrt { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3711.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is not provided, so it cannot be written out in LaTeX format. Please provide the image for the expression to be written out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is the formula for a square.\n\nThe formula for a square is given by the equation:\n\nx = (a/2) \\* (b/2) \\* sin(y/2)\n\nwhere a and b are the length of the sides of the square and y is the angle between the two sides of the square.\n\nThe image shows the formula for a square with sides of length 5 cm and an angle of 30 degrees. The x, y and z coordinates of the image are given by the following equations:\n\nx = (5/2",
        "gt_answers": "\\sqrt { 2 } = - \\sqrt { 2 } k\n",
        "image_path": "./data/HME100K/test_images/test_3713.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\frac{x+3}{x+1}=\\frac{x+1}{x+3}$$\\frac{x+3}{x+1}=\\frac{x+1}{x+3}$In LaTeX format, this is written as$\\frac{x+3}{x+1}=\\frac{x+1}{x+3}$$\\frac{x+3}{x+1}=\\frac{x+1}{x+3}$The formula expresses the ratio of the sum of three numbers to the sum of one and one.\n\n##",
        "gt_answers": "y _ { 2 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3714.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is:\n\n$x^2 + 4x + 4 = 0$\n\nTo solve for the roots of the equation, we can use the quadratic formula:\n\n$x = \\frac{-b \u00b1 \u221a(b^2 - 4ac)}{2a}$\n\nSubstituting the values given in the image, we get:\n\n$x = \\frac{-(-4) \u00b1 \u221a((-4)^2 - 4\\times 1\\times 2)}{2\\times 1}$\n\nExpanding the square",
        "gt_answers": "\\frac { x - 3 } { 2 } + \\frac { y - 2 } { 3 } = 4\n",
        "image_path": "./data/HME100K/test_images/test_3715.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is p = r \\* b + 4.\n\np = r \\* b + 4",
        "gt_answers": "P _ { ( B ) } = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3716.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\sqrt{2x^2 + 3x - 4}$",
        "gt_answers": "( 1 . 5 \\times 0 . 8 + 1 . 5 \\times 0 . 5 + 0 . 8 \\times 0 . 5 ) \\times 2 = 4 . 7 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_3717.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:x4y3x3y4x2y2x2x3y4x3x4y2x2x2x3y4x3x4y2x2x2x3y4x3x4y2x2x2x3y4x3x4y2x2x2x3y4x3x4y2x2x2x3y4x3x4y2x2x2x3y4x3x4y2x2x2x3y4x3",
        "gt_answers": "3 \\times \\frac { 1 } { 3 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3718.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: f(x) = (x^2 - 5x + 6) / (x - 2).",
        "gt_answers": "\\sqrt { 4 } - 1\n",
        "image_path": "./data/HME100K/test_images/test_3719.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$ 2x + 3y = 10 $$\n\nwhere $x$ and $y$ are the coordinates of the points in the image.",
        "gt_answers": "\\frac { 2 x - 3 } { 4 } + 1 = \\frac { x + 2 } { 5 } + \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3721.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by the formula:$$\\frac{x+4y}{2x-y}=5$$This can be written in LaTeX format as:$$\\frac{x+4y}{2x-y}=5$$The variable x represents the numerator of the fraction, and y represents the denominator. The expression evaluates to 5 when x = 3 and y = 4.",
        "gt_answers": "\\angle 2 = \\frac { 1 } { 2 } \\angle A C D = \\angle 1\n",
        "image_path": "./data/HME100K/test_images/test_3722.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\left(\\frac{3\\times(1-5)+4\\times3}{6+2}\\right)\\times \\left(\\frac{1}{2}\\right)$$",
        "gt_answers": "x _ { 1 } = 0 , x _ { 2 } = - 3 , x _ { 3 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_3723.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$x^2 + 4x - 5 = 0$$",
        "gt_answers": "y _ { 2 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3724.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is \\frac{1}{3}+2\\frac{1}{5}+4\\frac{1}{7}+6\\frac{1}{9}+8\\frac{1}{11}+10\\frac{1}{13}+12\\frac{1}{15}+14\\frac{1}{17}+16\\frac{1}{19}+18\\frac{1}{21}+20\\frac{1}{23}+22\\frac{1}{25}+24\\frac{1}{27}+26",
        "gt_answers": "2 F C + 3 C l 2 = 2 F e C l 3\n",
        "image_path": "./data/HME100K/test_images/test_3726.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{equation}\na + b = c\n\\end{equation}\n```",
        "gt_answers": "\\frac { 7 . 5 } { 2 . 5 } = \\frac { x } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3728.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$ \\begin{aligned}\n    x &= \\frac{a^2 - b^2}{a + b} \\quad \\text{(using the formula for the difference quotient)}\\\\\n    x &= \\frac{a^2 - 2ab + b^2}{2a + b} \\quad \\text{(expanding the numerator)}\\\\\n    x &= \\frac{a^2 - ab + \\frac{b^2}{2}}{2a + b} \\quad",
        "gt_answers": "= \\frac { \\sqrt { 1 8 } } { \\sqrt { 3 } + \\sqrt { 2 } } = \\frac { \\sqrt { 1 8 } ( \\sqrt { 3 } - \\sqrt { 2 } ) } { 1 }\n",
        "image_path": "./data/HME100K/test_images/test_3731.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression shown in the image is:\n\n$$ \\begin{align\\*} x &= \\frac{2}{5} \\left( {3y + 2} \\right) \\left( {2z + 1} \\right) \\left( {4w - 3} \\right) \\left( {5x + 1} \\right) \\end{align\\*} $$",
        "gt_answers": "x = 2 y = -\n",
        "image_path": "./data/HME100K/test_images/test_3732.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is:$$\\frac{x\\_{i}}{x\\_{i+1}}=\\frac{\\frac{x\\_{i+1}}{x\\_{i+2}}}{\\frac{x\\_{i+2}}{x\\_{i+3}}}$$This can be rewritten as:$$\\frac{x\\_{i}}{x\\_{i+1}}=\\frac{\\frac{x\\_{i+1}}{x\\_{i+2}}}{\\frac{x\\_{i+2}}{x\\_{i+3}}}=\\frac{\\frac{x\\_{i+1}}{",
        "gt_answers": "O B = O D = \\frac { 1 } { 2 } B D\n",
        "image_path": "./data/HME100K/test_images/test_3733.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$ \\frac{b + 2d}{b + d} = \\frac{b - d}{b} $$\n\nwhere b and d are the number of black and white pixels, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the integral of the function f(x) = sin(x) from 0 to \u03c0, which can be written as:\u222b0\u03c0sin(x)dx.\n\nIn LaTeX format, this formula would be written as:\u222b0\u03c0sin(x)dx.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clearly written. However, based on the symbols, it appears to be a mathematical expression involving trigonometry and exponents. The formula is likely to be complex and difficult to read without further information.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is shown below:\n\nThe expression represents the product of the lengths of the sides of a triangle.",
        "gt_answers": "\\frac { 1 } { a _ { n + 1 } } - \\frac { 1 } { a _ { n } } = 5\n",
        "image_path": "./data/HME100K/test_images/test_3738.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: z(t) = a \\* ( t - t0 )^2 + b \\* sin(t), where t is time and t0 is the initial time.",
        "gt_answers": "\\angle E K G = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3739.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle with width x and height y is:A = xyThe equation for the perimeter of a rectangle with width x and height y is:P = 2(x + y)To find the perimeter of the rectangle in the image, we can count the number of squares along the edge of the image. There are 3 squares on each side, so the perimeter is 3(3 + 3) = 3\\*5 = 15. To find the area, we can use the formula above:A = 5*5 = 25.",
        "gt_answers": "x _ { 3 } = - \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3740.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ac}\\_{10}\\text{b}\\_1\\text{yt}\\_1\\text{o}\\_1\\text{g}\\_0$$",
        "gt_answers": "A C ^ { 2 } = 1 6 + 6 4 = 8 0\n",
        "image_path": "./data/HME100K/test_images/test_3741.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression for the formula in the image using LaTeX format:\n\nLet's denote the variables in the formula as follows:\n\nLet's denote the coefficients in the formula as follows:\n\nNow, we can write out the formula in LaTeX format:\n\nHere's the image for reference:\n\n![Image of the formula with the variables and coefficients denoted in LaTeX format](https://i.imgur.com/4aUZhk6.png)",
        "gt_answers": "\\frac { C D } { C A } = \\frac { C A } { C B }\n",
        "image_path": "./data/HME100K/test_images/test_3742.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the definition of the product of two binomials: (x + 2) and (y - 3). It can be written as:",
        "gt_answers": "2 x + ( x + 2 ) ^ { 4 } = 2 0\n",
        "image_path": "./data/HME100K/test_images/test_3743.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n&#x2208;&#x2202;x&#x2202;y&#x2208;&#x2202;z&#x2202;&#x2202;x&#x2202;y&#x2208;&#x2202;z&#x2202;&#x2202;x&#x2202;y&#x2208;&#x2202;",
        "gt_answers": "7 . 1 5 2 < 7 . 1 \\square 2\n",
        "image_path": "./data/HME100K/test_images/test_3745.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with base b and height h can be written as: A = bh. This formula can be derived by considering the rectangle as two triangles, one with base b and height h, and the other with base h and height b. The area of each triangle is (1/2)bh, and the total area of both triangles is the sum of their areas, which is (1/2)bh + (1/2)hb = bh.",
        "gt_answers": "y = 4 - \\sqrt { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3748.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{b}{2a} + \\frac{c}{2}$$",
        "gt_answers": "\\overrightarrow { A E } = \\frac { \\sqrt { 2 } } { 2 } \\overrightarrow { A D }\n",
        "image_path": "./data/HME100K/test_images/test_3749.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is given by:\n\nc = \u221a(a^2 + b^2)\n\nwhere c is the distance from the origin to the point (a, b).",
        "gt_answers": "C = 4\n",
        "image_path": "./data/HME100K/test_images/test_3750.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is: A = (r^2) \\* pi.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression in the image:\n\n\\begin{align\\*}\na + b &= c \\\nc - b &= a \\\na - c &= b \\\nb + c &= a \\\n\\end{align\\*}\n\nThis expression represents the associative property of addition, which states that the sum of two numbers is equal to the sum of the parts of each number. In other words, if we add two numbers, we can get the same result by adding the parts of each number separately and then combining them. The associative property is true for any two",
        "gt_answers": "x \\div 2 \\times 2 = 1 8 0 \\times 2\n",
        "image_path": "./data/HME100K/test_images/test_3752.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: $\\frac{36}{4}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick, ->] (0,0) -- (4,0) node[below] {$x$};\n\\draw[thick, ->] (0,0) -- (0,4) node[left] {$y$};\n\\filldraw (2,2) circle [radius=2pt];\n\\node [right] at (2,2) {$\\text{ImageContent}$};\n\\end{tikzpicture}\n\\end{center}\n\nThis expression",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\text{p} \\_{eq}=\\frac{3V}{2}\\cdot\\frac{2R}{1}\\cdot\\frac{5I}{2}\\cdot\\frac{2t}{1}\\cdot\\frac{2r}{1}\\cdot\\frac{2m}{2}\\cdot\\frac{1000}{1} = \\frac{3V}{2}\\cdot\\frac{2R}{1}\\cdot\\frac{5I}{2}\\cdot\\frac{2t}{1}\\cdot\\frac{2r}{1}\\cdot",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is given by:x3 + y3 = 4xy2 + y2 = 4x2 - 3xy + y = 3x - 4y = - 3y = - 3\\frac{x^3 + y^3}{x^2 + y^2} = \\frac{4xy^2 + y^2}{4x^2 - 3xy + y} = \\frac{-3xy + y}{3x - 4y} = -\\frac{3y}{3x - 4y} = -3y\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: 5+1+5+1 = 12.\n\nLaTeX format:\n$$5+1+5+1=12$$",
        "gt_answers": "a _ { n + 1 } - a _ { n } = n = 7\n",
        "image_path": "./data/HME100K/test_images/test_3759.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is an image of a mathematical expression written in LaTeX format:$$\\frac{a^2+b^2}{2ab}=\\frac{a(a+b)}{b}$$The expression represents the geometric mean of two numbers, a and b. The numerator is the sum of the squares of a and b, and the denominator is the product of a and b. The fraction simplifies to the ratio of the sum of a and b to their product.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image using LaTeX format is:\n\n$$\\frac{1}{3}x^2 + \\frac{1}{4}x - \\frac{1}{2}x + 1 = \\frac{1}{4}x^2 + \\frac{1}{4}x - \\frac{1}{4}x + 1$$\n\nThis expression is equivalent to the given image expression.",
        "gt_answers": "x - 3 y = 3\n",
        "image_path": "./data/HME100K/test_images/test_3761.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x2223;&#x22",
        "gt_answers": "a + ( - \\frac { 1 } { a } )\n",
        "image_path": "./data/HME100K/test_images/test_3762.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as follows:\n\n$$\\frac{1}{2}(x + 2y) = \\frac{1}{4}x + \\frac{3}{4}y$$\n\nThis equation represents a line that passes through the point $(1, 2)$ and has a slope of $\\frac{1}{2}$.",
        "gt_answers": "x = \\frac { 1 0 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_3763.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression given in the image is:\n\n![Image Content](https://www.quickchart.com/chart?bkg=white&c=%7B%0A%20%20type%20%20%7D)\n\nIn LaTeX format, this expression is written as:\n\n\\begin{align\\*}\n\\text{type}\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the rectangle with a perimeter of 40 and a width of 8 is given by the formula:\n\nA = lw\n\nwhere l is the length and w is the width. Substituting the given values, we get:\n\nA = 8(40)\n\nA = 320 ft2\n\nTherefore, the area of the rectangle is 320 ft2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:$$\\frac{l\\_2}{l\\_1}+\\frac{l\\_3}{l\\_2}+\\frac{l\\_4}{l\\_3}+\\frac{l\\_5}{l\\_4}+\\frac{l\\_6}{l\\_5}+\\frac{l\\_7}{l\\_6}+\\frac{l\\_8}{l\\_7}+\\frac{l\\_9}{l\\_8}+\\frac{l\\_10}{l\\_9}+\\frac{l\\_11}{l\\_10}+\\frac{l\\_12}{l\\_11",
        "gt_answers": "\\angle 1 = 3 0 ^ { \\circ } \\angle 2 = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3769.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given below.\n\n\\begin{align\\*}\n  f(x) = \\frac{1}{x^2 + 4x - 16}\n\\end{align\\*}\n\nThe image shows a parabola with its axis of symmetry at the origin. The equation of the parabola is given by y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = 1, b = - 4, and c = - 16. Substituting these values into",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n&#x2208;p=&#x2202;E&#x2202;t&#x22C5;&#x2202;H&#x2202;t&#x22C5;&#x2202;V&#x2202;t\" role=\"presentation\">\u222bp=\u2202E\u2202t\u22c5\u2202H\u2202t\u22c5\u2202V\u2202t\u222bp=\u2202E\u2202t\u22c5\u2202H\u2202t\u22c5\u2202V\u2202t\\int\\_p",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not visible to me as there is no image provided. Please provide the image so that I can assist you with the LaTeX format.",
        "gt_answers": "2 5 < x < 4 0\n",
        "image_path": "./data/HME100K/test_images/test_3772.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{a + 5}{b - 3}$$\n\nWhere,\n\na = number 7\nb = number 13",
        "gt_answers": "\\frac { 3 } { 7 } + \\frac { 1 } { 6 } = \\frac { 2 4 } { 5 6 } + \\frac { 7 } { 5 6 } \\leq \\frac { 3 1 } { 5 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3773.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX code for the expression in the image:\n\n\\begin{center}\n\\begin{minipage}{0.4\\textwidth}\n\\begin{equation}\n4x^2 + 9y^2 = 24\n\\end{equation}\n\\end{minipage}\n\\end{center}\n\nThis is a quadratic equation in two variables, $x$ and $y$. The constants 4 and 9 are coefficients of $x^2$ and $y^2$, respectively, and the constant 24 is the constant term. The equation is asking",
        "gt_answers": "4 u = 3 6\n",
        "image_path": "./data/HME100K/test_images/test_3774.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{Im}\\_{ijk} = \\frac{1}{2}(\\text{Im}\\_{ij}+\\text{Im}\\_{ik})-\\frac{1}{2}\\text{Re}\\_{ij}$$\n\nwhere $\\text{Im}\\_{ijk}$ represents the imaginary part of the complex number $z\\_{ijk}$, $\\text{Im}\\_{ij}$ represents the imaginary part of the complex number $z\\_{ij}$, and $\\text{Re}\\_{ij}$ represents the real part of the complex number $z\\",
        "gt_answers": "\\frac { 1 } { 2 } \\times \\frac { t } { 4 } \\times ( t - \\frac { 1 } { 2 } t ) = \\frac { 3 t } { 1 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3775.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is:\n\n$$ \\begin{aligned} V &= I \\cdot R \\cdot t \\end{aligned} $$\n\nwhere V is the voltage, I is the current, R is the resistance, and t is the time.",
        "gt_answers": "5 = 4 a + b\n",
        "image_path": "./data/HME100K/test_images/test_3776.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image provided is a diagram of a formula for calculating the number of solutions to a system of linear equations. The diagram shows two equations with two variables on the left side, and the solution on the right side. The formula is written in LaTeX format as follows:\n\nLet x and y be two variables.\nThen the system of linear equations is given by:\n\n2x + 3y = 7\nx - y = 0\n\nTo find the number of solutions to the system, we can use the following steps:\n\n1. Solve the system of equations for x and y.\n2",
        "gt_answers": "\\frac { b } { \\sin B } = \\frac { c } { \\sin C } \\Rightarrow \\sin c = \\frac { \\sin B } { b } \\times C = \\frac { \\frac { \\sqrt { 2 } } { 2 } } { 2 \\sqrt { 2 } } \\times 2 \\sqrt { 3 } = \\frac { \\sqrt { 3 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3777.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$2x + 3y = 10$$\n\nThis is a linear equation in two variables, where the constant term is 10 and the coefficient of x is 2 and the coefficient of y is 3. The solution to this equation is the set of values of x and y that make the equation true.\n\n$$2x + 3y = 10$$\n\nExpanding the equation, we get:\n\n$$2x + 3y = 10$$\n\nMultiplying",
        "gt_answers": "2 \\times 2 \\times 2 = 8 ( d m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_3778.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the volume of a sphere can be written as follows:\n\n$$V = \\frac{4}{3}\\pi r^3$$\n\nwhere $r$ is the radius of the sphere.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a trapezium is given by the formula:A=1bh(a+b)wherea and b are the lengths of the parallel sides and h is the height of the trapezium. Using LaTeX format, the expression can be written as:A=\\frac{1}{2}bh\\left(a+b\\right)where a and b are the lengths of the parallel sides and h is the height of the trapezium.\n\nNote that the above expression assumes that the trapezium is a solid object with uniform thickness h. If the thickness of",
        "gt_answers": "\\Delta F E B \\sim \\Delta B E A\n",
        "image_path": "./data/HME100K/test_images/test_3780.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed as:\n\nA = \u03c0r^2\n\nWhere A is the area of the circle, r is the radius of the circle, and \u03c0 is the mathematical constant pi, which is approximately equal to 3.14.",
        "gt_answers": "4 0 \\div 8 = 5\n",
        "image_path": "./data/HME100K/test_images/test_3781.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear, so it cannot be written in LaTeX format. However, the image appears to show a mathematical expression written on a piece of paper. The expression is likely a mathematical equation or formula written in mathematical notation, such as symbols and algebraic expressions.\n\nThe expression may involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The specific details of the expression depend on the context and the purpose of the formula. Without further information, it is not possible to provide a specific LaTeX representation of the expression in the image.",
        "gt_answers": "( x _ { 1 } + x _ { 2 } ) + 2 x _ { 2 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_3782.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the equation is given by:\n\nG = 5r^2 + (r/2)^2 + 1/4r^2 - 3/2r^2 + 3/4r^2\n\nUsing the LaTex format for mathematical expressions:\n\nG = \\frac{5r^2 + \\left(\\frac{r}{2}\\right)^2 + \\frac{1}{4}r^2 - \\frac{3}{2}r^2 + \\frac{3}{4}r^2}{r^3}\n\nwhere r is the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x3 + x2 - 3x - 4x2 + 5x + 1.",
        "gt_answers": "x _ { 3 } = \\frac { 4 \\sqrt { 7 } } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_3784.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n<latex>1 - ( 4x^2 + 4y^2 )</latex>",
        "gt_answers": "A = 1 2 - 2 - 4 = 6\n",
        "image_path": "./data/HME100K/test_images/test_3785.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$m = \\frac{x^2 + y^2}{r^2}$$where x and y are the coordinates of the point on the circle, and r is the radius of the circle.\n\nThe image is of a circle with a center at the origin, and two points on the circle: A(1,2) and B(3,4). The coordinates of point A are (1,2), and the coordinates of point B are (3,4). The radius of the circle is 2.\n\nUsing the formula, we",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a piece of paper with mathematical expressions written on it in black ink. The paper appears to have several calculations written on it, including multiplication, division, and addition. The expressions are written in a formula style, with letters and numbers arranged in mathematical notation. Some of the calculations appear to be derivatives or integrals, while others appear to be algebraic expressions. There are also some references to calculus, including limits and derivatives.\n\nIn LaTeX format, the mathematical expressions in the image can be written as follows:\n\n\\begin{align\\*}\na + b &= c \\\n\\frac{a}{b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\begin{center}\n\\textsf{Text in Chinese}\n\\end{center}\n\n```This is a simple example of how to typeset text in Chinese using LaTeX. The \\textsf{} command is used to create bold text, and the \\textmd{} command is used to create medium text. The \\texttildelow{} command is used to create italic text, and the \\textsf{} command is used to create bold text. The \\textasciicircum{} command is used to create a ring above a character, and the \\textasciitilde{}",
        "gt_answers": "( x ^ { 2 } - 2 x + 1 ) = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3788.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\frac{a+b}{2}=\\frac{a-b}{2}\n```",
        "gt_answers": "x = \\frac { 2 1 } { 2 } \\div \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3789.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: f = 9.8 m/s^2.\n\nHere is how you could write it out in LaTeX format:\n\n$$f = 9.8 \\ m/s^2$$",
        "gt_answers": "m > - \\frac { 1 } { 2 } .\n",
        "image_path": "./data/HME100K/test_images/test_3790.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\begin{aligned} 2x + 3y &= 7 \\Rightarrow x + 2y &= 5 \\Rightarrow x &= 2y - 5 \\Rightarrow y &= \\frac{5 - 2x}{2} \\Rightarrow \\frac{5 - 2x}{2} + x &= 2y \\Rightarrow 2y + \\frac{5 - 2x}{2} &= x \\Rightarrow 2y + \\frac{7 - 2x}{2} &= x \\Rightarrow x = \\frac{2",
        "gt_answers": "3 y + \\frac { 4 } { y } = 8\n",
        "image_path": "./data/HME100K/test_images/test_3791.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$5\\times\\frac{6}{9} = 25\\frac{6}{9}$$This is a multiplication of 5 times the fraction 6/9, which is equal to 25/9.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{x} = \\frac{a + 2b + 3c}{4} \\qquad \\text{y} = \\frac{a + 3b + 4c}{5} \\qquad \\text{z} = \\frac{a + 4b + 5c}{6}$$\n\nwhere $a, b, c$ are arbitrary constants.",
        "gt_answers": "\\textcircled { 1 } A \\times \\frac { 6 } { t } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3794.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by: $\\frac{3xy + 4x - 2y}{5y + 3x}$.",
        "gt_answers": "= \\frac { 3 } { \\sqrt { 2 } - 1 } = 3 \\sqrt { 2 } + 3\n",
        "image_path": "./data/HME100K/test_images/test_3795.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot write out the expression of the formula in the image using LaTeX format because I cannot see the image. Can you please provide the image?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by: $\\frac{1}{2}m\\frac{v^2}{2}+\\frac{1}{2}mv^2-\\frac{1}{2}m\\frac{v^2}{2}+\\frac{1}{2}mv^2=\\frac{1}{2}mv^2$\n\nThis is the formula for the kinetic energy of an object moving at a constant velocity. It is given by the sum of the kinetic energy associated with the object's mass and its velocity, and the potential energy associated with the object's gravitational field.",
        "gt_answers": "4 d m ^ { 3 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_3797.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given below:\n\n![ImageContent](https://i.imgur.com/i4vvvxk.png)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image using LaTeX format is $\\frac{1}{4x^2+2x+1}$.\n\nNote that the denominator is $4x^2+2x+1$, and the numerator is $\\frac{1}{4x^2+2x+1}$. To write this in LaTeX, we can use the following code: $\\frac{1}{4x^2+2x+1}$.\n\nLaTeX is a typesetting language that is commonly used in mathematics to write mathematical expressions in a clear and concise manner. It uses a special set of characters and symbols",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$$\\frac{4\\left(\\frac{4\\left(\\frac{1}{3}+\\frac{1}{6}\\right)}{2}+\\frac{1}{5}\\right)}{3}$$\n\\end{center}\n\nThe formula calculates the average of the number of people in a room who smoke cigarettes. The formula first calculates the average number of smokers per person using the expression $\\frac{4\\left(\\frac{1}{3}+\\frac{1}{6}\\right)}{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 3x + 2y = 14.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed as: A = pi \\* r^2, where r is the radius of the circle. In this case, the radius is 2.5 cm. So the area of the circle is: A = pi \\* 2.5^2 = 2.5^2 \\* pi = 6.28 \\* pi = 6.28 \\* 3.14 = 20.08 cm^2.",
        "gt_answers": "\\angle B = \\angle A O F = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3806.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\frac{d^2x}{dt^2} = \\frac{k}{m} \\frac{dx}{dt} - \\frac{b \\omega^2}{m^2} x\n\n```",
        "gt_answers": "\\frac { 1 } { 4 } = 2 0\n",
        "image_path": "./data/HME100K/test_images/test_3807.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows using LaTeX format:\n\n$$x = \\frac{2y}{y + 1}$$",
        "gt_answers": "x = \\frac { 5 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_3808.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is $A = \\pi r^2$, where $A$ is the area, $r$ is the radius of the circle, and $\\pi$ is the mathematical constant approximately equal to 3.14159. So, the formula would be $A = \\pi r^2$.",
        "gt_answers": "\\angle D E = \\frac { 1 } { 2 } \\angle B O D\n",
        "image_path": "./data/HME100K/test_images/test_3809.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: f(x) = x^2 + 6x - 8.",
        "gt_answers": "y = \\frac { 4 6 8 } { x } - 6 \\sqrt { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3810.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is \\frac{1}{\\sqrt{2}}.\n\nThis can be written in LaTeX format as:\n\n\\frac{1}{\\sqrt{2}}\n\nThe formula calculates the square root of 2. The numerator is 1 and the denominator is the square root of 2. The result is 1 over the square root of 2, which simplifies to 1/2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a mathematical expression in LaTeX format for the given image:\n\n\\begin{center}\n$\\frac{2(2n + 1)}{n^2 - 3n + 2}$\n\\end{center}\n\nThis expression represents the area of a right triangle with a hypotenuse of length 2n + 1 and legs of length n and n - 2.",
        "gt_answers": "\\widehat { B D } = \\widehat { C D }\n",
        "image_path": "./data/HME100K/test_images/test_3812.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$y = \\frac{5(x + 4) - 7}{2x - 10}$$\n\nHere's a breakdown of the formula:\n\n* $y$ is the dependent variable, which is the thing we're trying to find.\n* $5(x + 4)$ is the independent variable, which is the thing we're using to find $y$.\n* $-7$ is a constant value that is subtracted from the independent variable.\n* $2x -",
        "gt_answers": "\\frac { 3 - 4 x } { 9 } = 1 - \\frac { x - 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3813.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given by:\n\nx = sqrt(36) - 6\n\nwhich can be written in LaTeX format as:\n\n$$ x = \\sqrt{36} - 6 $$",
        "gt_answers": "x < \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3814.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{x^2+y^2}{2x+2y}=x^2+\\frac{y^2}{2x+2y}$$The formula is a parabola with vertex at the origin and passes through the points (2,1) and (1,3).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is A = \u03c0r^2. This formula can be written as A = \u03c0r^2 in LaTeX format.",
        "gt_answers": "x = \\frac { 1 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3816.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula for the expression given in the image is:$$\\frac{60}{40}=1.5$$This can be represented in LaTeX format as:$$\\frac{60}{40}=1.5$$",
        "gt_answers": "\\frac { 7 } { 1 2 } = \\frac { 3 5 } { 6 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3817.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\frac{4}{x}+\\frac{2}{y}+\\frac{1}{z}=\\frac{12}{xy+2z}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2}(3x + 4y) = 5$",
        "gt_answers": "\\vert a \\vert + 1 = 2\n",
        "image_path": "./data/HME100K/test_images/test_3819.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the image you provided:\n\n\\begin{center}\n\\begin{equation}\nf(x) = \\frac{1}{x^2 + 4}\n\\end{equation}\n\\end{center}\n\nThis is the formula for the function that is shown in the image.",
        "gt_answers": "x = \\frac { 4 } { 3 } \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3820.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX format of the expression in the image:\n\n\\begin{align}\ny &= x^2 + 5x - 3 \\\n\\end{align}\n\nHere, `y` is the dependent variable and `x` is the independent variable. The equation is in the form of a quadratic equation, with the constant term `3` added to the squared term `x^2`.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length 10 and width 4 is:\n\nA = l \\* w\n\nwhere l is the length of the rectangle and w is the width of the rectangle. The area of the rectangle is 10 \\* 4 = 40.",
        "gt_answers": "x : 3 = 5 : 7 5\n",
        "image_path": "./data/HME100K/test_images/test_3823.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\nf (x) = \u2211\\_{i=1}^n a\\_i \\* x^i\n\nwhere a\\_1, a\\_2,..., a\\_n are constants.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression of the formula in the image:\n\n$$\\text{The image shows the formula for the area of a triangle, given its base and height.}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To calculate the area of a rectangle with a base length of 4 cm and a height of 3 cm, you can use the formula for the area of a rectangle: A = l \\* w, where l is the length and w is the width. Substituting the given values, we have: A = 4 \\* 3 = 12 cm^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\includegraphics[width=0.5in]{image.png}\n\\end{center}\n\nIn the above expression, the `\\includegraphics` command is used to include the image in LaTeX. The `[width=0.5in]` argument specifies the width of the image to be 0.5 inches. The `:` in the expression is used to position the image in the center of the page.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression on the image:\n\n$$ 2x + 5y - 3z = 1 $$\n\nThis is a linear equation in three variables, with coefficients 2, 5, and -3 for the variables x, y, and z, respectively. The constant term is 1, which is the target value that the system must reach.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the formula in the image:\n\n$$\\begin{aligned}2x+3y&=14 \\quad \\Rightarrow \\quad 2x+3y=\\frac{14}{2}\\Rightarrow 2x=11 \\quad \\Rightarrow \\quad x=\\frac{5}{2}\\Rightarrow y=\\frac{8}{2}\\end{aligned}$$\n\nNote that the substitution of the variables has been made to simplify the expression. The equation is a linear equation of the form $ax+by=c$, where $a,b,c$ are constants.\n##",
        "gt_answers": "1 - \\frac { 3 } { 8 } - \\frac { 1 } { 8 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3832.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written as follows:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{1}{x}+\\frac{5}{x^2}+\\frac{9}{x^3}$$\n\nIn this formula, the variables are represented by the variables x, y, and z. The numerator of the fraction contains the terms of the polynomial equation, which are raised to different powers. The denominator is the variable x raised to the power of one.",
        "gt_answers": "5 \\div 6 = \\frac { 5 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_3834.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\frac{x+3y+2z}{x+y+z} = \\frac{11}{4}\n\nThis can be read as \"the sum of x plus three times y plus two times z, divided by the sum of x plus y plus z, is equal to 11 divided by four.\"",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ \\frac{a+b}{c+d} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write the expression of the formula in the image using LaTeX format.\n\nThe formula in the image is: $4x^2+6x+5$.\n\nHere's how it looks in LaTeX format:\n\n$$4x^2 + 6x + 5$$",
        "gt_answers": "x ^ { 2 } = 1 5 + \\frac { \\sqrt { 2 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3839.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the formula in LaTeX format: $\\ce{CH3CH2CH3CH2CH2CH3CH2CH2CH2CH3CH2CH3CH3CH2CH2CH2CH3CH2CH2CH2CH3CH2CH3CH3CH2CH2CH2CH2CH3CH2CH2CH2CH3CH2CH2CH2CH3CH2CH3CH2CH2CH2CH2CH3CH2CH2CH2CH2CH3CH2CH3CH2CH2CH2CH3CH2CH2CH2CH",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n$$\\begin{aligned} x^2 + 6x + 8 &= 0 \\quad \\Rightarrow \\quad x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} \\\n\\end{aligned}$$\n\nwhere $a = 1$, $b = 6$, and $c = 8$.",
        "gt_answers": "3 ( x - 2 ) - ( x - 1 ) = x ^ { 2 } - 4\n",
        "image_path": "./data/HME100K/test_images/test_3843.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:\n\n$$x + \\frac{1}{2}$$\n\nThe image shows a right triangle with base $x$ and height $1$. The sum of the base and height is equal to the height.",
        "gt_answers": "1 6 x : 2 1 ( 5 1 - x ) = 5 : 3\n",
        "image_path": "./data/HME100K/test_images/test_3844.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 3.5 cm is given by:\n\nA = (pi \\* r^2)\n\nwhere r is the radius of the circle.\n\nSubstituting the given values:\n\nA = (3.14 \\* 3.5^2) cm^2\nA = 22.56 cm^2\n\nTherefore, the area of the circle is 22.56 cm^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u2211(k=1n)(1/k) = 1/(n+1)\n\nIn LaTeX format, this can be written as:\n\n\\sum\\_{k=1}^n \\frac{1}{k} = \\frac{1}{n+1}\n\nwhere the sum symbol is represented by the \"\u2211\" command and the fraction symbol is represented by the \"/\" character. The subscript notation \"k=1n\" indicates that the variable \"k\" is equal to 1 and the upper bound of the sum is \"",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the area of a triangle. The formula is: A = (bh/2) where b is the base of the triangle and h is the height. In this case, b = 8 and h = 5, so A = (8 \\* 5/2) = 10.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the given formula: $\\frac{5x+6y}{x+5y}$\n\nExplanation:\nThe given formula is $\\frac{5x+6y}{x+5y}$, which is a ratio of polynomials. In LaTeX, we can write it as $\\frac{a}{b}$, where $a$ and $b$ are the polynomials.\nThe numerator $a$ is $5x+6y$, and the denominator $b$ is $x+5y$. To write these polynomials in LaTeX, we can use the $\\frac{}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Select the text in the image that corresponds to the formula. In this case, it is the number 1234567890.\n2. Type the formula using LaTeX syntax. The formula for the given image is 3x^2 + 2x - 5.\n3. Use the '\\frac' command to display the fraction. For example, if we want to display the fraction 1/2 in the formula, we would type '\\frac{1}{2",
        "gt_answers": "A F = \\frac { 1 } { 2 } B D \\Rightarrow\n",
        "image_path": "./data/HME100K/test_images/test_3849.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX code for the expression:\n\n\\begin{align}x + 4 = 3x - 1 \\Rightarrow x = \\frac{1}{2}x + 2\\end{align}\n\nThis equation is saying that the sum of x and 4 is equal to 3 times x minus 1. By dividing both sides by 3, we can simplify the equation to x + 1 = x + 2/3. Solving for x, we get x = 2/3. So the value of the expression is 2/3.",
        "gt_answers": "x _ { 2 } = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3851.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$\\text{B}=mg\\left(\\frac{h^2}{2b}+\\frac{v^2}{2a}\\right)$$\n\nwhere $m$ is the mass of the block, $g$ is the acceleration due to gravity, $h$ is the height of the block from the surface it is resting on, $a$ is the area of the surface the block is resting on, and $b$ is the coefficient of friction between the block and the surface.\n\nNote that this formula assumes that the block is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{4\\sqrt{2}}{2\\sqrt{7}}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length l and width w is given by: 0. The area of a rectangle with length l and width w is given by the formula A = lw. The formula for the area of a rectangle with length l and width w is given by: 0. The area of a rectangle with length l and width w is given by the formula A = lw. The formula for the area of a rectangle with length l and width w is given by: 0. The area of a rectangle with length l and width w is given by the formula A = lw. The formula",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is:\n\n(p + 2q) / (p + 3q) = 2p - 3q\n\nThis equation is derived from the formula for the geometric mean, which is given by:\n\nGM = n / (1 + (n - 1)r)\n\nwhere n is the number of quantities being averaged, r is the common ratio of the quantities, and GM is the geometric mean. To simplify the formula, we can rearrange it as follows:\n\nn / (1 + (n - 1)r) = GM",
        "gt_answers": "P _ { 2 } = \\frac { 1 } { 3 } P _ { ( A C ) }\n",
        "image_path": "./data/HME100K/test_images/test_3855.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is:A = \u03c0r^2, where r is the radius of the circle. To find the radius of the circle in the image, we can use the formula for the area of a circle and solve for r. The formula is:A = \u03c0r^2, where r is the radius of the circle. Substituting the given values, we have:A = \u03c0r^2A = \u03c0r^2A = \u03c0r^2r = 2.5r = 2.5Substituting the value for r,",
        "gt_answers": "a = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3856.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is 3x^2 + 4y^2 - 5xy.\n\nThis is the formula for the distance between the point (x, y) and the point (a, b) in two-dimensional space. The variable x represents the horizontal distance and y represents the vertical distance. The variable a represents the x-coordinate of the second point and b represents the y-coordinate of the second point. The term -5xy represents the negative slope of the line connecting the two points.",
        "gt_answers": "1 2 \\times 1 2 = 1 4 4 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_3857.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: (x + y) / (x - y) = 2, where x and y are the coordinates of the two points on the line.",
        "gt_answers": "6 + \\frac { x } { 3 } = \\frac { 8 - 2 x } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3861.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The expression in the image can be written as follows:\n\nsin&#x2061;a&#x2061;2 sin&#x2061;a&#x2061;2cos&#x2061;a&#x2061;2sin&#x2061;a&#x2061;2sin&#x2061;a&#x2061;2cos&#x2061;a&#x2061;2cos&#x2",
        "gt_answers": "S i n A = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3862.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by: $ $\\frac{\\frac{5}{4}}{\\frac{4}{3}}=\\frac{5}{6}$ $ $ $\\frac{5}{4}=\\frac{5}{6}$ $ $\\frac{4}{3}=1$ $ $\\frac{4}{3}=1$ $ $ $ $\\frac{5}{6}=\\frac{5}{6}$ $ $\\frac{5}{6}=1$ $ $ $\\frac{1}{1}=\\frac{1}{1}$ $ $\\frac{1}{1}=\\frac{1}{1}$ $ $\\frac{1}{",
        "gt_answers": "1 1 y = 3 3\n",
        "image_path": "./data/HME100K/test_images/test_3863.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX formula for the expression shown in the image:\n\n$$\\frac{2x^2+3x-5}{x^2+5x+8}$$\n\nThe expression represents a polynomial division of the form $\\frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials. To simplify the expression, we can factor out the common factor of $x^2$ from the numerator and denominator:\n\n$$\\frac{2x^2+3x-5}{x",
        "gt_answers": "x = \\frac { 9 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3864.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $$ p = 2 \\cdot (m + 3) $$ where p is the number obtained by adding 3 to the product of m and 2.\n\nThe formula can be read as: 'p equals 2 times m plus 3'.",
        "gt_answers": "\\rho = \\frac { m } { V } = \\frac { 2 k g } { 2 . 5 \\times 1 0 ^ { - 3 } m ^ { 3 } } = 8 0 0 k g / m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3866.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written in the image is as follows:\n\n![](https://i.imgur.com/q3VGj1S.png)x^2+y^2=r^2\\",
        "gt_answers": "x = \\pm 3 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3867.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{5 \\times 4 \\times 3}{2 \\times 2 \\times 1}$\n\nThis formula represents the factorial of the number 5, which is the product of all positive integers less than or equal to 5. The result is 120.",
        "gt_answers": "( 5 . 5 - 2 . 5 ) x + 5 - 5 \\times 4 8 = 4 8 0\n",
        "image_path": "./data/HME100K/test_images/test_3869.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\begin{aligned} f(x) &= \\frac{1}{x} \\cdot \\frac{x+3}{x+1} \\cdot \\frac{x+2}{x+5} \\cdot \\frac{x+4}{x+9}\\\n\\end{aligned}$$",
        "gt_answers": "x = \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3871.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image provided is a mathematical formula, but it is not clear what it represents. Can you provide more context or information about the formula?",
        "gt_answers": "x = 7 o r x = - 1\n",
        "image_path": "./data/HME100K/test_images/test_3872.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\nLet $f(x) = \\frac{1}{x^3 + 2x^2 - 3x + 1}$. Find the local maximum and minimum values of $f(x)$ on the interval $[-2,2]$.\n\nThe derivative of $f(x)$ is given by:\n\n$$f'(x) = \\frac{3x^2 - 5x - 1}{(x^3 + 2x^2 - 3x + 1)^2}$$\n\nTo",
        "gt_answers": "7 \\times 7 \\times 7 = 3 4 3 d m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3873.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression for the formula in the image using LaTeX format:\n\n$$\\begin{aligned}x^2 + 2 &= 14 \\Rightarrow 2x^2 = 16 \\Rightarrow x^2 = 8\\end{aligned}$$\n\nThe formula is a quadratic equation in standard form, where the variable x is raised to the second power and is multiplied by 2, resulting in the equation $2x^2 = 16$. Solving for x, we get $x = \\frac{1}{2}$, which is the only solution to the equation",
        "gt_answers": "\\frac { A B } { D F } = \\frac { A D } { C D }\n",
        "image_path": "./data/HME100K/test_images/test_3875.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{a^2+b^2}{2ab}=\\frac{a^2+b^2-ab}{2ab}=\\frac{a+b}{2a}=\\frac{a+b}{2b}=\\frac{a-b}{2a}=\\frac{a-b}{2b}=\\frac{a^2-b^2}{2ab}=\\frac{a-b}{2a}=\\frac{a-b}{2b}=\\frac{a-b}{2b}=\\frac{a-b}{2a}=\\frac{a",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by the equation:\n\nx^2 + y^2 = (a + b)^2\n\nwhere a and b are constants. To solve for x and y, we can substitute the values of a and b into the equation and solve for x and y. For example, if a = 3 and b = 4, the equation becomes:\n\nx^2 + y^2 = (3 + 4)^2\n\nSimplifying this equation gives:\n\nx^2 + y^2 = 7\n\nTo solve for x and y, we",
        "gt_answers": "x = - 1 \\frac { 1 } { 3 } - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3877.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is not provided.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you would use the following code:\n\n\\begin{align}\n\\frac{dV}{dt} &= \\frac{d(W \\sin(t))}{dt} \\\n&= \\frac{dW}{dt} \\sin(t) + W \\cos(t) \\frac{d\\theta}{dt} \\\n&= W \\cos(t) \\frac{d\\theta}{dt} \\\n&= W \\cos(t) (-\\frac{1}{2}V^2) \\\n&= -\\",
        "gt_answers": "6 0 = ( 7 ) + ( 3 3 )\n",
        "image_path": "./data/HME100K/test_images/test_3879.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{1}{2}\\left(x + \\frac{1}{4}\\right) + \\frac{1}{4}\\left(y + \\frac{1}{4}\\right) = 1$$\n\nHere, the formula is a system of linear equations in two variables x and y, which represents a line in two dimensions. The fractional coefficients before each variable x and y indicate that the variables are multiplied by a fraction, which makes the coefficients fractional rather than whole numbers. The fractional coefficients before x and y",
        "gt_answers": "\\frac { 1 } { 1 2 } x - \\frac { 1 } { 6 } + 1 = 7\n",
        "image_path": "./data/HME100K/test_images/test_3880.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image provided is a simple mathematical expression that represents a fraction. The numerator is 15, and the denominator is 6. To find the result, we can divide 15 by 6, which gives us 2.5.\n\nIn LaTeX format, we can write the expression as follows:\n\n\\frac{15}{6}\n\nor\n\n\\frac{15}{6}\n\nBoth of these expressions represent the same value of 2.5, which can be simplified further if needed.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the number of squares in an image can be written as:n22+n22=n22\\binom{n}{2} + \\binom{n}{2} = \\binom{n}{2}n22\u200b+n22\u200b=n22\u200bHere, n22\u200b is the number of squares in the first row, n22\u200b is the number of squares in the second row, and n22\u200b is the number of squares in the third row.n22\u200b+n22\u200b=n22\u200b\\binom{n}{2",
        "gt_answers": "- 2 a = - \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3882.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: \\frac{3x + 4y}{x + 2y} = 5.\n\nThis can be written as: $\\frac{3x + 4y}{x + 2y} = 5$",
        "gt_answers": "\\Delta = a ^ { 2 } - 4 \\times 4 \\times 4 < 0\n",
        "image_path": "./data/HME100K/test_images/test_3883.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To display the image in LaTeX format, you can use the `\\includegraphics` command from the `graphicx` package. The syntax is:\n\n\\begin{center}\n\\includegraphics[width=\\textwidth]{image\\_file\\_name.jpg}\n\\end{center}\n\nwhere `width` specifies the width of the image and `image\\_file\\_name.jpg` is the name of the image file.\n\nHere is the LaTeX formula for the expression of the formula in the image:\n\n\\begin{center}\n\\begin{align*}\n    \\frac{d}{dt}\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n![Latex Formula](https://latex.codecogs.com/svg.image?%5C%5C%22%7B%5C%5C%22%5C%22%7D%22%5C%5C%22%7B%5C%5C%22%5C%22%7D%22%7D)",
        "gt_answers": "\\angle A C E = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_3885.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the formula in LaTeX format, you can use the following LaTeX code:\n\n\\begin{center}\n$\\frac{a+b}{c+d}$\n\\end{center}\n\nwhere $a,b,c,d$ are the letters in the formula. This will display the formula in the center of a page. You can also use other LaTeX commands to format the formula, such as using fractions, exponents, and other mathematical symbols.",
        "gt_answers": "x _ { 1 } = 0 . x _ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3886.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$\\frac{x^2 - 5x + 6}{x - 2}$$\n\nThis code represents the given expression, which is the difference of the quadratic polynomial $\\frac{x^2 - 5x + 6}{x - 2}$ evaluated at $x = 3$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\nF = ma\n```",
        "gt_answers": "F _ { 1 } L _ { 1 } = F _ { 2 } L _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3889.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n3x + 4y = 3(2x + 3y)\n\nTherefore, the solution to the problem is x = -3 and y = -4.",
        "gt_answers": "3 \\times 9 + 6 = 3 3\n",
        "image_path": "./data/HME100K/test_images/test_3890.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as:$$R = \\frac{V^2}{2L}$$where $R$ is the resistance, $V$ is the voltage applied across the resistor, and $L$ is the length of the resistor. This equation states that the resistance of a resistor is inversely proportional to the square of the voltage applied to it and directly proportional to the length of the resistor.",
        "gt_answers": "\\frac { U _ { 1 } } { U _ { 2 } } = \\frac { R _ { 1 } } { R _ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_3891.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{1}{2}(2x + 3) - 5 $$\n\nThis formula is a polynomial of degree 1, which means it has one term. It is equal to half of the sum of x and 3, minus 5. The fraction symbol $\\frac{1}{2}$ is used to denote the division of the numerator and denominator by 2. The $2x$ term represents the linear term of the polynomial, while the $3$ term represents the constant term. The $-5$ term represents",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x}{y}$.",
        "gt_answers": "7 \\times 9 0 = 9 7\n",
        "image_path": "./data/HME100K/test_images/test_3894.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n\\begin{align\\*}\nx + 5 = 7\n\\end{align\\*}\n\nThe above equation represents the formula in the image. The equation says that the sum of 5 and the number represented by the image is 7.\n\nThe equation can be written in LaTeX format as follows:\n\n\\begin{align\\*}\nx + 5 = 7\n\\end{align\\*}\n\nIn this equation, the variable x is represented by the variable x",
        "gt_answers": "1 - \\frac { 5 } { 1 2 } = \\frac { 7 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3895.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$ 3x + 2y = 7 $$",
        "gt_answers": "1 2 k ^ { 2 } = k ^ { 2 } + 1\n",
        "image_path": "./data/HME100K/test_images/test_3896.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{equation} x^2 + 2x + 1 = 0 \\end{equation}\n\nNote that the equation is in standard form, with the leading coefficient of 1 for the constant term.",
        "gt_answers": "x _ { 4 } = - \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3898.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw (0,0) -- (1,1) -- (1,0) -- cycle;\n\\filldraw (0,0) circle (2pt) node[left] at (0,0) {$ \\begin{aligned} x &= 3 \\\\ y &= 4 \\end{aligned}$};\n\\filldraw (1,0) circle (2pt) node[below] at (1,0) {$ \\begin{aligned} x &=",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format, so it cannot be written out as an equation. It shows the chemical formula for sodium sulfate, Na2SO4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \\frac{x}{y+2}.",
        "gt_answers": "x : \\frac { 2 5 } { 2 } = \\frac { 1 2 } { 5 } : 3\n",
        "image_path": "./data/HME100K/test_images/test_3901.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\frac{1}{2} \\cdot \\frac{1}{3} \\cdot \\frac{2}{5} \\cdot \\frac{4}{6} = \\frac{1}{60}$$\n\nTo obtain this result, we use the formula:\n\n$$\\frac{a}{b} \\cdot \\frac{c}{d} \\cdot \\frac{e}{f} = \\frac{a \\cdot c \\cdot e}{b \\cdot d \\cdot f}$$\n\nWe substitute the values given in the image",
        "gt_answers": "R = \\frac { R _ { 0 } } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3902.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{d}S = \\frac{\\text{d}Q}{\\text{d}T} \\times \\frac{T}{S} $$\n\nwhere dQ/dT is the derivative of the heat with respect to temperature, and T/S is the slope of the melting curve.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is a mathematical formula for calculating the number of seconds it takes to fly from one city to another. It appears to be a calculation of the time it takes to fly from New York to Los Angeles, using the equation 5 hours 45 minutes = 5 \\* 60 + 45 minutes. The equation is written in the form of minutes \\* 60 = time in hours. The answer is 5 \\* 60 = 300 minutes = 5 hours.\n\nYou can write the equation as follows:\n\n5 hours = 5 \\*",
        "gt_answers": "\\angle D O E = 3 6\n",
        "image_path": "./data/HME100K/test_images/test_3905.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given formula:$$\\frac{1}{\\sqrt{2}}\\times\\sqrt{1+\\frac{1}{4}}=\\frac{1}{\\sqrt{2}}\\times\\sqrt{1+\\frac{1}{4}}$$Note that the formula has two terms in the numerator and denominator, which are both raised to the same power. The fraction in the denominator is simplified to $\\frac{1}{\\sqrt{2}}\\times\\sqrt{1+\\frac{1}{4}}$, which can be further simplified to $\\frac{1}{\\sqrt{2}}\\times\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is:\n\nA = \u03c0r^2A = \\frac{\\pi}{r^2}A=\u03c0r2\u200bwhere r is the radius of the circle.\n\nTo find the area of the circle in the image, we can use the formula above with the given radius, 3.58 mm.\n\nA = \u03c0r^2A = \\frac{\\pi}{r^2}A=\u03c0r2\u200b= 3.58 mmA = \\frac{\\pi}{r^2}A=3.58 mmThere",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression for the sum of two numbers. The formula is:2 + 2 = 4.",
        "gt_answers": "3 \\div 4 = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3908.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as follows in LaTeX format:\n\n\\begin{align\\*}\nA = \\frac{\u03c0r^2}{4}\n\\end{align\\*}\n\nwhere $A$ is the area of the circle, $r$ is the radius of the circle, and $\u03c0$ is the mathematical constant pi.",
        "gt_answers": "2 u - v = 7\n",
        "image_path": "./data/HME100K/test_images/test_3909.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{mg}{V^2}$.\n\nHere is the LaTeX code for the expression:\n\n\\frac{mg}{V^2}\n\nThe formula represents the weight-to-displacement ratio, which is a measure of the stiffness of a material. It is calculated by dividing the weight of an object by the displacement it experiences when subjected to a given force. The result is a dimensionless quantity that can be used to compare the stiffness of different materials.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$ $\\frac{a+b}{c+d}=\\frac{a}{c} + \\frac{b}{d}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we need to use the LaTeX command to define the variables and their values, and then use the LaTeX commands to perform the arithmetic operations. The formula in the image is given by:\n\n$$\\text{BMI} = \\frac{w}{h}$$\n\nwhere w and h are the weight and height of the person, respectively. In LaTeX format, we can write this as:\n\n$$\\text{BMI} = \\frac{w}{h}$$\n\nHere, we have used the `\\text` command to define the variable name",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with width w and length l is given by:\n\nA = lw\n\nThis formula can be derived using the definition of an area, which is the amount of space inside a two-dimensional shape, such as a rectangle. The width and length of the rectangle are multiplied together to find the area.",
        "gt_answers": "\\frac { A M } { D M } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3919.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick] (0,0) -- (1,0) -- (1,1) -- (0,1) -- cycle;\n\\filldraw (0,0) circle (2pt) node[below] {$ x$};\n\\filldraw (1,0) circle (2pt) node[below] {$ y$};\n\\filldraw (1,1) circle (2pt) node[left] {$ z$};\n\\filld",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{x^2 + 3x - 5}{x - 2}$.",
        "gt_answers": "5 x = 1 5\n",
        "image_path": "./data/HME100K/test_images/test_3923.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:17x + 8y = 60xy = (17 \\* 8) + (8 \\* x)y = 136x + 8y = 60xy = (17 \\* 8) + (8 \\* x)y = 136\\begin{aligned}17x + 8y &= 60 \\\\ xy &= (17 \\* 8) + (8 \\* x)\\end{aligned}17x + 8y &= 60 \\\\ x",
        "gt_answers": "1 7 - 9 = 8\n",
        "image_path": "./data/HME100K/test_images/test_3924.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format of the expression:\n\n$$\\frac{2\\times 4+3\\times 5}{6\\times 7}$$\n\nThis expression represents the following fraction:\n\n$$\\frac{2+3}{6+7}$$\n\nwhich simplifies to:\n\n$$\\frac{5}{13}$$",
        "gt_answers": "\\frac { 2 x - 1 } { 3 } \\leq 2\n",
        "image_path": "./data/HME100K/test_images/test_3925.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\text{m\\_dn + 3} = 5$$This is a simple equation with two variables on the left side and one variable on the right side. The variable on the left side, m\\_dn, represents the monthly interest rate of the bond. The variable on the right side, 3, represents the coupon rate of the bond. The equation tells us that the total interest paid over the life of the bond will be equal to 5. This means that the coupon rate of the bond is equal to 3% and the monthly interest",
        "gt_answers": "M N : D N = 2 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3926.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length x and width y is:\n\nA = xy\n\nTo find the area of the rectangle in the image, you would use the formula with the values of x and y given in the image. The length of the rectangle is 4 and the width is 3, so the area is:\n\nA = 4 \u00d7 3 = 12\n\nTherefore, the area of the rectangle in the image is 12 square units.",
        "gt_answers": "x _ { 1 } = \\frac { - \\sqrt { 6 } + 3 \\sqrt { 6 } } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3928.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by:\n\n$ \\frac{1}{1+x^2} $",
        "gt_answers": "A B ^ { 2 } = x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } = 8\n",
        "image_path": "./data/HME100K/test_images/test_3929.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\nx3 + 5x2 - 3x + 1\n\nThis is a polynomial equation of degree 3, where x is the independent variable and the coefficients are the constants 3, 5, and 1.",
        "gt_answers": "x _ { 3 } = - \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3930.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image you provided is not visible. Please provide a visible image for me to write out the expression in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation of a quadratic function. It has a vertex at the origin (0,0) and passes through the points (3, 2) and (1, -4). The equation is y = ax^2 + bx + c, where a, b, and c are constants. The value of a is 3, b is 2, and c is -4.",
        "gt_answers": "k ^ { 2 } = 2 ^ { 2 } + ( 4 - k ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3932.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a fraction: 8/9.\n\nTo write it out in LaTeX format, you would type:\n\n8/9",
        "gt_answers": "v = \\sqrt { g R \\tan \\theta }\n",
        "image_path": "./data/HME100K/test_images/test_3933.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 64 - 3(x + 2)64 - 3(x + 2)64 - 3(x + 2)64 - 3(x + 2)64 - 3(x + 2)64 - 3(x + 2)64 - 3(x + 2)64 - 3(x + 2)64 - 3(x + 2)64 - 3(x + 2)64 -",
        "gt_answers": "\\frac { 3 } { x _ { 1 } } + \\frac { 3 } { x _ { 2 } } = 6\n",
        "image_path": "./data/HME100K/test_images/test_3934.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} 3x^2 + 2x - 5 &= 3x^2 + 2x + 3x + 5 - 3x^2 - 2x\\\n&= 5x + 3\\\n&= 5x + 3x + 2\\\n&= 7x + 5\\\n&= 7x + 5x + 2\\\n&= 9x + 7\\\n&= 9x + 7x + 2\\",
        "gt_answers": "\\frac { 3 } { 4 } < 0 . 7 6 < 1 . 5 < 1 \\frac { 3 } { 5 } < \\frac { 1 5 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_3935.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be expressed as follows:\n\n$$\\text{Image Content}$$\nwhere $I$ is the image, $t$ is the time variable, $k$ is the constant of proportionality, and $v$ is the velocity of the image.",
        "gt_answers": "y _ { 1 } = \\frac { \\sqrt { 1 0 } } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3936.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given as:\n\n$$ \\frac{a}{b} = \\frac{100 - 4b}{4a + 20b} $$\n\nwhere $a$ and $b$ are any real numbers.",
        "gt_answers": "A B = \\sqrt { 4 ^ { 2 } + 3 ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_3937.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{x\\_{n+1}}{x\\_n}=\\frac{x\\_{n+1}}{x\\_{n+2}}=\\frac{x\\_{n+2}}{x\\_{n+3}}=\\frac{x\\_{n+3}}{x\\_{n+4}}=\\frac{x\\_{n+4}}{x\\_{n+5}}=\\frac{x\\_{n+5}}{x\\_{n+6}}=\\frac{x\\_{n+6}}{x\\_{n+7",
        "gt_answers": "\\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_3938.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is: y = mx + b, where m is the slope of the line, x is the independent variable, and b is the y-intercept of the line. The image shows the equation of a line in slope-intercept form.",
        "gt_answers": "k = 0 \\Rightarrow\n",
        "image_path": "./data/HME100K/test_images/test_3939.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is written as follows:\n\n$$\\begin{aligned}E(C\\_f) &= \\frac{1}{2}\\left[\\left(1+\\frac{C\\_f}{C\\_m}\\right)\\left(1-\\frac{C\\_f}{C\\_m}\\right) + \\left(1-\\frac{C\\_f}{C\\_m}\\right)\\left(1+\\frac{C\\_f}{C\\_m}\\right)\\right] - \\frac{1}{4}\\left(1-\\frac{C\\_f}{C\\_m}\\right)^2 \\ \\mathrm{",
        "gt_answers": "\\Delta F E C \\sim \\Delta F B A .\n",
        "image_path": "./data/HME100K/test_images/test_3941.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula in the image using LaTeX format, we can write:\n\n\\begin{center}\n\\begin{aligned}\nx &= \\frac{a}{b} \\times \\frac{b}{c} \\times \\frac{c}{d} \\times \\frac{d}{e} \\times \\frac{e}{f} \\times \\frac{f}{g} \\times \\frac{g}{h} \\times \\frac{h}{i} \\times \\frac{i}{j} \\times \\frac{j}{k} \\times \\frac{k}{l}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{center}\n\\begin{tabular}{c}\n$\\frac{1}{2}(x\\_{max} + y\\_{max})$\\\n\\end{tabular}\n\\end{center}\n\nwhere $x\\_{max}$ and $y\\_{max}$ are the maximum values of the $x$ and $y$ coordinates, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $\\frac{1}{2}x^2 + 3x - 5$.",
        "gt_answers": "2 3 : 0 0 - 9 : 0 0 = 1 9\n",
        "image_path": "./data/HME100K/test_images/test_3945.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by: $ $\\frac{3x^2+2x+1}{x^2+x+1}$ $ $\\frac{3x+1}{x+1}$ $\\frac{3}{x+1}$$\\frac{3\\frac{3x+1}{x+1}}{\\frac{3x+1}{x+1}}$ $\\frac{3x+1}{x+1}$ $\\frac{3x^2+2x+1}{x^2+x+1}$ $\\frac{3x^2+2x+1}{x^",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{x^2+y^2}{2xy} $$",
        "gt_answers": "p ( x , - \\frac { 1 } { 2 } x ^ { 2 } - x + 4 )\n",
        "image_path": "./data/HME100K/test_images/test_3947.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\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}{3",
        "gt_answers": "1 2 0 \\div 1 2 = 1 0 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_3949.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as: 1+1=2.\n\nThis is a simple arithmetic expression that states that the sum of 1 and 1 is equal to 2. The formula is written in LaTeX format using the `+` symbol to represent addition and the `=` symbol to represent equality.",
        "gt_answers": "5 1 2 \\div 6 7 = 7 \\cdots\n",
        "image_path": "./data/HME100K/test_images/test_3950.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{m}{n}$$\n\nwhere $m$ and $n$ are the masses of the two objects in the formula.",
        "gt_answers": "x = - \\frac { C } { A }\n",
        "image_path": "./data/HME100K/test_images/test_3952.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not clear as the image is not visible. Please provide the image for me to be able to answer your question.",
        "gt_answers": "1 0 + \\sqrt { 3 } = x +\n",
        "image_path": "./data/HME100K/test_images/test_3953.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\text{GST} = \\frac{\\text{COD}}{\\text{BOD}} \\times \\frac{\\text{MLSS}}{\\text{MLV}} $$\n\nwhere:\n\n* GST is the General Sewerage System tariff\n* COD is the cost of sewage disposal\n* BOD is the biochemical oxygen demand\n* MLSS is the monthly load of sewage\n* MLV is the monthly load of suspended solids",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the equation for the area of a right triangle. The area of a right triangle is given by the formula:\n\nA = (1/2) \\* base \\* height\n\nwhere base is the length of the hypotenuse (the side opposite the right angle) and height is the length of the altitude (the line connecting the vertex to the base).",
        "gt_answers": "a = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3955.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\frac{1}{2}x^2 + \\frac{1}{4}x^4 = \\frac{1}{2}(x+2)^2 + \\frac{1}{4}(x+2)^4 = \\frac{1}{2}x^2 + \\frac{9}{4}x^4 = \\frac{1}{2}(x+2)^2 + \\frac{9}{4}(x+2)^4 = \\frac{1}{2}x^2 + \\frac{9}{4}",
        "gt_answers": "\\frac { 2 x } { ( x + 3 ) ( y - 1 ) } + \\frac { 1 } { x + 3 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3957.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222babf(x)dx+\u222bcdg(x)dx\\int\\_{a}^{b} f(x) dx + \\int\\_{c}^{d} g(x) dx\u222ba\u200bb\u200bf(x) dx + \u222bc\u200bd\u200bg(x) dx\u222ba\u200bb\u200bf(x) dx + \u222bc\u200bd\u200bg(x) dxwhere `a` and `b` are the lower and upper limits of the first integral, respectively, `c` and `d` are the",
        "gt_answers": "\\frac { \\sqrt { 3 } } { 3 } = \\frac { \\sqrt { 1 5 } } { 6 } h\n",
        "image_path": "./data/HME100K/test_images/test_3958.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given formula:$$x^2 + 5x - 10$$This expression represents the parabolic function with an equation of $x^2 + 5x - 10$. The variable $x$ is used to represent the independent variable in the equation, while the constants 2, 5, and 10 represent the coefficients of the equation.\n\nNote that the LaTex code for the expression uses the $x$ variable to represent the independent variable, and the $2$, $5$, and $10$ constants to represent the coefficients of",
        "gt_answers": "x = \\frac { 3 } { a + 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3959.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{4x^2+6x+4}{2x+3}$$The numerator is the polynomial function $$4x^2+6x+4$$ and the denominator is the polynomial function $$2x+3$$The fraction is then evaluated at the point x=3, which gives the value $$\\frac{52}{9}$$",
        "gt_answers": "\\frac { 1 } { 4 } x - \\frac { 1 } { 2 } - 3 + 4 = x\n",
        "image_path": "./data/HME100K/test_images/test_3960.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$g(x)=\\frac{2x^2+6x-5}{3}$$\n\nThis formula is a quadratic function with a leading coefficient of 2, a constant term of 6, and a quadratic term of -5. The variable x is raised to the second power and multiplied by a constant coefficient of 2, added to a constant term of 6, and subtracted by a quadratic term of -5 to produce the final result.",
        "gt_answers": "g ( 1 - \\frac { 3 } { 5 } s ) = \\frac { 1 } { 2 } ( 2 a 5 + V _ { p } ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_3961.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is: \\frac{a}{b}\n\nwhere a is the numerator and b is the denominator. In this case, a is 100 and b is 20. So, the formula would be written as $\\frac{100}{20}$.",
        "gt_answers": "1 0 \\times 1 0 \\times 6 = 6 0 0 c m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3962.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = lwA = (bh)\u00b2lwA = (bh)\u00b2where l is the length, w is the width, and h is the height.\n\nFor a rectangle with a perimeter of 24 units and a width of 8 units, the area can be calculated as follows:\n\nA = 8(8)\u00b224 = 256 sq unitsA = 8(8)\u00b224 = 256 sq unitsThe area of the rectangle is 256 square units.",
        "gt_answers": "\\frac { x } { x + 1 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_3963.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $$ $\\frac{3x^2 + 2x - 4y^2 - 5y + 4}{x - y}$$",
        "gt_answers": "1 0 \\times 8 \\times 2 = 1 6 0 c m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3964.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is not provided. Please provide the equation for the image.",
        "gt_answers": "5 \\frac { 1 } { 2 } - 3 \\times 1 = a + \\frac { 1 } { 4 } \\times 1\n",
        "image_path": "./data/HME100K/test_images/test_3965.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is:\n\nA = pi \\* r^2,\n\nwhere A is the area, pi is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. The image shows the formula written out in LaTeX format:\n\n\\begin{equation} A = \\pi \\* r^2 \\end{equation}",
        "gt_answers": "\\sqrt { 2 5 + x ^ { 2 } } = \\sqrt { 9 + ( 1 6 - x ) ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_3967.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$\\frac{3x^2+5x+7}{2x+3}$$Using LaTeX format, this can be written as:$$\\frac{3x^2+5x+7}{2x+3}$$",
        "gt_answers": "\\frac { 3 } { 1 6 } \\times \\frac { 8 } { 2 7 } = \\frac { 1 } { 1 8 }\n",
        "image_path": "./data/HME100K/test_images/test_3968.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n1 - (cos\u00b2x + sin\u00b2x)\u00b2\n\nThe image shows a graph of a function with an x-intercept at x = pi/6 and a y-intercept at y = 3. The function has a maximum value of 5 at x = pi/6. To find the maximum value, we need to find the derivative of the function and set it equal to zero.\n\nFirst, we can simplify the function using the following steps:\n\n(1 - cos\u00b2x) - sin\u00b2x + 2sin\u00b2x +",
        "gt_answers": "\\cos x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3969.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x + y = 7.",
        "gt_answers": "x = \\frac { 2 } { a }\n",
        "image_path": "./data/HME100K/test_images/test_3970.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 1 + \\frac{1}{3} + \\frac{2}{5} + \\frac{1}{4} = \\frac{13}{15} $$",
        "gt_answers": "x _ { 1 } = \\frac { - 3 + \\sqrt { 1 3 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3971.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:$$x = \\frac{2y+3z-5}{y-z}$$where x, y, and z are variables.",
        "gt_answers": ": \\frac { h ( n + 1 ) } { 2 } < s < \\frac { h ( n + i ) } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3972.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is $\\frac{1}{2}(2x+5)\\sqrt{x+3}$",
        "gt_answers": "\\frac { 1 } { 3 } x = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3973.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{10}{5} = 2$.",
        "gt_answers": "\\frac { 1 0 0 x - 1 0 0 } { 2 5 } - \\frac { 1 0 0 x } { 1 2 5 } = \\frac { 6 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3974.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n$$\\text{sin}(x) + \\text{cos}(x) = \\frac{\\text{sin}(x) + \\text{cos}(x)}{\\sqrt{2}}$$\n\nThis can be derived by expanding the expression for the dot product of two vectors, which is given by:\n\n$$\\text{sin}(x) \\cdot \\text{cos}(x) = \\frac{1}{2} (\\text{sin}(x)^2 + \\text{cos}(x)^2)$$\n\nMultiplying",
        "gt_answers": "y = \\frac { 1 } { 4 } x + 1\n",
        "image_path": "./data/HME100K/test_images/test_3976.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear, as it appears to be a group of symbols rather than a mathematical expression. However, if you provide me with the image, I can try to interpret the formula and write it out in LaTeX format.",
        "gt_answers": "( 1 2 \\times 4 ) + ( 1 2 \\times 5 ) + ( 4 \\times 5 ) \\times 2 = 2 5 6 ( c m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_3978.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=1]\n\\draw[step=1cm,black!20!white] (0,0) grid (2,2);\n\\draw[thick,->] (0.5,1) -- (1.5,1) node[right] {$ \\frac{5}{4}$};\n\\draw[thick,->] (0.5,0) -- (1.5,0) node[right] {$ \\frac{1}{2}$};\n\\draw",
        "gt_answers": "( 2 5 ) < ( 5 2 ) < ( 6 3 ) < ( 6 5 ) < ( 7 2 ) < ( 9 4 )\n",
        "image_path": "./data/HME100K/test_images/test_3979.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{100 - 20}{15} $$\n\nwhich simplifies to:\n\n$$ \\frac{80}{15} $$\n\nor\n\n$$ \\frac{5}{3} $$\n\nwhich represents the fraction of 5/3.",
        "gt_answers": "\\overrightarrow { B E } \\bot \\overrightarrow { O S }\n",
        "image_path": "./data/HME100K/test_images/test_3980.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression in LaTeX format, which is used to represent mathematical symbols and operations in mathematical equations. The expression is:\n\n`r + sin(45\u00b0)`\n\nwhere `r` is a variable representing the radius of a circle and `sin(45\u00b0)` is the sine of an angle of 45 degrees. The expression calculates the sum of the radius and the sine of an angle.",
        "gt_answers": "x = \\frac { 1 } { 3 - 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3981.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{x}=\\frac{a+b+c}{3}$$\n\nwhere $\\text{a}$, $\\text{b}$, and $\\text{c}$ are the digits in the image, with $\\text{a}$ being the leftmost digit, $\\text{b}$ being the middle digit, and $\\text{c}$ being the rightmost digit.\n\nThe numerator of the formula is the sum of the digits, which is $a+b+c$. The denominator is $3$, which is the number of terms in",
        "gt_answers": "4 0 \\times \\frac { 5 } { 1 6 } = \\frac { 2 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_3984.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression for the formula in the image using LaTeX format:\n\n$$\\ce{HCOOH -> H2O + CO2}$$\n\nIn this equation, the reactant is ethanoic acid (HCOOH) and the product is water (H2O) and carbon dioxide (CO2).",
        "gt_answers": "A a N O _ { 3 } + N a C l = A g C l \\downarrow + N a N O _ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_3985.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by: A = \u03c0r^2A = \\pi r^2A=\u03c0r2\\pi r^2where \u03c0 is the mathematical constant that is approximately equal to 3.14. The area of the circle is the product of its radius and the square of its radius.\n\nNote: This formula is written in LaTeX format. To view it properly, you need to have the LaTeX package installed on your computer.",
        "gt_answers": "x _ { 1 } = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_3986.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{a+b}{c+d}$$\n\nWhere a, b, c, and d are the coefficients of the quadratic formula.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows an algebraic expression involving exponential and logarithmic functions. The expression is'log1 + 1 = log2 + 2'which is an identity equation. The right side of the equation is equal to the left side, so the equation is satisfied for any values of'x'.\n\nTo rewrite the expression in LaTeX format, we can use the following code:\n\n\\log\\_1 + 1 = \\log\\_2 + 2\n\nThe caret symbol (^) is used to denote exponentiation. The subscript 1 and 2 indicate that the base of each logarithm",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it appears to be broken. Please provide a working image for me to see and answer your questions.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression in the image:\n\n\\begin{equation}\n2 + \\sqrt{2} = 3\n\\end{equation}\n\nNote that the equation uses the Chinese language, which is written vertically from right to left. The equals sign is represented by the word \"=\" in Chinese, and the multiplication symbol is represented by the word \"\\*\".",
        "gt_answers": "2 a + \\frac { 2 } { 3 } \\pi = \\frac { 3 } { 2 } \\pi\n",
        "image_path": "./data/HME100K/test_images/test_3990.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The chemical formula in the image is:\n\n\\[\\ce{C6H12O6}\\]\n\nThis is the formula for glucose, which is a type of sugar that is found in many foods. The molecule consists of six carbon atoms, twelve hydrogen atoms, and six oxygen atoms. The carbon atoms are bonded to each other in a ring structure, with the hydrogen atoms bonded to the carbon atoms and the oxygen atoms bonded to the carbon atoms in double bonds. The double bonds between the carbon and oxygen atoms give glucose its characteristic sweet",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$ \\frac{a + 3b + 4c + 5d}{b + 2c + 3d} = \\frac{2a + 5b + 6c + 8d}{3a + 4b + 5c + 6d} $\n\nThis can be derived by applying the formula for the fractional change of a polynomial with a common denominator. The numerator of the fraction is the difference between the values of the polynomial at the original and target expressions, while the denominator",
        "gt_answers": "\\frac { A G } { E G } = \\frac { G H } { C G }\n",
        "image_path": "./data/HME100K/test_images/test_3994.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image you provided is not clear enough for me to read the expression of the formula written on it. Can you please provide a clearer and more visible image for me to work with?",
        "gt_answers": "x _ { 2 } = - \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_3996.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the given expression:\n\n$$\\begin{aligned} 0.5x^2 + 0.5x - 0.25 &= 0 \\ \\ \\Rightarrow \\ \\ x &= 0.5\\end{aligned}$$\n\nThis is a quadratic equation in one variable, with the left-hand side being the function of $x$ and the right-hand side being the constant function of zero. The $\\Rightarrow$ symbol indicates that the equation is satisfied if the equation on the left-hand side is equal to the equation on the right-hand side",
        "gt_answers": "0 . 0 8 = \\frac { 8 } { 1 0 0 }\n",
        "image_path": "./data/HME100K/test_images/test_3997.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$36\\times x^2 + 24x - 8$",
        "gt_answers": "2 3 0 - 1 5 0 = 8 0 ( m )\n",
        "image_path": "./data/HME100K/test_images/test_3998.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a square is given by the expression: A = s^2, where s is the side length of the square. The side length is denoted by the variable s in the expression.\n\nTo calculate the area of the square, we can substitute the value of s, given in the image, into the formula:\n\nA = 4^2 = 16\n\nTherefore, the area of the square is 16.",
        "gt_answers": "6 0 : 5 4 = \\frac { 1 0 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_3999.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{(x + 2y)}{(x + 3y)} $$\n\nThe image shows a line segment between two points, one with coordinates (2, 2) and the other with coordinates (4, 4). The equation of the line passing through these two points is given by:\n\n$$ y - y\\_1 = m(x - x\\_1) $$\n\nwhere m is the slope of the line.\n\nThe line is perpendicular to the x-axis, so its slope is -2",
        "gt_answers": "\\frac { 2 } { 3 } + \\frac { 2 } { 5 } = \\frac { 2 } { 5 } x - \\frac { 1 } { 3 } x\n",
        "image_path": "./data/HME100K/test_images/test_4000.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To calculate the number of bonds in the given molecule, we can use the Lewis structure approach. We start by counting the number of valent electrons in the molecule, which is 4.\n\nThe molecule has two double bonds and one single bond, so the molecule has a total of 6 valent electrons in bonds. Therefore, the molecule has 6 bonds.\n\nIn LaTeX format, the answer would be written as:\n\n\\documentclass[a4paper, 12pt]{article}\n\n\\begin{document}\n\nTo",
        "gt_answers": "B C \\bot A C , \\angle 1 = 4 8 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4001.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: $\\frac{7+5i}{4-i^2}$.",
        "gt_answers": "x = ( 3 . 7 5 )\n",
        "image_path": "./data/HME100K/test_images/test_4002.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\begin{aligned} \\frac{p}{q} \\times \\frac{r}{s} &= \\frac{p \\times r}{q \\times s} \\quad \\text{by substitution} \\\n\\\\&= \\frac{pr}{qs} \\quad \\text{by simplifying} \\\n\\\\&= \\frac{p}{s} + \\frac{r}{q} \\quad \\text{by adding the fractions} \\\n\\\\&= \\frac{p}{s} + \\frac{q}{p} \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: f(x) = 2x^3 + 5x^2 - 7x + 2.\n\nHere's how to write it in LaTeX format:\n\nf(x) = \\left(2x^3 + 5x^2 - 7x + 2\\right)",
        "gt_answers": "x = \\frac { 5 } { 2 } \\div \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4004.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: 4x + 3y - 3 = 12x + 2y - 6 = 2x + 2y = 8x + 2y = 8y = 4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression:\n\n$$\\frac{\\frac{1}{2}\\cdot 3 + \\frac{1}{4}\\cdot 4 + \\frac{1}{8}\\cdot 8}{\\frac{1}{3}\\cdot 3 + \\frac{1}{4}\\cdot 4 + \\frac{1}{8}\\cdot 8} = \\frac{9 + 8 + 8}{3 + 4 + 8} = \\frac{29}{25} = 1.16$$\n\nThe expression is $\\frac{\\frac{",
        "gt_answers": "\\frac { 6 } { 5 } = 1 \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4006.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \\frac{2x}{x+1}.\n\nThis formula represents the fractional change in the variable x when the value of x is increased by 1. To find the derivative of this formula with respect to x, we can use the power rule of differentiation, which states that the derivative of x^n is nx^(n-1).\n\nTherefore, the derivative of \\frac{2x}{x+1} with respect to x is: \\frac{2(x+1) - 2x}{(x+1)^",
        "gt_answers": "8 x = \\frac { 4 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4007.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows in LaTeX format:\n\n$$\\begin{aligned} x &= \\frac{1}{4} \\times 8 + \\frac{1}{4} \\times 2 \\\\ y &= \\frac{1}{4} \\times 8 + \\frac{1}{4} \\times 2 \\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is: $\\text{ImageContent}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical formula written in LaTeX format. The formula is as follows:\n\n$$ dfa\\_t = \\frac{dfa\\_t - dfa\\_t - 1}{\\frac{1}{dfa\\_t} - \\frac{1}{dfa\\_t - 1}}$$\n\nwhere $dfa\\_t$ is the degree of freedom at time $t$.",
        "gt_answers": "D F \\bot A C\n",
        "image_path": "./data/HME100K/test_images/test_4010.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format of the expression in the image:\n\n\\begin{align\\*} 36 - 4x^2 &= 9 \\ \\ \\ \\ \\ \\ 36 - 4x^2 &= 9 \\end{align\\*}\n\nIn this expression, the variable x is raised to the power of 2, and the expression is equal to 9. The equals sign (=) is used to indicate that the two sides of the equation are equal. The align environment is used to align the equation properly on the page.",
        "gt_answers": "\\frac { 3 6 } { 4 8 } = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4012.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression for the formula in the image using LaTeX format. Here it is:$$$$ \\frac{1}{3} \\times \\frac{4}{5} \\times \\frac{6}{7} \\times \\frac{8}{9}$$This formula calculates the average of the numbers 1, 4, 6, 8, and 9, using the formula $\\frac{a}{b} \\times \\frac{c}{d} \\times \\frac{e}{f} \\times \\frac{g}{h}$, where $a$, $b$, $",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not provided, so I cannot write it out using LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{\\mathrm{d}x}{\\mathrm{d}t} = \\frac{v}{m}$$\n\nwhere $x$ is the position of the object, $t$ is time, $v$ is the velocity of the object, and $m$ is the mass of the object.",
        "gt_answers": "\\sqrt { 2 x - 4 } = 1 + \\sqrt { x + 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4015.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe expression for the formula in the image using LaTeX format is:\n\n$$\\frac{a^2+b^2}{2ab}$$\n\nwhere $a$ and $b$ are the lengths of the two sides of the rectangle in the image.\n```",
        "gt_answers": "x + y = 3 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_4016.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{T} = \\frac{1}{2} \\left( \\frac{h\\_1 + h\\_2}{h\\_1 - h\\_2} \\right) \\left( \\frac{2 \\left( x - \\frac{h\\_1 + h\\_2}{2(h\\_1 - h\\_2)} \\right)}{h\\_2 - h\\_1} \\right)$$",
        "gt_answers": "2 1 + \\frac { 7 } { y }\n",
        "image_path": "./data/HME100K/test_images/test_4017.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned}\n& (x+4)(x-3)=0 \\\n\\Rightarrow x=-4,-3 \\\n\\Rightarrow x=3,4 \\\n\\Rightarrow x=-3,4 \\\n\\Rightarrow x=4,3 \\\n\\Rightarrow x=-3,4 \\\n\\Rightarrow x=4,3 \\\n\\Rightarrow x=-3,4 \\\n\\Rightarrow x=4,3 \\\n\\Rightarrow x=-3,4 \\\n\\Rightarrow x=4,3 \\\n\\Rightarrow x",
        "gt_answers": "\\frac { 7 } { 8 } = \\frac { 7 2 } { 6 3 } \\frac { 6 3 } { 7 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4019.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula:\n\n\\begin{align\\*}\n 3x^2 + 2x - 5 &= 0 \\\n  \\begin{aligned}\n   3x^2 + 2x &= 5 \\\n    x^2 + x &= 5/3 \\\n    (x + 1/3)^2 &= 5 \\\n    x + 1/3 &= \\pm 5/3 \\\n    x &= 1/3 \\\n  \\end{aligned}\n\\end{align\\*}$",
        "gt_answers": "- 2 \\overrightarrow { a } + 4 \\overrightarrow { b } = ( 1 0 , 2 )\n",
        "image_path": "./data/HME100K/test_images/test_4021.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:$$\\sqrt \\_{2} (1+\\sqrt \\_{2}) = 3$$This can be written in LaTeX format as:$$\\sqrt\\_2 (1+\\sqrt\\_2) = 3$$The equation represents the relationship between two variables in a mathematical equation, where the left side is the square root of 2, and the right side is the sum of 1 and the square root of 2. The equation has a solution of 3, which is the result of substituting the values into the equation.",
        "gt_answers": "u = u _ { 1 } + u _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4022.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{z+2}{4} $$\n\nwhere z is any integer.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\text{SIN}\\left(\\frac{\\text{x}}{\\text{a}}\\right)\\text{= cos}\\left(\\frac{\\text{x}}{\\text{a}}\\right)$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle with a radius of 4 is given by:\n\nA = \u03c0r^2\n\nwhere r is the radius of the circle.\n\nSo, the area of the circle is:\n\nA = \u03c0(4)^2\n\n= 16\u03c0\n\nTherefore, the area of the circle is 16\u03c0 square units.",
        "gt_answers": "l _ { 1 } : y = 2 x - 2 ) = 3\n",
        "image_path": "./data/HME100K/test_images/test_4025.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is: $\\text{s} = \\text{c} + \\frac{\\text{a}}{\\text{t}}$ where $\\text{s}$ is the slope of the line, $\\text{c}$ is the y-intercept of the line, $\\frac{\\text{a}}{\\text{t}}$ is the equation of the line.",
        "gt_answers": "W = - b ^ { 2 } + 1 6 x + 2 1 0\n",
        "image_path": "./data/HME100K/test_images/test_4026.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{d}{dx} \\left(\\frac{1}{2}x^2+5x-7\\right) = \\frac{d}{dx}\\left(\\frac{1}{2}x^2+7x\\right)$$This is the derivative of $\\frac{1}{2}x^2+5x-7$ with respect to $x$.\n\nThe derivative of $\\frac{1}{2}x^2+7x$ with respect to $x$ is $\\frac{d}{dx}\\left(\\",
        "gt_answers": "\\angle A O E = \\angle B A E = 9 0 ^ { \\circ } .\n",
        "image_path": "./data/HME100K/test_images/test_4027.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I'll do my best to help you with your question.\n\nHere's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\frac{1}{2}m\\_1 + \\frac{1}{2}m\\_2 + \\frac{1}{2}m\\_3 = \\frac{1}{2}(m\\_1 + m\\_2 + m\\_3)\n\\end{center}\n\nThis formula calculates the sum of the masses of three objects in a system. The mass of each object is represented by the variable $m\\_1",
        "gt_answers": "M N = M l = \\frac { 1 } { 4 } m ^ { 2 } + 1\n",
        "image_path": "./data/HME100K/test_images/test_4029.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is: x = 2y - 3z, where x, y, and z are variables. The solution is obtained by solving the equation for x and substituting the values of y and z.\n\nSubstituting y = 5 and z = 2 into the equation, we get: x = 2(5) - 3(2) = 7 - 6 = 1. So, the solution is x = 1.",
        "gt_answers": "x _ { 1 } + x _ { 2 } = \\frac { - 2 k } { 1 - k ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_4030.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$ \\text{F} = \\text{mgh} $$\n\nwhere $\\text{F}$ is the force, $\\text{m}$ is the mass of the object being lifted, $\\text{g}$ is the acceleration due to gravity, and $\\text{h}$ is the height to which the object is lifted.",
        "gt_answers": "( 1 - a , 2 a - 5 ) = ( 1 - 2 , 2 \\times 2 - 5 )\n",
        "image_path": "./data/HME100K/test_images/test_4033.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is not provided. Please provide the image to get the formula.",
        "gt_answers": "x = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4034.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ E = \\frac{1}{2}mv^2 $$\n\nwhere E is the energy of the object, m is its mass, and v is its velocity.",
        "gt_answers": "( 3 8 5 - 3 2 5 ) \\div 3 = 2 0\n",
        "image_path": "./data/HME100K/test_images/test_4035.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX formula for the expression:\n\n\\begin{align\\*} 3x^2 + 4x - 2 = 0 \\end{align\\*}\n\nIn this equation, x is the variable, and the coefficient of x^2 is 3, the coefficient of x is 4, and the constant term is -2.",
        "gt_answers": "y _ { 3 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4036.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned}\na & = \\frac{1}{2} \\times 6 + \\frac{1}{3} \\times 9 \\\\\na & = 6 + 3 \\\\\na & = 9\n\\end{aligned}$$",
        "gt_answers": "\\angle A G D = 1 8 0 ^ { \\circ } - 7 0 ^ { \\circ } = 1 1 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4037.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{LBFC} = \\frac{2}{\\sqrt{1-r^2}} $$\n\nwhere $r$ is the radius of the circle in the formula.",
        "gt_answers": "\\angle E = \\angle B F C = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4038.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Can you please provide a different image or description of the expression?",
        "gt_answers": "\\frac { a } { \\cos A } = \\frac { b } { \\cos B } = \\frac { c } { \\sin C }\n",
        "image_path": "./data/HME100K/test_images/test_4039.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:\n\n$$\\text{T}_5=\\frac{1}{10}\\times\\frac{1}{2}\\times\\frac{1}{4}\\times\\frac{1}{5}\\times\\frac{1}{8}=\\frac{1}{400}$$\n\nHere, T5 is the time taken by an object to fall from a height of 160 m to the ground. The formula uses the formula for the time of fall of an object under the influence of gravity. The time is calculated by multiplying the acceleration due to gravity (g",
        "gt_answers": "S _ { n } = \\frac { 1 } { 3 ^ { n } } + \\frac { - 1 } { 3 ^ { 2 } } + \\frac { - 3 } { 3 ^ { 3 } } + \\cdots + \\frac { 3 - 2 n } { 3 n }\n",
        "image_path": "./data/HME100K/test_images/test_4040.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:3x^2+2x+1. This can be derived by substituting x=4 into the given equation:3(4)^2+2(4)+1=49. This is the correct answer.",
        "gt_answers": "\\frac { 3 x - 2 } { 5 } \\geq \\frac { 2 x + 1 } { 3 } - 1\n",
        "image_path": "./data/HME100K/test_images/test_4042.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Determine the variables and constants in the formula.\n2. Write out the formula using the variables and constants.\n3. Use LaTeX format to typeset the formula.\n\nUsing these steps, we can write out the formula in the image as follows:\n\nThe formula is given by:\n\n`x^2 + 3x - 5 = 0`\n\nIn LaTeX format, this can be written as:\n\n`x^2 + 3x -",
        "gt_answers": "\\times 1 8 = \\frac { 1 2 } { 5 } ( k m )\n",
        "image_path": "./data/HME100K/test_images/test_4043.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$$\\text{P}(x) = \\frac{1}{4} \\times \\frac{1}{4} + \\frac{1}{4} \\times \\frac{1}{4} + \\frac{1}{4} \\times \\frac{1}{4} + \\frac{1}{4} \\times \\frac{1}{4} = \\frac{1}{4} + \\frac{1}{4} + \\frac{1}{4} + \\frac{1}{4} = \\frac{1}{2}$$",
        "gt_answers": "= ( x + \\sqrt { 5 } y i ) ( x - \\sqrt { 5 } y i )\n",
        "image_path": "./data/HME100K/test_images/test_4045.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:\n\n$$ A = l \\times w $$\n\nwhere l is the length of the rectangle and w is the width of the rectangle.\n\nThe length of the rectangle in the image is 6 cm and the width is 5 cm. Therefore, the area of the rectangle is:\n\n$$ A = 6 \\times 5 = 30 $$\n\nSo the area of the rectangle is 30 cm^2.",
        "gt_answers": "0 . 5 1 1 < 0 . 5 0 1 < 0 . 5 1 < 0 . 5\n",
        "image_path": "./data/HME100K/test_images/test_4046.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by the equation:\n\nx + 3y = 25\n\nwhere x and y are the coordinates of the points in the image. The equation represents a straight line with a slope of 3 and a y-intercept of 25.",
        "gt_answers": "x = \\frac { 3 5 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_4047.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:\n\n$$ 2x^2 + 2y^2 = 2(x + y)^2 $$\n\nThis is the formula for the distance between two points in a two-dimensional space.",
        "gt_answers": "D A = D ^ { \\prime } A\n",
        "image_path": "./data/HME100K/test_images/test_4048.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, the formula in the image is the derivative of a function f(x) with respect to x. It can be written as:$$\\frac{d f(x)}{dx}$$This formula represents the rate of change of the function at any given point x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is not shown in the image, so it cannot be written in LaTeX format.",
        "gt_answers": "4 x ^ { 2 } . + 4 ( n - 1 ) x + n ^ { 2 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_4050.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression of the formula in the image:\n\n\\begin{align\\*}\n\\text{number of even integers divisible by 3} & = \\sum\\_{i=1}^{\\infty}\\left\\lfloor\\frac{3n}{2}\\right\\rfloor \\\\\n& = \\sum\\_{i=1}^{\\infty}\\left(\\left\\lfloor\\frac{3n}{2}\\right\\rfloor - \\left\\lfloor\\frac{3n-2}{2}\\right\\rfloor\\right) \\\\\n& = \\sum\\_{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by:\n\nA = \u03c0r^2\n\nWhere r is the radius of the circle.",
        "gt_answers": "m \\geq - \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4052.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. First, we need to identify the variables in the formula. In this case, the variables are x, y, and z.\n2. Next, we need to write out the formula using LaTeX format. To do this, we can use the following syntax:\n\n$$ \\text{expression} $$\n\nWhere $\\text{expression}$ is the mathematical expression we want to write out in LaTeX format.\n\n3. Applying the above syntax to the given formula, we get:",
        "gt_answers": ": O B = \\frac { 1 } { 2 } A B = 5\n",
        "image_path": "./data/HME100K/test_images/test_4053.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\ce{Ca2+ + 2e- -> Ca}\\quad $$",
        "gt_answers": "C u O + 2 H C l = C u C l _ { 2 } + H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_4055.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n\u222b \u222b \u222b \\int \\int \\int \u222b \u222b \\int \\int \u222b \u222b \u222b \u222b \\int \\int dydxdydxdydxdydxdydy.\u222b \u222b \u222b\\int \\int \\int \\int \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \\int \\int dydxdydxdydxdydxdydxdydy\u222b\u222b \u222b \u222b\\int \\int \\int \\int \u222b \u222b \u222b \u222b \u222b",
        "gt_answers": "y = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4056.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![](https://i.imgur.com/image.png)\n\nwhere k is the constant of proportionality, b is the y-intercept, and m is the slope of the line.",
        "gt_answers": "1 . k = \\frac { C ^ { 2 } _ { ( N O _ { 2 } ) } } { C _ { ( N _ { 2 } O _ { 4 } ) } } = \\frac { 0 . 4 \\times 0 . 4 } { 0 . 2 } = 0 . 8\n",
        "image_path": "./data/HME100K/test_images/test_4058.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:\n\n$$\\frac{\\frac{a}{b}+\\frac{c}{d}}{\\frac{e}{f}+\\frac{g}{h}}=\\frac{a\\frac{b}{c}+d\\frac{e}{f}}{b\\frac{c}{d}+h\\frac{g}{f}}$$\n\nThis formula can be derived from the distributive property of multiplication over addition. The numerator is the product of the fractions $\\frac{a}{b}$ and $\\frac{c}{d}$, while the denominator is the sum",
        "gt_answers": "A F = A D = B C = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_4059.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{3x - 5y + 4z}{x + y - 3z}$.",
        "gt_answers": "x = - \\frac { 1 2 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4061.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by the equation:\n\n$$ \\text{d}x/dt = v $$\n\nwhere $v$ is the velocity of the car at time $t$. The velocity of the car is given by the formula:\n\n$$ v = \\frac{a}{m} $$\n\nwhere $a$ is the acceleration of the car and $m$ is the mass of the car.\n\n$$ a = \\frac{v^2 - v\\_0^2}{t} $$\n\nwhere $v\\_0$ is the initial velocity of the car.",
        "gt_answers": "\\angle A D B = \\angle D B C .\n",
        "image_path": "./data/HME100K/test_images/test_4062.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $\\sqrt{x^2+y^2}$.",
        "gt_answers": "\\frac { 3 } { 4 } ( x - 2 . 7 ) = 4 ^ { \\cdot } 5\n",
        "image_path": "./data/HME100K/test_images/test_4063.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\na + b = c\n\\end{align\\*}\n\nwhere 'a', 'b', and 'c' are variables. The image shows a formula written in blue ink on a white background, with the variables underlined in blue ink and the equation symbol written in blue ink above the variables. The equation is a simple arithmetic expression that states that the sum of two variables is equal to a third variable.",
        "gt_answers": "x = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4064.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 3 + 2x = 11 $$\n\nThe formula for the image is a linear equation with a slope of 5 and a y-intercept of 5. The equation can be written in slope-intercept form as:\n\n$$ y = mx + b $$\n\nSubstituting m = 5 and b = 5 into the equation, we get:\n\n$$ y = 5x + 5 $$\n\nwhich can be simplified to:\n\n$$ y = 5x $$\n\nThere",
        "gt_answers": "5 1 . 5 - 5 0 = 1 . 5 ( k g )\n",
        "image_path": "./data/HME100K/test_images/test_4065.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n\\begin{center}\n$\\frac{3}{4} \\times \\left(\\frac{1}{2}\\right) \\times \\left(\\frac{1}{4}\\right) \\times \\left(\\frac{1}{2}\\right) = \\frac{3}{8}$\n\\end{center}\n\nHere's a breakdown of how to write each term in LaTeX format:\n\n\\begin{itemize}\n\\item The first term is $\\frac{3}{4}$, which is written as $\\",
        "gt_answers": "- 1 ^ { 2 } + H D ^ { 2 } = D E \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_4067.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->] (-2,0) -- (2,0) node[right] {$x$};\n\\draw[->] (0,-1) -- (0,3) node[above] {$y$};\n\\filldraw (0,1) circle (2pt) node[above right] {$P$};\n\\filldraw (-1,1) circle (2pt) node[above right] {$Q$};\n\\filldraw (1,",
        "gt_answers": "( x + 5 ) ( x - 1 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_4068.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: $\\frac{y - x}{x}$.",
        "gt_answers": "F _ { 1 } l _ { 1 } = F _ { 2 } l 2\n",
        "image_path": "./data/HME100K/test_images/test_4070.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression that is written in LaTeX format. The expression is 6 / 4.\n\nLaTeX format:\n\n\\frac{6}{4}\n\nThe fraction expression represents the ratio of 6 to 4. In LaTeX format, this is written using the \\frac{} command. The numerator is 6, and the denominator is 4.",
        "gt_answers": "\\frac { 3 } { 8 } + \\frac { 4 } { 8 } = \\frac { 7 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_4071.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \\frac{x^2+y^2}{x+y}= \\frac{99}{13}.",
        "gt_answers": "x _ { 2 } = \\frac { - 1 - \\sqrt { 5 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4072.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the sum of three numbers: 2, 3, and 4. In LaTeX format, this can be written as:\n\n\\begin{align\\*}\n2 + 3 + 4 &= 9\n\\end{align\\*}\n\nAlternatively, the formula can be written as:\n\n\\begin{align\\*}\n2 + 3 + 4 &= 9\n\\end{align\\*}\n\nBoth of these formulas are equivalent and represent the same mathematical expression.",
        "gt_answers": "\\frac { 3 } { 4 } = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4073.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as follows:",
        "gt_answers": "[ ( - m ) ^ { 3 } ] ^ { 2 } = m ^ { 3 \\times 2 } = m ^ { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_4074.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the derivative of x^2 with respect to x, which is given by:$$\\frac{d}{dx}x^2=2x$$In LaTeX format, this can be written as:$$\\frac{d}{dx}x^2=2x$$This formula represents the rate of change of x^2 with respect to x, or the slope of the tangent line to the curve y = x^2 at the point (x, x^2).",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4075.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 1 + 3 = 4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image does not have a formula written on it, so I cannot write out an expression for it using LaTeX format.\n\nHowever, if you provide a formula written in LaTeX format, I can help you evaluate it. Please share the formula with me.",
        "gt_answers": "3 \\div 4 = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4078.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is 5x55555+3x33333+6x66666+7x77777+8x88888+9x99999+10x101010+11x111110+12x121212+13x131313+14x141414+15x151515+16x161616+17x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: $\\frac{1}{3}\\left(1+\\frac{1}{2}\\right)\\left(2+\\frac{1}{3}\\right) = \\frac{1}{3}\\left(1+\\frac{1}{2}\\right)\\left(3\\right) = \\frac{1}{3}\\left(1+\\frac{1}{2}\\right)\\left(3\\right) = \\frac{1}{3}\\left(2+\\frac{1}{2}\\right)\\left(3\\right) = \\frac{1}{3}\\left(2",
        "gt_answers": "3 5 \\times 9 = 8 x\n",
        "image_path": "./data/HME100K/test_images/test_4080.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} a + 2b + 3c &= 9 \\\n\\frac{a}{3} + \\frac{2b}{4} + \\frac{3c}{6} &= \\frac{9}{6} \\\n\\frac{a}{3} + \\frac{2b}{4} + \\frac{3c}{6} &= \\frac{3}{2} + \\frac{2}{3} + \\frac{3}{6} \\\n\\frac{a}{3}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a handwritten note that reads, \"a d d b u\" in black ink on a white background. The letters are written in a neat, cursive style, with the words slightly spaced apart. The note appears to have been written with a pen or marker.\n\nThe expression for this image using LaTeX format would be:\n\n\\begin{center} a d d b u \\end{center}\n\nNote: LaTeX is a typesetting language that is commonly used for mathematical and scientific writing. It allows for the creation of complex mathematical equations and symbols in a typeset format, making",
        "gt_answers": "A D / / B C\n",
        "image_path": "./data/HME100K/test_images/test_4083.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX code for the expression in the image:\n\n\\begin{center}\n\\begin{aligned}\n& \\text{Average Directional Index} \\\\\n= \\frac{\\sum\\_{i=1}^{n} (\\mathbf{a}\\_i \\cdot \\mathbf{r}\\_i) / (\\mathbf{a}\\_i \\cdot \\mathbf{a}\\_i)}{\\sum\\_{i=1}^{n} (\\mathbf{r}\\_i \\cdot \\mathbf{r}\\_i) / (\\mathbf{a",
        "gt_answers": "A Q \\bot C D\n",
        "image_path": "./data/HME100K/test_images/test_4084.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{center}\n$A = \\frac{B+2C}{2}$\n\\end{center}\n\nThis is a formula for a geometric sequence, where $A$ is the nth term and $B$ and $C$ are the first two terms. The denominator is $2$ and the numerator is the sum of $B$ and $2C$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the given image:\n\n$$\\frac{5 + \\frac{4}{2}}{6} = \\frac{9}{12}$$\n\nNote: The image provided is not clear, so I have assumed that the fraction is $\\frac{5}{4}$. If this is not the case, please provide a clearer image for me to work with.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$ N = \\frac{1}{2} \\cdot 10 + \\frac{1}{2} \\cdot 9 = \\frac{1}{2} \\cdot (10 + 9) = \\frac{1}{2} \\cdot 19 = 9.5$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n&#x03C3;h = &#x2212;&#x03C3;h(x, t)dt\" role=\"presentation\">\u222bh=\u2212h(x,t)dt\u222bh=\u2212h(x,t)dt\\int h(x, t) \\ dt\n\nwhere h(x, t) is the heat capacity of the object at position x and time t, and &#x2212;h(x, t)\" role=\"presentation\">\u2212h(",
        "gt_answers": "A H = \\frac { 8 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4088.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the derivative of f(x) with respect to x.",
        "gt_answers": "D K = \\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_4089.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the given formula:\n\n$$\\text{Mi\\_1} = \\frac{\\text{Mi\\_2}\\cdot\\text{N}}{\\text{N} + \\text{Mi\\_2}}$$\n\nwhere $\\text{Mi\\_1}$ is the modified formula for mass fractionation of the substances in the mixture, $\\text{Mi\\_2}$ is the mass of the substance in the mixture that is not present in the original mixture, $\\text{N}$ is the total mass of the mixture, and $\\text{N}",
        "gt_answers": ", 2 x + y = 0\n",
        "image_path": "./data/HME100K/test_images/test_4090.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not provided, so it cannot be written out using LaTeX format. However, assuming that the equation is in Chinese, it can be written as follows:\n\n$$x=\\frac{a^2+b^2}{2ab}$$\n\nThis equation represents the distance between the origin and a point on the Cartesian plane given by the coordinates $(a,b)$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} \\text{Area} &= \\text{Base} \\times \\text{Height} \\\n&= \\frac{2x+3y+4}{2x-y+5} \\times \\frac{3y-2x+4}{2x+y-5} \\\n&= \\frac{2x+3y+4}{2x-y+5} \\times \\frac{3y-2x+4}{2x+y-5} \\\n&= \\frac{2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the formula in the image:\n\n\\begin{center}\n\\frac{a}{b}\n\\end{center}\n\nWhere `a` and `b` are the values in the formula. Let me know if you have any further questions!",
        "gt_answers": "4 m = 1 2 m = 3\n",
        "image_path": "./data/HME100K/test_images/test_4098.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression given in the image is:\n\n$\\text{5 kg}\\times\\text{2.3 kg/L} = \\text{5 kg}\\times\\frac{2.3 kg}{L}$\n\nwhich simplifies to:\n\n$\\text{5 kg}\\times\\frac{2.3 kg}{L} = \\text{2.3 kg}\\times\\text{L}$\n\nor\n\n$\\text{11.5 kg}\\times\\text{L} = \\text{2.3 kg}\\times\\text{L}$\n\nwhich can",
        "gt_answers": "5 3 5 0 m = ( 5 . 3 5 ) k m\n",
        "image_path": "./data/HME100K/test_images/test_4099.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression that shows how to calculate the area of a triangle. The triangle has two equal sides (a and b) and one hypotenuse (c). The area of the triangle is calculated by multiplying the base by the height and dividing by two: 12 = (base x height) / 2. The image shows the formula being applied to a triangle with base 10 and height 8. The area of the triangle is 120/(10 x 8) = 120/80 = 1.5. The formula for the area of a",
        "gt_answers": "\\overrightarrow { b } = - \\overrightarrow { c }\n",
        "image_path": "./data/HME100K/test_images/test_4100.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I cannot see the image you provided. Can you please provide a different image for me to work with?",
        "gt_answers": "6 \\div \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4101.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as:\n\n\\begin{center}\n$x^{2} + 4x + 4 = 0$\n\\end{center}\n\nThis is a quadratic equation in the form of ax^{2} + bx + c = 0, where a = 1, b = 4, and c = 4. The solutions to this equation are the values of x that make the equation true, which are the roots of the quadratic polynomial. These are the values of x that satisfy the equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, you can use the following LaTeX code:\n\n$$\\frac{a \\cdot b + b \\cdot c + c \\cdot a}{a + b + c}$$\n\nThis formula calculates the sum of the products of the three numbers a, b, and c, and divides that sum by the sum of the three numbers. The result is the sum of the three numbers.\n\nAlternatively, you can use the following LaTeX code to write out the formula in the image:\n\n$$\\frac{a \\cdot b +",
        "gt_answers": "x = \\frac { 7 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_4106.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the line in the image is given by:\n\ny = (1/4)\\*x^2 + (5/2)\\*x + (3/4)\\*x^2 + (1/2)\\*x - 2\n\nor in LaTeX format:\n\n$ y = \\frac{1}{4}x^2 + \\frac{5}{2}x + \\frac{3}{4}x^2 + \\frac{1}{2}x - 2 $",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{equation}\n\\frac{3x + 5}{2x - 1} = \\frac{3(2x - 1) + 5}{2(2x - 1)} = 5 + \\frac{3}{2}x = \\boxed{5 + \\frac{3}{2}x}\n\\end{equation}\n\\end{center}\n\nIn this formula, the numerator is 3x + 5, and the denominator is",
        "gt_answers": "\\frac { 5 0 } { 1 } = 5 0\n",
        "image_path": "./data/HME100K/test_images/test_4110.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle is given by A = \u03c0r^2, where r is the radius of the circle. For the given image, the radius can be calculated as the distance from the center of the circle to the outer edge. The radius is given by r = (di/2)^(1/2), where di is the diameter of the circle. Substituting this value into the equation for A, we get A = \u03c0(di/2)^(1/2)^2 = \u03c0d^2/4.",
        "gt_answers": "4 = k \\pi + \\frac { \\pi } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4111.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is: $\\frac{x+6}{x-2}$.",
        "gt_answers": "3 x + 3 - 4 + 6 x = 6\n",
        "image_path": "./data/HME100K/test_images/test_4112.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: y = x^2 + 4x - 8.\n\nThe image shows a graph of the equation y = x^2 + 4x - 8. The graph is a parabola that opens upwards and has its vertex at the origin. The equation represents a quadratic function with a maximum value of 4 at x = 1 and a minimum value of - 4 at x = - 1.",
        "gt_answers": "x = \\frac { 5 a + 1 } { a }\n",
        "image_path": "./data/HME100K/test_images/test_4113.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as follows:\n\n$$ 2x^2 + 3x - 5 $$\n\nThe image shows a graph with a parabolic shape, which represents a quadratic equation. The equation has a vertex at the origin and passes through the points (2, 3) and (2, -5). The x-intercepts of the parabola are at x = -3 and x = -5, and the y-intercept is at y = 3.",
        "gt_answers": "\\sqrt { x + 5 } - \\sqrt { 2 x - 7 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_4114.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the expression shown in the image:\n\n\\begin{center}\n\\(k \\* m\\)\n\\end{center}\n\nwhere\n\n* k is the acceleration due to gravity (approximately 9.81 m/s^2)\n* m is the mass of the object being accelerated\n\nThis formula represents the net force acting on an object due to the acceleration produced by the earth's gravitational field.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image:\n\n$$\\begin{aligned} r^2 + r^2 &= r^2 \\\\ r^2 - r^2 &= -r^2 \\end{aligned}$$\n\nThis is the equation of a circle with center at the origin and radius $r$. The left side of the equation is the square of the radius, while the right side is the difference of squares of the radius, which is equal to $-r^2$.",
        "gt_answers": "\\frac { V _ { 1 } } { V _ { 2 } } = \\frac { R _ { 1 } } { R _ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_4116.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$4x^2 + 4x - 12$",
        "gt_answers": "8 x + 8 = 9 x - 1 2\n",
        "image_path": "./data/HME100K/test_images/test_4117.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a polynomial equation of degree 2 with the roots $x = - 1$ and $x = 2$. The equation can be written as:\n\n$$x^2 - 3x - 2 = 0$$\nExpanding the equation using the binomial theorem, we get:\n$$x^2 - 3x = 2$$\nFactoring the left side, we get:\n$$(x - 1)(x + 2) = 2$$\nMultiplying both sides by $(x + 2)$, we get:\n$$x",
        "gt_answers": "0 . 6 6 > 0 . 6 4 > 0 . 6 0 6 > 0 . 6 0 4\n",
        "image_path": "./data/HME100K/test_images/test_4118.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center} $\\frac{1}{2}(bh + ch) = \\frac{1}{2} (b + c)h + \\frac{1}{2} (b + c)c$ \\end{center}\n\nNote: the formula is written in red ink on the blackboard.",
        "gt_answers": "( t + 1 ) \\lambda + t ^ { 2 } + \\sin 1 + 7 0 ( \\lambda \\leq - 1 )\n",
        "image_path": "./data/HME100K/test_images/test_4119.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\begin{aligned} x &= \\frac{5}{3} \\cdot \\frac{6}{4} \\cdot \\frac{7}{5} \\cdot \\frac{8}{6} \\cdot \\frac{9}{7} \\cdot \\frac{10}{8} \\cdot \\frac{11}{9} \\cdot \\frac{12}{10} \\\\&= \\frac{20}{12} \\cdot \\frac{26}{20} \\cdot \\frac{33}{26} \\",
        "gt_answers": "\\angle E F P = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4120.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by:\n\nA = (r^2) \\* pi\n\nWhere r is the radius of the circle and pi is the mathematical constant approximately equal to 3.14159.\n\nThe area of the circle in the image is given by:\n\nA = (10^2) \\* pi\n= 100 \\* 3.14159\n= 314.159 square units.\n\nTherefore, the area of the circle in the image is 314.1",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n\\begin{align\\*}\nL = \\frac{1}{2} \\* m \\* g \\* t^2\n\\end{align\\*}\n\nwhere\n\n* L is the distance traveled by the object\n* m is the mass of the object\n* g is the acceleration due to gravity, which is approximately 9.8 meters per second squared\n* t is the time taken for the object to travel the distance L\n\nThis formula represents the kinematic equation for an object's displacement",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $\\frac{x+5}{x-3}$. The variable x is the denominator in the formula, which is subtracted from the numerator 5 to find the value of x.",
        "gt_answers": "2 y - 5 = \\pm 7\n",
        "image_path": "./data/HME100K/test_images/test_4123.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 5 + 10 + 6 = 21.\n\nTo write this in LaTeX format, you can use the following code:\n\n5 + 10 + 6 = 21\n\nThe \"=\" symbol in LaTeX is represented by the \"=\" operator. The \"+\" symbol is represented by the \"\\+\" operator. So, to write the formula in LaTeX format, you just need to replace the symbols with their corresponding operators.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mi>a</mi><mo>=</mo><mrow><mi>d</mi><mo>+</mo><mi>f</mi></mrow></mfrac></mrow></mfrac></mrow></mfrac></mfrac></mrow></mrow></mrow></mrow></mrow></mrow></mrow></mrow></mrow",
        "gt_answers": "\\frac { A E } { A D } = \\frac { E C } { D F }\n",
        "image_path": "./data/HME100K/test_images/test_4127.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image you provided is not visible to me, as it appears to be a blank white box with the text \"Img\" in the center. Can you please provide a different image or a clear description of the formula you want me to write out in LaTeX format?",
        "gt_answers": "x = \\sqrt { 2 } - 5\n",
        "image_path": "./data/HME100K/test_images/test_4128.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: x + 2 = 5. To write it in LaTeX format, you would use the following code: $\\text{x + 2 = 5}$. This will display the equation with the correct mathematical notation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{2x^2}{x+3}=5$$This formula is used to find the value of x that satisfies the equation.",
        "gt_answers": "2 3 x = \\frac { 5 2 9 } { 6 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4131.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{Time} = \\frac{4}{3}\\text{distance} $$\nwhere $\\text{Time}$ is the time taken to travel a distance of 4 km and $\\text{distance}$ is the distance traveled.",
        "gt_answers": "= 9 0 ^ { \\circ } - 2 0 ^ { \\circ } = 7 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4132.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX code for the image you provided:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\node [at=(0,0), draw, rounded corners, text width=2.5cm, text height=1.5cm] at (0,0) {\n\\begin{CJK}{UTF8}{min}\n\u4e2d\u6587\n\\end{CJK}};\n\\node [at=(2,0), draw, rounded corners, text width=2.5cm, text height=1.5cm] at (2,0) {",
        "gt_answers": "\\therefore \\frac { 1 } { x } = \\frac { 1 } { a _ { 1 } }\n",
        "image_path": "./data/HME100K/test_images/test_4133.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n![ImageContent](https://www.mathworks.com/help/symbolic/ref/imagelabel.html)\n\nwhere 'ImageContent' is the name of the image file that you provided. This formula uses the 'image' function in MATLAB to display the image file specified by the variable 'ImageContent'.",
        "gt_answers": "\\angle E A P - \\angle F P A\n",
        "image_path": "./data/HME100K/test_images/test_4134.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows in LaTeX format:\n\n\\begin{center}\n$\\frac{d^2x}{dt^2} + \\frac{d^2y}{dt^2} + \\frac{d^2z}{dt^2} = \\frac{d^2x}{dt^2} + \\frac{d^2y}{dt^2} + \\frac{d^2z}{dt^2} + m\\frac{dx}{dt} + m\\frac{dy}{dt} + m\\frac{dz}{dt}$\n\\",
        "gt_answers": "\\angle D B E = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4136.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\nx^2 + (a + b)x + c = 0\n\nwhere,\na = -1\nb = 1\nc = 1\n\nTherefore, the roots of the equation are given by:\nx = -b / (2a) = -1 / (2(-1)) = -1 / 2\nx = -b / (2a) = 1 / (2(1)) = 1 / 2\n\nTherefore, the image shows the equation with two real roots, -1 /",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{t^2-t}{2t}$$where t is the time in seconds.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX formula for the expression in the image:\n\n$$\\frac{\\text{m}}{\\text{b}} + \\frac{\\text{a}}{\\text{m}} = \\frac{\\text{c}}{\\text{b}}$$\n\nIn this formula, m, a, and b represent the measurements in the image. The variable c represents the constant value that we can calculate using the formula.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:$$\\frac{x^2+2x+3}{x^2-x+1}=\\frac{2x+3}{x-1}$$This expression represents the formula written on the chalkboard in the image. The expression can be simplified further using the distributive property of multiplication over addition:$$\\frac{x^2+2x+3}{x^2-x+1}=\\frac{2x+3}{x-1}=\\frac{2x+3}{x}+\\frac",
        "gt_answers": "x = \\frac { 2 } { m + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4141.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\frac{l}{\\sin\\theta}$$\n\nWhere l is the length of the hypotenuse of the right angled triangle and $\\theta$ is the angle opposite the hypotenuse.",
        "gt_answers": "\\angle B O A = 1 5 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4142.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe expression is:\n\n$$1 + \\frac{1}{2} = \\frac{3}{2}$$\n\nThe LaTeX code for the equation is:\n\n$$1 + \\frac{1}{2} = \\frac{3}{2}$$\n```\n\nIn this equation, the variable x is 1, and the variable y is $\\frac{1}{2}$. The equation evaluates to $\\frac{3}{2}$, which is written as $\\frac{3}{2}$.\n```",
        "gt_answers": "P Q = \\sqrt { 4 ^ { 2 } + 1 4 ^ { 2 } } = 2 \\sqrt { 5 3 } .\n",
        "image_path": "./data/HME100K/test_images/test_4143.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write out the expression of the formula in the image using LaTeX format.\n\nFirst, let's draw the triangle in the image using LaTeX. We can use the `\\draw` command to draw a triangle. The syntax for this command is:\n```scss\n\\draw (x1, y1) -- (x2, y2) -- (x3, y3) -- cycle;\n```\nwhere `(x1, y1)` is the starting point of the first side of the triangle, `(x2, y2)` is the ending point of the first side,",
        "gt_answers": "\\frac { 1 } { V } + \\frac { 2 } { 3 V } = \\frac { 3 } { 3 V } + \\frac { 2 } { 3 V } = \\frac { 5 } { 3 V } ( h\n",
        "image_path": "./data/HME100K/test_images/test_4144.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression:\n\n\\begin{center}\n$3x^2 + 5x + 7 = 0$\n\\end{center}\n\nTo simplify this expression, we can use the quadratic formula:\n\n$$x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$$\n\nwhere $a = 1$, $b = 5$, and $c = 7$. Substituting these values into the formula, we get:\n\n$$x = \\frac{-5 \\pm \\sqrt",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is $\\ $A = l \\* w$, where l is the length and w is the width.\n\nUsing the information provided in the image, we can calculate the area of the rectangle by finding the length and width.\n\nThe length of the rectangle is 3cm and the width is 5cm.\n\nTherefore, the area of the rectangle is $\\ $A = 3 \\* 5 = 15$ cm^2$\n\nTherefore, the area of the rectangle is $\\ $A = 3 \\* 5 = 15",
        "gt_answers": "( 5 + 1 ) = 5 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_4147.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length l and width w is:\n\nA = l \\* w\n\nTherefore, the area of the rectangle in the image is:\n\nA = 5 \\* 2\n= 10 square units\n\nNote: The LaTeX code for the formula is:\n\n$ A = l \\* w $\n\nwhere l and w are variables representing the length and width of the rectangle, respectively.",
        "gt_answers": "a = \\frac { 5 } { 2 } g\n",
        "image_path": "./data/HME100K/test_images/test_4148.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n\u222b \u222b A dx + \u222b \u222b B dy = \u222b \u222b (A + B) dy\n\nwhere A and B are any functions.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{4}{\\sqrt{64 + 32}} = \\frac{4}{2 \\sqrt{32}} = 2 $$\n\nwhere $4$ is the numerator and $\\frac{64 + 32}{2}$ is the denominator.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by:\n\nA = (pi \\* r^2) / 4\n\nwhere r is the radius of the circle.\n\nSubstituting the given values, we get:\n\nA = (3.1416 \\* 1.3^2) / 4\n= 3.1416 \\* 1.99\n= 6.3834\n\nTherefore, the area of the circle is 6.3834 square units.",
        "gt_answers": "\\widehat { B D } = \\widehat { C D }\n",
        "image_path": "./data/HME100K/test_images/test_4151.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$x = \\frac{3mg}{\\sin^2\\theta}$$\n\nwhere $\\theta$ is the angle of inclination of the plane, and $m$ is the mass of the object. The formula calculates the x-coordinate of the object's position at the bottom of the inclined plane, given its mass and the angle of inclination.",
        "gt_answers": "G D = \\frac { 1 } { 2 } A C\n",
        "image_path": "./data/HME100K/test_images/test_4152.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the volume of a cylinder can be expressed as:\n\nV = \u03c0r^2h\n\nwhere r is the radius of the cylinder and h is its height.",
        "gt_answers": "t = 8 , t = 1 1\n",
        "image_path": "./data/HME100K/test_images/test_4153.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{Area} = \\frac{1}{2} \\times \\frac{1}{2} \\times L = \\frac{1}{4} L^2$$\n\nwhere L is the length of the rectangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$I = \\frac{V\\_{p}-V\\_{n}}{2}$$\n\nwhere $V\\_p$ is the positive voltage of the power supply and $V\\_n$ is the negative voltage of the power supply.",
        "gt_answers": "x = \\frac { 1 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4156.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $x^2 + 4x - 8$. The x-intercepts are at $x = -4$ and $x = -2$. The y-intercept is at $y = 0$. The equation of the line is $y = mx + b$, where $m = 2$ and $b = -8$. The equation of the parabola is $y = ax^2 + bx + c$, where $a = 1$, $b = 4$, and $c = 0$. The equation of the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not visible to me as the image is not provided. However, assuming that the equation is written in LaTeX format, it would be expressed as follows:\n\n$$3x + 4y = 7$$\n\nThis equation represents a line in the Cartesian plane with a slope of 3 and an intercept at (0, 4).",
        "gt_answers": "y _ { 4 } = - \\frac { 7 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4159.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula in the image is:<br>$ P = \\frac{1000\\times 2}{1000 \\times 1}$<br>In LaTeX format, this formula would be written as:<br>$ P = \\frac{1000 \\times 2}{1000 \\times 1}$<br>Note that this formula is simply dividing 1000 by 1000, so it is equal to 1. This formula is often used in physics to calculate the pressure of a gas in a closed system.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $ $\\frac{m}{b}$ $\\frac{a}{b}$ $\\frac{c}{b}$ $\\frac{d}{b}$ $\\frac{e}{b}$ $\\frac{f}{b}$ $\\frac{g}{b}$ $\\frac{h}{b}$ $\\frac{i}{b}$ $\\frac{j}{b}$ $\\frac{k}{b}$ $\\frac{l}{b}$ $\\frac{m}{b}$ $\\frac{n}{b}$ $\\frac{o}{b}$ $\\frac{p}{b}$ $\\frac{q}{b}$ $\\",
        "gt_answers": "x = \\frac { . 1 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_4161.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "x = 1 5 \\times \\frac { 1 0 } { 2 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4165.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n![](https://i.imgur.com/image.jpg)\n\nwhere $\\text{A}$ is the area of the circle with radius $\\text{r}$ and $\\text{B}$ is the area of the triangle with base $\\text{b}$ and height $\\text{h}$.",
        "gt_answers": "\\angle A D B = 4 5 ^ { \\circ } + \\angle 2 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4166.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula in the image using LaTeX format, we can write:\n\n$$x + \\frac{a}{b} = 2$$\n\nwhere a and b are the coefficients of the quadratic equation.\n\nThe right-hand side of the equation represents the point where the parabola intersects the x-axis. The left-hand side represents the point where the parabola intersects the y-axis.\n\nBy substituting the given values of a and b into the equation, we get:\n\n$$x + \\frac{29}{4} = 2$$",
        "gt_answers": "\\frac { 1 } { . x + y } = a\n",
        "image_path": "./data/HME100K/test_images/test_4168.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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$$\\text{L\\_c = 0.46 \\* (1000/t)$$\n\nWhere L\\_c is the critical value for the given equation, t is the time of observation, and 1000 is a constant.",
        "gt_answers": "\\angle A C D = 4 8 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4169.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{s}=\\frac{a\\cdot b}{c}\\text{.}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows:\n\n$$\\text{ImageContent}$$\nwhere $\\text{ImageContent}$ is the image itself.",
        "gt_answers": "B E + E F = C F + E F\n",
        "image_path": "./data/HME100K/test_images/test_4171.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the following LaTeX code:\n\n$$\\frac{1000}{100}+\\frac{1000}{200}+\\frac{1000}{500}=\\frac{1000}{500}$$\n\nwhich simplifies to:\n\n$$\\frac{1000}{500}=\\frac{1000}{200}+\\frac{1000}{500}=\\frac{100}{20}+\\frac{100}{50}=\\frac{1}{2",
        "gt_answers": "9 \\times 5 = 4 5 d m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4172.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\text{V} = \\frac{1}{2}\\text{m} \\left(\\text{a} + \\frac{1}{2}\\text{b}\\right) \\left(\\text{c} + \\frac{1}{2}\\text{d}\\right)$$\n\nwhere $\\text{V}$ is the volume of the rectangular prism, $\\text{m}$ is the mass of the object, $\\text{a}$ and $\\text{b}$ are the lengths of the two parallel sides of the prism",
        "gt_answers": "B E = \\frac { 1 } { 2 } A B\n",
        "image_path": "./data/HME100K/test_images/test_4173.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given by:\n\n$x^2 + 2x + 1 = 0$\n\nThis is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 1$, $b = 2$, and $c = 1$. The solutions to this equation are the values of $x$ that make the equation true, which are the roots of the quadratic polynomial.\n\nTo find the solutions, we can use the quadratic formula:\n\n$x = {-b \u00b1 sqrt(b^2 -",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4175.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$$ f(x) = \\left \\{\\begin{matrix} 0 & x < 0 \\ \\ 0 & x \\geq 0 \\end{matrix} \\right \\} $$\nThis is a Heaviside step function, also known as the Dirac delta function, which is defined as:\n$$ \\delta(x) = \\left \\{\\begin{matrix} 0 & x < 0 \\ \\ 1 & x \\geq 0 \\end{matrix} \\right \\} $$\nThe Heaviside step function",
        "gt_answers": "H _ { 2 } O _ { 2 } \\xlongequal { M n O _ { 2 } } H _ { 2 } O + O _ { 2 } \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_4176.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by:$$\\frac{1}{3x^{2}+2x+1}=-\\frac{1}{4}$$This is a quadratic equation with two solutions. The solutions are given by:$$x=\\frac{2\\pm\\sqrt{15}}{4}$$Thus, the solutions are x = 2 \u00b1 \u221a15/4.",
        "gt_answers": "f ^ { \\prime } ( x ) = x ^ { 2 } - 2 a x - a\n",
        "image_path": "./data/HME100K/test_images/test_4177.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the slope of a line passing through the points (x1, y1) and (x2, y2) can be written as:\n\n$$\\frac{y2-y1}{x2-x1} = \\frac{2x+5}{3x+5}$$\n\nExpanding the right side of the equation gives:\n\n$$\\frac{2x+5}{3x+5} = \\frac{2(x+1)+5-3(x+1)+5}{3(x+1)+5-3(x+1)+5}$$",
        "gt_answers": "5 0 \\div 2 = 2 5 ( m )\n",
        "image_path": "./data/HME100K/test_images/test_4179.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{1}{3x^2 + 5x - 2}$.",
        "gt_answers": "y = \\frac { n } { m + \\sqrt { 2 } } ( x + \\sqrt { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_4180.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\nx = 2(m \u2212 5) + 6m + 4\n\nThis formula represents a linear equation with a slope of 3 and a y-intercept of 12. The equation passes through the point (5, 10) and has a slope of 3.",
        "gt_answers": "1 2 \\times \\frac { 2 } { 3 } = 8 ( k m / h\n",
        "image_path": "./data/HME100K/test_images/test_4181.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: x^4 - x^3 + x^2 - x + 1.\n\nHere is the formula written in LaTeX format: $\\frac{x^4 - x^3 + x^2 - x + 1}{x^3 - x^2 + x - 1}$.",
        "gt_answers": "x = - \\frac { 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4183.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: b = ( a + c ) / 2. This formula is derived from the image, which shows the sum of the two angles and the center angle of the triangle.",
        "gt_answers": "b = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4184.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $\\frac{2x^2+x-3}{x^2-x+2}$.",
        "gt_answers": "x ^ { 2 } = \\frac { 5 } { m - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4186.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the area of a rectangle, which is given by the formula:\n\nA = l \u00d7 w\n\nwhere l is the length of the rectangle and w is the width of the rectangle. In this case, the length is 5 cm and the width is 6 cm, so the area of the rectangle is:\n\nA = 5 cm \u00d7 6 cm = 30 cm\u00b2",
        "gt_answers": "1 9 0 \\times 5 = 9 4 0 ( k m ) .\n",
        "image_path": "./data/HME100K/test_images/test_4187.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[fill=blue] (0,0) rectangle (1,1);\n\\node[above right] at (0.5,0.5) {$$\\frac{a}{b} = c$$};\n\\node[below left] at (0,0.5) {$a$};\n\\node[above left] at (0,0) {$b$};\n\\node[below right] at (1,0.5) {$c$};\n\\end{tikzpicture",
        "gt_answers": "\\frac { 1 } { 4 } \\cdot x + \\frac { 1 } { 2 } = x\n",
        "image_path": "./data/HME100K/test_images/test_4189.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n\u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0\u221e \u222b\u2212\u221e \u222b0",
        "gt_answers": "\\frac { 5 } { 8 } = \\frac { 5 \\times 5 } { 8 \\times 5 } = \\frac { 2 5 } { 4 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4190.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given by: $$ I = \\frac{m}{d} $$ where $m$ is the mass of the object and $d$ is its distance from the observer.",
        "gt_answers": "\\angle A B O = \\frac { \\sqrt { 3 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4192.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I am sorry, but I cannot see the image that you have provided. Can you please provide me with the image so that I can assist you in writing the LaTeX expression for the formula?",
        "gt_answers": "n = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4195.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: $\\frac{4a + 3b}{5} = \\frac{14}{5}$",
        "gt_answers": "\\frac { 3 } { 4 } \\times \\frac { 4 } { 5 } = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4196.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\text{b}=\\frac{a}{c}$$where a, b, and c are the lengths of the sides of the triangle, as shown in the image.",
        "gt_answers": "\\overrightarrow { B D } = ( - 1 , 1 , 0 ) .\n",
        "image_path": "./data/HME100K/test_images/test_4197.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle can be written as:\n\nA = (1/2) \\* base \\* height\n\nwhere base is the length of the base of the triangle and height is the length of the height of the triangle. In the image, the base is 10 cm and the height is 15 cm, so the area of the triangle is:\n\nA = (1/2) \\* 10 cm \\* 15 cm\n= 50 cm^2",
        "gt_answers": "1 1 2 < 1 2 9\n",
        "image_path": "./data/HME100K/test_images/test_4198.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "1. The formula is a\u00b2+b\u00b2=c\u00b2 in LaTeX format.\n\n2. The formula is a\u00b2+b\u00b2=c\u00b2 in LaTeX format.\n3. The formula is a\u00b2+b\u00b2=c\u00b2 in LaTeX format.\n4. The formula is a\u00b2+b\u00b2=c\u00b2 in LaTeX format.\n5. The formula is a\u00b2+b\u00b2=c\u00b2 in LaTeX format.\n6. The formula is a\u00b2+b\u00b2=c\u00b2 in LaTeX format.\n7. The formula is a\u00b2+b\u00b2=c\u00b2 in LaTeX format.",
        "gt_answers": "A C : B C = 2 : 1 = 2 , E F :\n",
        "image_path": "./data/HME100K/test_images/test_4199.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{2\\times 4 + 3\\times 3 + 1\\times 2 + 1}{2\\times 3 + 3\\times 2 + 1\\times 1 + 1}$$\n\nAlternatively, we can write the formula as:\n\n$$\\frac{2+4+3+1+1}{2+3+2+1+1}$$\n\nwhich simplifies to:\n\n$$\\frac{10}{15}$$\n\nSo the result",
        "gt_answers": "4 \\times 3 = 1 2 ( d m )\n",
        "image_path": "./data/HME100K/test_images/test_4201.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by: A = \u03c0r^2. In LaTeX format, this formula can be written as: A = \\pi r^2.",
        "gt_answers": "x = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4202.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Can you please provide a different image or describe the expression in LaTeX format?",
        "gt_answers": "\\cos ( \\frac { 2 k + 1 } { 3 } \\pi x - \\frac { \\pi } { 6 } ) = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4203.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given as:\n\n$$x^2 + 3x - 2 = 0$$\n\nExpanding the equation, we get:\n\n$$x^2 + 3x - 2 = 0$$\n\nSimplifying the equation, we get:\n\n$$x(x + 3) - 2 = 0$$\n\nFactoring the left side of the equation, we get:\n\n$$(x + 3)(x - 2) = 0$$\n\nMultiplying the factors on the right side of the equation, we get",
        "gt_answers": "h ^ { \\prime } ( x ) = x ^ { 2 } - 2 x - 3\n",
        "image_path": "./data/HME100K/test_images/test_4204.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length 5 and width 6 is:\n\nA = lw\n\nwhere l is the length and w is the width.\n\nTherefore, the area of the rectangle in the image is:\n\nA = 5 \u00d7 6 = 30",
        "gt_answers": "4 = b ^ { 2 } - 4 a c = 9 + 3 2 = 4 1 > 0\n",
        "image_path": "./data/HME100K/test_images/test_4205.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{d^2x}{dt^2} + \\frac{k}{m} \\cdot \\frac{dx}{dt} = \\frac{k}{m} \\cdot x$$This is the second order ordinary differential equation for the motion of an object under the influence of a spring with spring constant $k$ and mass $m$. The first term on the left represents the rate of change of the object's position with respect to time, while the second term on the right represents the force exerted on the object by the spring.",
        "gt_answers": "C H _ { 4 } + 2 O _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4206.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:\n\nA = l x w\n\nwhere l is the length of the rectangle and w is the width of the rectangle.",
        "gt_answers": "P Q = \\sqrt { 4 ^ { 2 } + 1 4 ^ { 2 } } = \\sqrt { 2 2 } = 2 \\sqrt { 5 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4207.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$x = \\frac{1}{2} - \\frac{1}{4}$\n\nThis formula can be read as, `x is equal to one half minus one fourth'.",
        "gt_answers": "\\angle E B F = \\frac { 1 } { 2 } \\angle A B C = 3 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4208.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$ 2 \\times 2 + 3 \\times 4 = 14 $$",
        "gt_answers": "P = \\rho g h = 1 0 0 0 k g / m ^ { 3 } \\times 9 . 8 N / k g \\times 0 . 1 5 m = 1 4 7 0 P a .\n",
        "image_path": "./data/HME100K/test_images/test_4210.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression in the image:\n\n$$\\frac{b + 2g}{4c} = \\frac{c + 2g}{4c} \\quad \\Rightarrow \\quad \\frac{b - c}{2c} = \\frac{2c - c}{2c} \\quad \\Rightarrow \\quad \\frac{b}{2c} = \\frac{c - 2g}{2c} \\quad \\Rightarrow \\quad \\frac{2c - g}{c} = \\frac{c - 2g}{c}$$\n\nAl",
        "gt_answers": "\\frac { B G } { D G } = \\frac { A G } { C G } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4211.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is:\n\nA = \u03c0r^2\n\nwhere A is the area of the circle and r is the radius of the circle. The formula can be written mathematically as:\n\nA = \u03c0r^2\n\nwhere A is the area of the circle and r is the radius of the circle. The formula can also be written in LaTeX format as:\n\nA = \\pi r^2\n\nwhere A is the area of the circle and r is the radius of the circle.",
        "gt_answers": "2 0 0 \\times 2 = 4 0 0 ( c m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_4213.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length l and width w is given by the equation: A = l x w.\n\nIn LaTeX format, the equation can be written as:\n\n\\[ A = l \\times w \\]\n\nThis formula can be used to calculate the area of any rectangle with known length and width.",
        "gt_answers": "\\cos \\alpha = \\pm _ { 1 } ^ { 2 6 }\n",
        "image_path": "./data/HME100K/test_images/test_4214.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the given expression:\n\n$$\\frac{1+3\\left(\\frac{5}{6}\\right)}{\\left(\\frac{7}{8}\\right)}$$\n\nExplanation:\n\n* The expression is $\\frac{1+3\\left(\\frac{5}{6}\\right)}{\\left(\\frac{7}{8}\\right)}$, where $x = \\frac{5}{6}$ and $y = \\frac{7}{8}$.\n* The numerator of the fraction is $\\frac{1+3x}{y}$, which simplifies",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given by the following expression: $\\sqrt{x^2 + y^2}$. This is the formula for the distance between two points in a two-dimensional space.",
        "gt_answers": "x = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4217.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:\n\nA = l x w\n\nWhere l is the length of the rectangle and w is the width of the rectangle.\n\nThe formula for the perimeter of a rectangle is given by:\n\nP = 2l + 2w\n\nWhere l is the length of the rectangle and w is the width of the rectangle.\n\nThe formula for the volume of a cube is given by:\n\nV = l x w x h\n\nWhere l is the length of the cube, w is the width of the cube, and h is",
        "gt_answers": "- \\frac { 1 } { x ^ { 2 } } + \\frac { 1 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_4218.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r can be written as:A=\u03c0r225\u03c0r2=\u03c0r2\\frac{A}{\\sqrt{2}} = \\frac{\\pi r^2}{2\\sqrt{\\pi r^2}}=\\frac{\\pi r^2}{\\sqrt{2}}A=2\u03c0r2\u200b\u03c0r2\u200b=2\\sqrt{2}\u03c0r2\u200b\u200bThe expression can be rewritten using LaTeX format as:A=\u03c0r225\u03c0r2=\u03c0r2\\frac{A}{\\sqrt{2}} = \\",
        "gt_answers": "c \\frac { 1 } { 4 } : 8 = 1 2 : \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_4219.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2x^2 - 2x + 1. This can be derived by substituting x = 4 into the formula and simplifying.2x^2 - 2x + 1 = 8 - 2 + 1 = 7",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:5x2-3y2z.",
        "gt_answers": "s = 3 m\n",
        "image_path": "./data/HME100K/test_images/test_4221.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image that you have provided. Can you please give me the image?",
        "gt_answers": "\\frac { 2 } { 1 0 } = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4222.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, you would use the following LaTeX code:\n\n\\begin{center}\n\\begin{align*}\n    f(x) &= 2x^2 - 3x + 1 \\\n\\end{align*}\n\\end{center}\n\nThis LaTeX code represents the equation of a parabola with vertex at the origin and a minimum value of -1/3 at x=1/3. The function f(x) is defined for all real values of x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: $\\frac{x}{x-3}$.\n\nThe formula is derived from the equation $x^2 - 6x + 8 = 0$, which can be factored as $(x-2)(x+4) = 0$. Squaring both sides, we get $(x-2)^2(x+4)^2 = 0$, which simplifies to $(x-2)(x+4)(x-2)(x+4) = 0$. Multiplying out the terms, we get $x^2 - 6x + 8",
        "gt_answers": "( x + 3 ) ( x - 3 ) ( x + \\sqrt { 2 } ) ( x - \\sqrt { 2 } ) .\n",
        "image_path": "./data/HME100K/test_images/test_4225.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the triangle shown in the image can be found using the formula for the area of a triangle:\n\nA = (1/2) \\* b \\* h\n\nwhere b is the base of the triangle and h is the height.\n\nFor the given triangle:\nb = 5\nh = 10\n\nTherefore, the area of the triangle is:\nA = (1/2) \\* 5 \\* 10 = 25",
        "gt_answers": "C D E C = \\angle B E C\n",
        "image_path": "./data/HME100K/test_images/test_4226.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} \\frac{d^2y}{dx^2} + \\frac{3dydx}{dx} - \\frac{9y^3}{x^3} = \\frac{1}{x^2} \\end{aligned}$$",
        "gt_answers": "n = - 3\n",
        "image_path": "./data/HME100K/test_images/test_4227.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is given by:\n\n\\begin{align\\*}\ny = \\frac{x^2 - 4x + 4}{x - 2}\n\\end{align\\*}\n\nIn this formula, x and y are variables, and the expression is in the form of a polynomial division, where the denominator is the linear polynomial x - 2.",
        "gt_answers": "( 6 \\times 4 + 6 \\times 5 + 4 \\times 5 ) \\times 2 = 1 4 8 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_4228.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2}x^2 - \\frac{1}{2}x - 15$.",
        "gt_answers": "\\overline { C D } = \\overline { E B }\n",
        "image_path": "./data/HME100K/test_images/test_4229.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is as follows:\n\n$$ 1 + 3x^2 + 5x^4 + 7x^6 $$\nThis expression is the sum of the series of powers of x from the first to the fourth term.",
        "gt_answers": "3 x ^ { 2 } - ( 2 x - 1 ) ^ { 2 } - ( 2 x - 1 ) + 3 = 0\n",
        "image_path": "./data/HME100K/test_images/test_4230.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:2x + 2y = 6x - y = 2x + 2y = 4xy = 4y2.",
        "gt_answers": "2 a ^ { 2 } - 6 a - 2 = 0\n",
        "image_path": "./data/HME100K/test_images/test_4231.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$\\text{The equation of a line in the plane is given by: y = mx + b, where m is the slope of the line and b is the y-intercept.}$$\n\n$$\\text{The equation of a line in the plane is given by: y = mx + b, where m is the slope of the line and b is the y-intercept.}$$\n\n$$\\text{The equation of a line in the plane is given by: y = mx + b, where m is the slope of the line and b is the y-intercept",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is as follows:$$\\frac{x^2 - y^2}{\\sqrt{x^2 + y^2}} = \\frac{r^2 - (r - 1)^2}{\\sqrt{r^2 + (r - 1)^2}}$$This is the formula for the distance between two points in a two-dimensional space. The numerator is the difference between the squares of the x and y coordinates of the two points, while the denominator is the square root of the sum of the squares of the x and y coordinates of the two points. The equation shows",
        "gt_answers": "= - 1 + \\frac { 2 } { a - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4233.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image given is:\n\n\\begin{center}4x^2+9y^2=16\\end{center}\n\nThis is a quadratic equation in the form of Ax^2+Bx+C=0, where A=4, B=9, and C=16. The solutions to the equation are the values of x and y that make the equation true. In this case, the solutions are x=4 and y=4, which satisfy the equation.",
        "gt_answers": "\\frac { 1 } { 2 } \\div \\frac { 1 } { 8 } = 4\n",
        "image_path": "./data/HME100K/test_images/test_4234.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{\\text{Area}}{\\text{Circumference}}$.\n\nThis formula is used to calculate the area of a circle relative to its circumference. The formula is derived from the definition of pi as the ratio of the circumference of a circle to its diameter.",
        "gt_answers": "y _ { B C } = k x + b\n",
        "image_path": "./data/HME100K/test_images/test_4235.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\n4\\frac{x^2 - 6x + 8}{x - 2} &= \\frac{4x^2 - 14x + 24}{x - 2}\\\n&= \\frac{4(x - 2)(x + 1)}{x - 2}\\\n&= (x + 1) \\\n&= 5\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: r = w / t, where w is the weight and t is the time taken to lift the weight to the desired height.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a circle with a radius of 3 cm and center at the origin is:x^2 + y^2 = r^2where r is the radius. The image shows a circle with center at the origin and a radius of 3 cm.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\begin{aligned} a & = \\frac{1}{3} \\left(\\frac{1}{2}\\right)^{2} \\left(\\frac{1}{4}\\right)^{3} \\left(\\frac{3}{4}\\right)^{4} \\left(\\frac{1}{5}\\right)^{5} \\left(\\frac{3}{5}\\right)^{6} \\left(\\frac{1}{6}\\right)^{6} \\left(\\frac{3}{6}\\right)^{7} \\left(\\frac{1",
        "gt_answers": "a _ { m } ^ { 2 } + b n ^ { 2 } + 2 a m b n > a n ^ { 2 } + 6 m ^ { 2 } + 2 a n b m\n",
        "image_path": "./data/HME100K/test_images/test_4241.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clearly visible as it is written on a piece of paper with a red pen. However, it appears to be a mathematical expression involving multiplication and addition of numbers. The numbers in the image appear to be the values used in the expression. It is difficult to determine the exact expression without more information or context.\n\nTo write out the expression using LaTeX format, you would need to take a clear photograph of the image and use it to create a LaTeX document. Then, you can use LaTeX commands to write out the mathematical expression, including multiplication and addition symbols, variables, and operators.\n\nHowever,",
        "gt_answers": "7 7 4 4 - 4 9 0 0 = 2 8 4 4 ( d m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_4242.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{sin}(x) = \\frac{1}{\\sqrt{5}}$$\n\nThe derivative of this expression with respect to x is given by:\n\n$$\\frac{d}{dx} \\text{sin}(x) = \\frac{1}{\\sqrt{5}}$$\nThe second derivative of this expression with respect to x is given by:\n\n$$\\frac{d^2}{dx^2} \\text{sin}(x) = -\\frac{1}{5}$$\nThe integral of this expression from",
        "gt_answers": "1 0 0 0 0 \\times \\frac { 1 } { 5 0 0 0 } = 2 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_4243.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we need to follow the steps below:\n\n1. Select the entire expression and copy it to the clipboard.\n2. Paste the expression into a LaTeX editor, such as Overleaf.\n3. Wrap the expression in a math mode by typing `$` before and after the expression.\n4. Format the expression with appropriate math formatting, such as using the `frac` command to display fractions.\n\nHere is the LaTeX code for the given formula:\n\n\\begin{align\\*}\n&#x2211",
        "gt_answers": "\\frac { 1 } { 2 } A M \\cdot O C = \\frac { 1 } { 3 } \\times 9\n",
        "image_path": "./data/HME100K/test_images/test_4244.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be expressed as:\n\n$$x + 2y = 16$$\n\nwhich can be solved for y as:\n\n$$y = \\frac{16 - x}{2}$$\n\nTherefore, the solution to the equation is x = 8.",
        "gt_answers": "\\cos \\alpha - \\sin \\alpha = - \\frac { \\sqrt { 3 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4246.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the equation in the image using LaTeX format is:\n\n\\begin{align\\*}\ny = \\frac{100x - 200}{x + 50}\n\\end{align\\*}\n\nThis equation is a linear equation with a slope of -2 and an y-intercept of -200. The equation passes through the point (0, -200) on the x-axis and has a slope of -2.",
        "gt_answers": "y = \\frac { 8 } { 5 } \\sqrt { 3 } - \\sqrt { 3 } = \\frac { 3 \\sqrt { 3 } } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4247.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX formula for the expression in the image:\n\n$$\\frac{1}{1+\\frac{1}{2}}=1-\\frac{1}{2}$$\n\nThis formula is equivalent to the expression on the image.",
        "gt_answers": "W = - 1 0 0 x + 5 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_4249.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is pi^2.",
        "gt_answers": "\\pi < \\alpha < \\frac { 3 } { 2 } \\pi\n",
        "image_path": "./data/HME100K/test_images/test_4250.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{f(x) = \\frac{5}{3} \\cdot \\frac{4}{x}}$$\n\nwhere $x$ is the variable being used in the formula.",
        "gt_answers": "m ^ { 2 } + \\frac { b } { a } m + \\frac { b ^ { 2 } } { 4 a ^ { 2 } } = \\frac { b ^ { 2 } } { 4 a ^ { 2 } } - \\frac { c } { a }\n",
        "image_path": "./data/HME100K/test_images/test_4251.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\nP = (25 \\* 15) / 10 = 375",
        "gt_answers": "B G \\bot E F\n",
        "image_path": "./data/HME100K/test_images/test_4252.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is written as: f(x) = x2 - 5x + 1.",
        "gt_answers": "\\frac { 1 5 } { 2 } + k < 5\n",
        "image_path": "./data/HME100K/test_images/test_4253.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is $\\sqrt(2)$.",
        "gt_answers": "y _ { 3 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4257.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ a = \\frac{b}{c}$$\n\nwhere $a$, $b$, and $c$ are the given numbers in the image.",
        "gt_answers": "A Q = \\frac { A B } { \\cos A } = \\frac { 2 0 } { \\frac { 1 } { 2 } } = 4 0 c m\n",
        "image_path": "./data/HME100K/test_images/test_4258.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:$$ 5\\frac{5+x}{7}-2$$",
        "gt_answers": "1 - \\frac { 2 } { 3 } \\div \\frac { 7 } { 8 } - \\frac { 4 } { 2 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4260.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format expression for the formula in the image:\n\n$$\\text{b} = \\frac{\\text{a}+\\text{c}}{\\text{2}}$$\n\nThis formula states that the value of \"b\" is equal to the sum of \"a\" and \"c\" divided by 2. The variables \"a,\" \"b,\" and \"c\" are all in the numerator, while \"2\" is in the denominator.",
        "gt_answers": "Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 } + H _ { 2 } \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_4261.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a quadratic function, with the variable x representing the position of the ball on the y-axis and the variable y representing the time it takes to get to that position. The equation can be written as:y = 0.5x^2+0.25x+10.25where x is the position of the ball on the x-axis and y is the time it takes to get to that position. The constant 0.25x represents the acceleration due to gravity, which is constant and affects the ball's movement. The constant 10.2",
        "gt_answers": "= \\frac { 3 - \\sqrt { 1 7 } } { 2 . } x _ { 2 } = \\frac { 3 + \\sqrt { n } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4262.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The equation written in LaTeX format for the image is: $ y = 2x - 3 $.",
        "gt_answers": "y _ { 1 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4263.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{a^2 + b^2}{2ab}$$",
        "gt_answers": "\\frac { 1 } { x + y } + \\frac { 2 } { x - y } = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4264.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is given below:\n\n$$50 + \\frac{4}{2} = \\frac{9}{1}$$\n\nHere, we have used the formulae to calculate the given expression.",
        "gt_answers": "B Q = A B \\tan A = 2 0 \\tan 6 0 ^ { \\circ } = 2 0 \\sqrt { 3 } c m\n",
        "image_path": "./data/HME100K/test_images/test_4265.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$x + 3y = 12$$",
        "gt_answers": "- \\frac { 1 } { 2 } x ^ { 2 } + 1 + x\n",
        "image_path": "./data/HME100K/test_images/test_4267.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\begin{aligned}x^2 + 2x - 3y^2 + 4y - 5z^2 + 6z - 7 = 0\\end{aligned}$$\n\nThis is a quadratic equation in the form of a polynomial equation, where the variable x is raised to the power of 2, y is raised to the power of 2, and z is raised to the power of 2.",
        "gt_answers": "\\sqrt { 3 y - 2 } = 3 - \\sqrt { y + 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4268.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\begin{align\\*} x^2 + 4x - 15 = 0 \\end{align\\*}$$",
        "gt_answers": "x = \\frac { 1 5 } { 1 6 }\n",
        "image_path": "./data/HME100K/test_images/test_4269.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\nx + 3y = 16\n\nThis equation represents a line in the coordinate plane with a slope of 3 and a y-intercept of 16.",
        "gt_answers": "\\frac { x } { 1 2 0 } = \\frac { x } { 1 6 0 } + 6\n",
        "image_path": "./data/HME100K/test_images/test_4270.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{1}{2} \\cdot 6 + \\frac{1}{4} \\cdot 8 = \\frac{1}{2} \\cdot 6 + \\frac{1}{4} \\cdot 8$",
        "gt_answers": "\\angle D E C + \\angle E C B = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4271.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not provided, so it cannot be written out in LaTeX format.",
        "gt_answers": "\\Delta A C D \\cong \\Delta C B E ( S A S ) \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_4272.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by A = l x w, where l is the length and w is the width. The image shows the formula written in Japanese.\n\nIn LaTeX format, the formula can be written as:\n\n$$ A = l \\times w $$\n\nwhere $A$ is the area, $l$ is the length, and $w$ is the width.",
        "gt_answers": "t = \\frac { 6 } { V }\n",
        "image_path": "./data/HME100K/test_images/test_4274.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n\\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} + \\frac{1}{32} + \\frac{1}{64} + \\frac{1}{128} + \\frac{1}{256}\n\\end{center}\n\nwhere the numerator is the sum of the fractions of 1 divided by 2, 1 divided by 4, 1 divided",
        "gt_answers": "\\frac { 1 } { 2 } : \\frac { 1 } { 3 } = 1 5 : 1\n",
        "image_path": "./data/HME100K/test_images/test_4276.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{x}{y}$.\n\nHere, the formula represents the proportion of x to y. The numerator, x, represents the number of red balls in the urn. The denominator, y, represents the total number of balls in the urn. The fraction bar indicates that the proportion is a ratio of two numbers.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula can be written as follows:\n\n\\begin{align\\*}\n&1 + \\frac{3x + 2y}{2} = \\frac{2(3x + 2y) + 4(3x + 2y)}{3} \\\n&\\Rightarrow 1 + \\frac{3x + 2y}{2} = \\frac{6x + 6y + 8}{3} \\\n&\\Rightarrow 1 + \\frac{3x + 2y}{2} = \\frac{2(3x + 2y",
        "gt_answers": "\\frac { 1 } { x } = \\frac { 1 } { 0 . 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4281.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n$$\\text{1 + 2x + 3y} = \\text{5}$$\n\nwhere $x$ and $y$ are variables.",
        "gt_answers": "( 2 0 + 2 x ) ( 4 0 - x ) = 1 2 0 0\n",
        "image_path": "./data/HME100K/test_images/test_4282.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not provided.",
        "gt_answers": "\\frac { 1 } { a ^ { 2 } - 9 } = \\frac { 1 } { ( a + 3 ) ( a - 3 ) } = \\frac { a + 3 } { ( a + 3 ) ^ { 2 } ( a - 3 ) }\n",
        "image_path": "./data/HME100K/test_images/test_4283.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that! Here's the LaTeX expression for the given formula in the image:\n\n\\begin{center}\n$y = \\frac{x}{x+2}$\n\\end{center}\n\nThis formula represents a linear function with slope of $\\frac{1}{2}$ and intercept at the origin. The domain of this function is all real numbers, and the range is all real numbers greater than or equal to zero.",
        "gt_answers": "\\frac { 1 5 ^ { x 1 6 0 } } { 1 0 0 } x - \\frac { 9 ^ { x 1 6 0 } } { 1 0 0 } = \\frac { 7 ^ { x 1 6 0 } } { 1 0 0 } x + 0 . 3 1 ^ { x 1 6 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4284.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ 2x^2 + 2y^2 = 25 $$\n\nThis equation represents a parabolic equation with the vertex at the origin. The x-coordinate of the vertex is given by the formula for the x-coordinate of the vertex of a parabolic equation with the given equation:\n\n$$ x = \\frac{-b}{2a} $$\n\nwhere $a$ is the coefficient of $x^2$ and $b$ is the coefficient of $y^2$ in the given equation. Subst",
        "gt_answers": "V A ^ { 2 } = 6\n",
        "image_path": "./data/HME100K/test_images/test_4286.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n$$\\frac{1}{2\\pi}\\int\\_{-\\infty}^{\\infty} \\frac{\\sin(x)}{x} dx = \\frac{1}{2}$$\n\nIn this expression, we're integrating the sine function over the interval $[-\\infty, \\infty]$ and evaluating the integral at $x=0$. The result is $\\frac{1}{2}$, which is the value of the function at $x=0$.",
        "gt_answers": "P F = - \\frac { 4 } { 3 } m ^ { 2 } + \\frac { 8 } { 3 } m + 4 - 4\n",
        "image_path": "./data/HME100K/test_images/test_4290.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written in LaTeX format as follows:\n\ndw dw dwd w d dwd dwdw dw dwdw dwd w dwd dw dwd dwdw dwd w dwd dwd dwdw dwd dwdw dwdw dwd dwd w dwd dwd dwdw dwdw dwdw dwd dwdw dwd w dwd dwdw dwdw dwdw dwd dwdw dwdw dwdw dwd dwdw dwdw dwdw dwd dwdw dwdw dwdw dwd",
        "gt_answers": "0 . 6 W = 6 V \\Delta I _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4291.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ (x+y)^4 = x^4 + 4xy^3 + 6x^2y^2 + 4x^3y + y^4 $$\n\nThis is obtained by expanding the expression $(x+y)^4$ using the binomial theorem.",
        "gt_answers": "x ^ { 2 } - 4 + 2 x ^ { 2 } + 6 x + 4 + 8 x + 8 = 0\n",
        "image_path": "./data/HME100K/test_images/test_4292.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n2 + 3 - 5 + 4 = 7\n\nThis can be written in LaTeX format as:\n\n$$2 + 3 - 5 + 4 = 7$$\n\nAlternatively, you can use the LaTeX code:\n\n$$2 + 3 - 5 + 4 = 7$$\n\nThe result is 7.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 4x + 3 = 8.",
        "gt_answers": "\\frac { 1 } { 2 } \\div \\frac { 1 } { 8 } = ( 4 )\n",
        "image_path": "./data/HME100K/test_images/test_4294.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is \\frac{a^2 + b^2}{2ab}.\n\nHere's the LaTeX code for the expression:\n\n\\begin{align\\*}\n\\frac{a^2 + b^2}{2ab}\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is not clear from the given image. Can you please provide more information or context about the image to help understand the formula?",
        "gt_answers": "\\frac { 4 } { 3 } y = - 8\n",
        "image_path": "./data/HME100K/test_images/test_4296.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression p(bc/b) can be written in LaTeX format as follows:\n\np(bc/b)=&#x2212;&#x2211;i=1n&#x2212;(bci)&#x2212;(bci)&#x2212;(bci)&#x2212;1\" role=\"presentation\">p(bc/b)=\u2212\u2211i=1n\u2212(bci)\u2212(bci)\u2212(bci)\u22121p(bc/b)=\u2212",
        "gt_answers": "P C ^ { 2 } = B P ^ { 2 } + B C ^ { 2 } -\n",
        "image_path": "./data/HME100K/test_images/test_4297.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} & \\text{The sum of the first } n \\text{ terms of the arithmetic series } a\\_n = 5 - 3n + 7n^2 - 5n^3 + 3n^4 - \\frac{1}{2}n^5 + \\frac{1}{6}n^6 - \\frac{1}{30}n^7 + \\frac{1}{243}n^8\\text{ is }}$$\n\n$$\\",
        "gt_answers": "( 4 - 0 . 5 ) 5 = 2 9\n",
        "image_path": "./data/HME100K/test_images/test_4298.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given below.\n\n$$\\text{sin}^{2}\\theta + \\text{cos}^{2}\\theta = 1$$",
        "gt_answers": "f ( x ) - f ^ { \\prime } ( x ) < 0\n",
        "image_path": "./data/HME100K/test_images/test_4299.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:\n\n\\begin{center}\n$latex 1+x^2=x^3+2x$\n\\end{center}\n\nThe expression can be derived by expanding the binomial $(1+x^2)$ using the distributive property of multiplication over addition, as follows:\n\n\\begin{center}\n$latex 1+x^2=1+x\\cdot x+x^2$\n\\end{center}\n\nSimplifying the expression by combining like terms gives:\n\n\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX formula for the given expression:$$x^4 - 4x^2 + 6x - 2$$The variable x is raised to the fourth power, then minus four times the square of x, plus six times x, and finally minus two.",
        "gt_answers": "x + y = -\n",
        "image_path": "./data/HME100K/test_images/test_4302.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n$$\\frac{100 - 25\\sqrt{x}}{30 + x}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is the formula for solving the image content in LaTeX format:\n\n$$\\text{Image Content} = \\frac{1}{2}\\left(\\text{Red Component}+\\text{Blue Component}\\right) + \\frac{1}{2}\\left(\\text{Green Component}+\\text{Yellow Component}\\right)$$",
        "gt_answers": "x = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4304.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format. However, assuming that the formula is given as f(x) = x^2 + 3x - 2, we can write it in LaTeX format as follows:\n\nf(x) = x^2 + 3x - 2.",
        "gt_answers": "A M = M B = 5 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4305.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is 2x2 + 3x3 + 4x4 + 5x5 + 6x6.",
        "gt_answers": "\\frac { 3 } { 4 } x = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4306.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{200}{5\\times 4}=\\frac{40}{10}$. This can be written as $\\frac{200}{5\\times 4}=\\frac{40}{10}$.",
        "gt_answers": "\\frac { 4 \\times 1 5 } { 3 } = 2 0\n",
        "image_path": "./data/HME100K/test_images/test_4307.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the formula in the image:\n\n\\begin{align\\*}\nP & = \\frac{a}{b} \\\\\nQ & = \\frac{c}{d} \\\\\nR & = \\frac{a+b}{c+d}\n\\end{align\\*}\n\nwhere a, b, c, and d are any real numbers. The formula gives the value of R when P and Q are given.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\sqrt{6} - \\sqrt{2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the volume of a cylinder can be written in LaTeX format as follows:\n\n\\frac{p}{2}r^2h + \\frac{p}{2}r^2 = V\\_{cyl}\n\nwhere p is the pressure of the gas inside the cylinder, r is the radius of the cylinder, h is the height of the cylinder, V\\_cyl is the volume of the cylinder.\n\nIn the equation, the pressure is on the left side, the volume is on the right side, and the gas constant R is not used.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n$\\frac{1}{4}(\\frac{3}{2})^{2}+\\frac{1}{4}(\\frac{3}{2})^{2}+\\frac{1}{4}(\\frac{3}{2})^{2}+\\frac{1}{4}(\\frac{3}{2})^{2}+\\frac{1}{4}(\\frac{3}{2})^{2}$\n\nThis formula calculates the sum of the squares of the numbers 1, 2, 3, and 4. The first term is $\\frac{1}{",
        "gt_answers": "( x + y - 5 ) ( x + y + 2 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_4314.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$a = \\frac{b}{c}$$where a is the result, b is the formula, and c is the given value.",
        "gt_answers": "x = \\frac { 2 1 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4317.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed as follows:A=\u03c0r^2where r is the radius of the circle. The area of a circle is given by the formulaA=\u03c0r^2where r is the radius of the circle. The formula for the area of a circle is given by the equationA=\u03c0r^2where r is the radius of the circle.",
        "gt_answers": "\\angle 5 + \\angle 4 = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4318.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\begin{aligned}\nx^2 + 2x - 12 &= 0 \\ \\Rightarrow x = \\frac{-2 \\pm \\sqrt{13}}{2}\n\\end{aligned} $$",
        "gt_answers": "x = \\frac { 1 1 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4319.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n\u222bf(x)dx=\u222b\u222bf(x)dxdydy=\u222b\u222b\u222bf(x)dxdxdy=\u222b\u222b\u222b\u222bf(x)dxdxdy=\u222b\u222b\u222b\u222b\u222bf(x)dxdxdy=\u222b\u222b\u222b\u222b\u222b\u222bf(x)dxdxdy=\u222b\u222b\u222b\u222b\u222b\u222bf(x)dxdxdy=\u222b\u222b\u222b\u222b\u222b\u222bf(x)dxdxdy=\u222b\u222b\u222b\u222b\u222b\u222bf(x)dxdxdy=\u222b\u222b\u222b\u222b\u222b\u222b\u222bf",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\nThe formula is for the area of a circle with a radius of 5 cm.",
        "gt_answers": "x _ { 2 } = 7\n",
        "image_path": "./data/HME100K/test_images/test_4322.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by A = l x w, where l is the length and w is the width. In this case, the length is 5 and the width is 6, so the area is 5 x 6 = 30.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Can you please provide the image so I can assist you?",
        "gt_answers": "/ n + b i - a + b i\n",
        "image_path": "./data/HME100K/test_images/test_4325.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image you provided is given by the following LaTeX formula:\n\n$$ \\text{V}\\_{avg}=\\frac{\\text{V}\\_{max}-\\text{V}\\_{min}}{\\text{2}} $$\n\nWhere,\n\n$$ \\text{V}\\_{max} $$\nis the maximum voltage of the image\n\n$$ \\text{V}\\_{min} $$\nis the minimum voltage of the image\n\n$$ \\text{2} $$\nis a constant factor to ensure that the average voltage is calculated correctly\n\nSo, the average voltage of the image is given by",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the sum of x3 and x4.",
        "gt_answers": "y = 3 x - 3 0 ( x \\geq 3 0 )\n",
        "image_path": "./data/HME100K/test_images/test_4327.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: $\\frac{3\\sqrt{5}}{4}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by:\n\n$$\\frac{3x+2y}{x+y}=\\frac{9}{5}+\\frac{7}{3}\\text{ or } \\frac{3x+2y}{x+y}=\\frac{16}{5}+\\frac{9}{3}$$",
        "gt_answers": "\\frac { 2 x } { 3 } = \\frac { 4 \\times - 8 } { 9 } - 5\n",
        "image_path": "./data/HME100K/test_images/test_4330.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is:\n\n<img>x + 2y = 4</img>",
        "gt_answers": "\\frac { x + 2 } { 3 } + 4 = 5\n",
        "image_path": "./data/HME100K/test_images/test_4331.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x^2 - y^2}{x + y}$.",
        "gt_answers": "a > c > b\n",
        "image_path": "./data/HME100K/test_images/test_4332.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by: A = l \u00d7 w, where l is the length and w is the width. The area of the rectangle in the image is A = 5 x 3 = 15 square units.",
        "gt_answers": ") - 1 ^ { 2 } + \\sqrt [ 3 ] { 6 4 } - ( - 2 ) x \\sqrt { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_4333.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$2x + 3y = 7$$",
        "gt_answers": "> - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4338.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: x + y = 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image in LaTeX format is: $\\frac{10}{100 + \\frac{1}{30}} \\times \\frac{500}{100 + \\frac{1}{30}}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n<LaTeX code>y = (x / a) ^ 2 - (b / x) ^ 2</LaTeX code>",
        "gt_answers": "x _ { 4 } = - 2 - \\sqrt { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4341.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n$$\\text{w+sh+oh} = \\frac{w+sh}{2} + \\frac{h}{3}$$\n\nwhere $w$ represents weight, $s$ represents speed, and $h$ represents height.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle is A = \u03c0r^2, where r is the radius of the circle.\n\nThe formula for the area of a rectangle is A = lw, where l is the length and w is the width.\n\nThe formula for the area of a triangle is A = (1/2)bh, where b is the base and h is the height.",
        "gt_answers": "F C = 6 \\sqrt { 2 } \\cdot 2 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4343.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 25 \\* (3/4)\\* 2 \\* 1.5 = 45 \\* 1.5 = 67.5 grams.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression:\n\n\\begin{center}\n\\begin{array}{c}\n 5 + 2x^2 + 7x - 11 \\\\\n 3x^2 + 4x + 2\n\\end{array}\n\\end{center}\n\nThis is the standard form for the equation of a parabola in two variables. The coefficients of the terms correspond to the x- and y-intercepts, respectively, and the constant term represents the y-intercept. The leading coefficient is the coefficient of the term that",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $ $\\sin \\beta$ = $\\frac{mgh}{L^2}$ $\\sin \\beta$ is the sine of the angle of release, m is the mass of the object, g is the acceleration due to gravity, h is the height of the object from its equilibrium position, and L is the length of the string. This formula represents the energy stored in the string as the object moves from its equilibrium position to the height of the string.\n\nNote: To display mathematical expressions in LaTeX format, you can use the following syntax: $\\sin \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is $\\text{y} = 3x^2 + 2x - 1$.",
        "gt_answers": "3 - 1 . 2 x = \\frac { 4 } { 5 } x - 1 2\n",
        "image_path": "./data/HME100K/test_images/test_4347.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the given formula in LaTeX format, follow these steps:\n\n1. Select the text that contains the formula and copy it to your clipboard.\n2. Open a LaTeX editor such as Overleaf, LaTeXi, or TeXstudio.\n3. Paste the copied text into the editor and format it as an equation using the built-in LaTeX equation editor or by typing the equation manually using the LaTeX syntax.\n4. Compile the document to generate a PDF output.\n\nHere's the LaTeX code for the given formula:\n\n\\begin{align}\nx &= \\",
        "gt_answers": "y _ { 2 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4348.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image given is the equation of a circle with radius r = 3.5 and center at the point (2, 1). The image shows a circle with center at the point (2, 1) and radius 3.5, and the equation is given as: x^2 + y^2 = r^2.\n\nUsing LaTeX format, the equation can be written as:\n\n\\begin{center}\nx^2 + y^2 = r^2\n\\end{center}\n\nThis equation describes a circle centered at (2, 1) with radius",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is not provided, so I cannot write out the formula using LaTeX format. Please provide the image so that I can write out the formula in LaTeX format.",
        "gt_answers": "\\Delta A B D \\sim \\Delta B C F\n",
        "image_path": "./data/HME100K/test_images/test_4351.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $\\frac{25}{3}$\\*$\\frac{30}{4}$\\*$\\frac{45}{6}$= $\\frac{600}{12}$",
        "gt_answers": "x = \\frac { 1 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4352.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent}$$",
        "gt_answers": "\\frac { a } { \\sin A } = 2 R\n",
        "image_path": "./data/HME100K/test_images/test_4353.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: $ f = \\frac{3}{2} \\cdot \\frac{2}{1} = 3 $",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 3x + 5y = 12.",
        "gt_answers": "x = - \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4356.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{2 \\times 3}{5 - 2}$.\n\nThe image shows the formula written in a handwriting style with a vertical line drawn through it. The numerator is 2 times 3, and the denominator is 5 minus 2. This results in the fraction $\\frac{2 \\times 3}{5 - 2}$.",
        "gt_answers": "m < \\frac { 3 x } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4357.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula using LaTeX format is:\n\n$$\\text{sin}\\left( \\frac{\\pi}{6} \\right) + 2 = \\frac{1}{2} \\times \\frac{1}{4} - \\frac{1}{4} \\times \\frac{1}{4} + \\frac{1}{2} \\times \\frac{1}{2} + \\frac{1}{2} \\times \\frac{1}{4} + 2 = \\frac{1}{2} \\times \\frac{1}{2} - \\frac{1}{",
        "gt_answers": "\\frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 1 } \\div \\frac { x ^ { 2 } - x } { x + 1 } - \\frac { 1 } { x } + 1\n",
        "image_path": "./data/HME100K/test_images/test_4358.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$$x = \\frac{a}{b}$$\n\nwhere $x$ is the variable being solved for, $a$ is the constant on the left side of the equation, and $b$ is the constant on the right side of the equation.\n\nNote that the fraction bar in the LaTeX expression is represented by the slash symbol (/), which is typically used in mathematical expressions to denote a fraction.",
        "gt_answers": "2 \\sqrt { S _ { 2 } } = \\sqrt { a _ { 1 } } + \\sqrt { S _ { 3 } }\n",
        "image_path": "./data/HME100K/test_images/test_4359.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{L\\_d + D\\_ac + S\\_as}{10}$$\n\nwhere:\n\n* $L\\_d$ is the letter L followed by the letter d, representing the letter d in the word 'bad'\n* $D\\_ac$ is the letter D followed by the letter c, representing the letter c in the word 'cash'\n* $S\\_as$ is the letter S followed by the letter s, representing the letter s in the word'savings'\n\nSo the formula",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a blackboard with the mathematical expression: x^2 + 3x + 5. The expression is written in red ink on the blackboard.\n\nLaTeX format: $\\left(\\frac{x}{2}\\right)^2 + 3x + 5$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This formula is a function that takes two variables as inputs and returns the product of their values. The formula is defined as follows:",
        "gt_answers": "x - \\frac { 1 } { 5 } + \\frac { 1 } { 5 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_4364.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a triangle can be written as:\n\nA = (1/2) \\* base \\* height\n\nwhere base is the length of the base of the triangle and height is the height of the triangle.\n\nFor example, if the base of a triangle is 5 cm and the height is 6 cm, the area of the triangle is:\n\nA = (1/2) \\* 5 \\* 6\n= (1/2) \\* 30\n= 15 cm^2\n\nNote that the unit of measurement for the base",
        "gt_answers": "x = \\frac { a ^ { 2 } } { c }\n",
        "image_path": "./data/HME100K/test_images/test_4366.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is written as follows:\n\n$$\\text{ImageContent}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\sqrt{4x^2 + 9}$. The variable x is the base of the radical, and the number 9 is the exponent. The formula represents the square root of the sum of the square of x and 9.\n\nNote that the formula is written in a different mathematical notation than the one used in the previous examples. In this notation, the radical symbol (\u221a) is used to represent the square root function, and the exponent notation (x^n) is used to represent the power of x in the exponent. The number inside the radical symbol represents the base of the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Could you please provide a valid image link?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is x^2 + 4x - 5y^2 = 2y.",
        "gt_answers": "y = - \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4370.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n<latex math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<semantics><mrow><msub><mi>2</mi><mi>x</mi></msub><mo>+</mo><msub><mi>3</mi><mi>y</mi></msub><mo>=</mo><mn>6</mn></mrow><annotation encoding=\"application/x-tex\">\\frac{2x + 3y}{4} = \\frac{",
        "gt_answers": "x ^ { 2 } + 2 + \\frac { 1 } { x ^ { 2 } } = 4\n",
        "image_path": "./data/HME100K/test_images/test_4371.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{x + 10}{x - 8} $$\n\nTo find the limit of the function as $x$ approaches 8 from the right, we can substitute $x = 8$ into the expression and see if the limit exists:\n\n$$ \\frac{8 + 10}{8 - 8} = \\frac{18}{0} $$\n\nThe limit does not exist, as it is undefined, so the function is not differentiable at $x = 8$.",
        "gt_answers": "\\tan ( \\pi + a ) = \\frac { 1 } { - 2 } .\n",
        "image_path": "./data/HME100K/test_images/test_4373.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n&#x2220;&#x2202;&#x2212;&#x2220;&#x2211;&#x2212;&#x2212;&#x2212;&#x2220;&#x2212;&#x2220;&#x2212;&#x2220;&#x2211;&#x2220;&#x2202;&#x22",
        "gt_answers": "\\frac { 5 } { 6 } \\div x = 2 . 6\n",
        "image_path": "./data/HME100K/test_images/test_4374.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given as:\n\ny = x\\*sin(x)\\*cos(x)\n\nThis formula is derived from the trigonometric identity, sin(x) = tan(x), which relates the sine and tangent of an angle to its opposite side. The formula uses this identity to calculate the product of x and the sine of x, multiplied by cos(x), which gives the value of y in terms of x.",
        "gt_answers": "y _ { 1 } = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4376.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned}3(a+b)+4(2a+3b)=11(a+2b)\\end{aligned}$$\n\nYou can see the image here: <Img>ImageContent</Img>",
        "gt_answers": "A B = \\frac { 2 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4377.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\u200b\n\n$$\\text{Ln}(x) = \\frac{1}{\\text{e}^x}$$",
        "gt_answers": "S = A B ( D H + C O ) \\div 2 = 3 \\times \\frac { 2 5 } { 2 } \\div 2 = \\frac { 7 . 5 } { 4 . }\n",
        "image_path": "./data/HME100K/test_images/test_4378.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n$$\\frac{3}{4}\\cdot \\frac{1}{2} + \\frac{1}{2} = \\frac{3}{4} + \\frac{1}{2}$$\n\n$$\\frac{1}{2} + \\frac{1}{2} = \\frac{1}{2}$$\n\n$$\\frac{1}{4} + \\frac{1}{2} = \\frac{3}{8}$$\n\nTherefore, the expression is $\\frac{3}{4}\\cdot \\frac{1}{2",
        "gt_answers": "1 0 0 x = 2 4 0 0\n",
        "image_path": "./data/HME100K/test_images/test_4379.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by the following LaTeX code:$$\\text{The formula for the area of a rectangle is } A = l \\times w$$This formula gives the area of a rectangle with a length of $l$ units and a width of $w$ units. The formula shows that the area of a rectangle is equal to the product of its length and width. This is a basic concept in geometry that is used to calculate the area of different shapes.\n\nThe formula can be used to find the area of any rectangle, regardless of its size or shape. For example, if you want",
        "gt_answers": "x ( \\frac { 1 } { 1 1 } + \\frac { 1 } { 1 3 } + \\frac { 1 } { 1 7 } ) = 4 1 ( \\frac { 1 } { 1 1 } + \\frac { 1 } { 1 3 } + \\frac { 1 } { 1 7 } )\n",
        "image_path": "./data/HME100K/test_images/test_4381.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is written as:$$ \\frac{a+b}{c+d}$$ where a, b, c, and d are positive integers.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$latex\\frac{dV}{dt} = \\frac{d}{dt}V - \\frac{dV}{dt} = \\frac{dV}{dt} - \\frac{d}{dt}V = 0$\n\nwhere $\\frac{dV}{dt}$ is the time derivative of the volume of the gas in the cylinder and $\\frac{d}{dt}V$ is the time derivative of the volume of the gas in the cylinder and piston.",
        "gt_answers": "S _ { 3 } = 1 0 c m\n",
        "image_path": "./data/HME100K/test_images/test_4384.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression in the image:\n\n\\begin{align\\*}\n2x^2 + 4x - 6 &= 0 \\\\\nx &= \\frac{1}{2} \\pm \\frac{\\sqrt{3}}{2}\n\\end{align\\*}\n\nNote that I assumed that the equation is in the form $ax^2+bx+c=0$, where $a\\neq0$. The solutions are obtained by solving for the roots of the quadratic equation, which are given by the formula $x=\\frac{b\\pm\\",
        "gt_answers": "1 2 \\div 2 = 6 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_4385.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n  \\frac{a + b}{2}\n\\end{center}\n\nwhere 'a' and 'b' are the two numbers in the image.",
        "gt_answers": "x _ { 1 } = 2 , x _ { 2 } = - 2\n",
        "image_path": "./data/HME100K/test_images/test_4386.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:$$\\text{r}\\_{2}=\\frac{100\\left(\\frac{10\\left(150\\text{mm}\\right)\\left(\\frac{1\\text{m}\\right)^2\\text{d}}{60\\text{s}}\\right)^2}{49\\left(\\frac{10\\text{mm}\\right)^2\\text{d}}{360\\text{s}}\\right)}$$\n\nThis formula represents the relationship between the resistance of a wire and its cross-sectional area, and the rate",
        "gt_answers": "\\frac { 3 } { x ^ { 2 } + 3 x } - ( x ^ { 2 } + 3 x ) = 2\n",
        "image_path": "./data/HME100K/test_images/test_4388.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression in the image:\n\n\\begin{center}\n\\begin{equation}\na + b = c\n\\end{equation}\n\\end{center}\n\nThis formula states that the sum of `a' and `b' is equal to `c'.",
        "gt_answers": "\\angle B O C = 1 2 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4389.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length 3 and width 4 is: area = length x width = 3 x 4 = 12 square inches.",
        "gt_answers": "a _ { 3 } - a _ { 2 } = 2 . \\cdots a _ { n } - a _ { n } - 1 = n - 1\n",
        "image_path": "./data/HME100K/test_images/test_4390.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \\frac{1}{3} - \\frac{4}{9}.",
        "gt_answers": "\\boxed { 5 } \\textcircled { + } \\boxed { 6 } = \\boxed { 1 1 } ( \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_4392.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{x} = \\frac{\\text{t} - \\text{t\\_0}}{\\text{t} - \\text{t\\_0} + \\frac{1}{2}\\text{g} \\times \\text{t}^2}$$",
        "gt_answers": "a + b + c = 0\n",
        "image_path": "./data/HME100K/test_images/test_4393.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$$2 + 3x + 4y = 6$$\n\nThis is a linear equation in three variables, with a constant term of 6 on the right-hand side. The variables are x and y, and the coefficient of x is 3 and the coefficient of y is 4. The equation is trying to find the values of x and y that make the equation true.",
        "gt_answers": "3 \\times \\frac { 1 } { 4 } = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4396.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:",
        "gt_answers": "\\frac { 6 - a } { 3 } - \\frac { 3 - a } { 2 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_4397.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$x^2+y^2=r^2$$This formula is a quadratic equation that describes a circle in the xy plane with a radius of r. The left side of the equation represents the square of the x value plus the square of the y value, which is equal to the square of the radius. The right side of the equation represents the square of the x value plus the square of the y value, which is equal to the square of the radius.",
        "gt_answers": "\\frac { 1 } { 2 } x - 7 = \\frac { 1 } { 3 } x + 3\n",
        "image_path": "./data/HME100K/test_images/test_4398.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle with width w and height h can be written as: A = wh.",
        "gt_answers": "O P _ { 2 } = \\sqrt { 1 4 } - 1\n",
        "image_path": "./data/HME100K/test_images/test_4399.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:5x3 + 4x2 + 3x + 1. The formula is written as follows:5x3 + 4x2 + 3x + 1. In LaTeX format, the formula would be written as: 5x3 + 4x2 + 3x + 1.\n\nIn LaTeX format, the expression would be written as:5x3 + 4x2 + 3x + 1. The expression is written as follows:5x3 + 4x2 + 3x + 1",
        "gt_answers": "5 x = - 5 S\n",
        "image_path": "./data/HME100K/test_images/test_4400.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:$$\\frac{5}{2} \\times 20 + \\frac{35}{4} \\times 15 = \\frac{50}{2} + \\frac{35}{4} = 100 + 26.25 = 126.25$$This is the sum of the fractions $\\frac{5}{2}$ and $\\frac{35}{4}$, multiplied by the numbers 20 and 15 respectively, and then added together.",
        "gt_answers": "\\frac { 9 2 } { 1 0 0 } = \\frac { 4 6 } { 5 0 } = \\frac { 2 3 } { 2 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4401.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Please provide the image so I can help you.",
        "gt_answers": "\\cdot \\vert \\overrightarrow { b } \\vert \\cos 6 0 ^ { \\circ } = \\overrightarrow { a } \\cdot \\overrightarrow { b } = 1\n",
        "image_path": "./data/HME100K/test_images/test_4402.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I'll help you write out the expression for the formula in the image using LaTeX format:\n\nThe formula is:\n\n$$G = \\frac{m\\ m}{r^2}$$\n\nWhere:\n\n* G is the gravitational force between two objects\n* m is the mass of each object\n* r is the distance between the two objects\n\nThe formula states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.",
        "gt_answers": "Z n + 2 A g N O _ { 3 } = Z n ( N O _ { 3 } ) _ { 2 } + 2 A g\n",
        "image_path": "./data/HME100K/test_images/test_4404.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression involving the sum of two squares, one with the value 7 and the other with the value 9. The expression is written as follows:$$\\sum\\_{i=1}^{3} i^2 = \\sum\\_{i=1}^{3} 9^2 = 9^2 + 9^2 + 9^2 = 9 \\times 9 = 81$$The equation shows that the sum of the squares of the first three integers is equal to 81.\n\n![](https://latex.codecogs.com/svg.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{10}{2x+3}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by:A=\u03c0r^2where r is the radius of the circle. The radius can be found by taking half of the diameter of the circle, which is given by:d=2rwhere r is the radius of the circle. Therefore, the formula for the area of the circle is:A=\u03c0r^2d=2r2r=d/2A = \u03c0r^2d = 2r2r = d/22r = d/2A = \u03c0r^2d = 2r2r = d",
        "gt_answers": "\\frac { C G } { A B } = \\frac { C F } { A F }\n",
        "image_path": "./data/HME100K/test_images/test_4408.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\text{C}_{6} \\cdot \\text{H}_{12} \\cdot \\text{O}_{4} = \\text{CO}_{2} + \\text{H}_{2} \\cdot \\text{O}$",
        "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_4409.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the rectangle with perimeter 68 can be written as:\n\nA = lw = 68 - 4 = 64 ft \\* 4 ft = 256 ft\u00b2\n\nTherefore, the area of the rectangle is 256 ft\u00b2.",
        "gt_answers": "E D = E B = \\frac { 1 } { 2 } A B\n",
        "image_path": "./data/HME100K/test_images/test_4410.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, the formula is: f(x) = x^2.\n\nHere is the LaTeX code for the formula:\n\n\\[f(x) = x^2\\]",
        "gt_answers": "0 . 2 \\times 0 . 2 \\times 0 . 2 ) \\div 0 . 2 = 0 . 0 4\n",
        "image_path": "./data/HME100K/test_images/test_4414.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by:$\\frac{1}{x + 2y} = \\frac{2}{x + y}$This can be rearranged as:$\\frac{x + 2y}{1} = \\frac{x + y}{2}$Simplifying the left side, we get:$\\frac{x + 2y}{1} = \\frac{x + y}{2}$Expanding the right side, we get:$\\frac{x + y}{2} = \\frac{x}{2} + \\frac{y}{2}$Combining the two sides,",
        "gt_answers": "d = 2\n",
        "image_path": "./data/HME100K/test_images/test_4415.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image can be written as follows:\n\n$$ \\frac{a}{b} = \\frac{a + 2b}{2a} $$\n\nThis is a ratio formula that shows how to find the ratio of two numbers.",
        "gt_answers": "e = 2\n",
        "image_path": "./data/HME100K/test_images/test_4416.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the area of a circle. The formula is given by the equation: A = (pi)r^2, where r is the radius of the circle. The formula shows that the area of a circle is equal to the square of the radius.",
        "gt_answers": "x = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4417.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation shown in the image is the derivative of the function f(x) = x^2 with respect to x.\n\nThe derivative of f(x) can be found by applying the power rule of differentiation:\n\nd/dx [f(x)] = d/dx [x^2] = 2x\n\nTherefore, the derivative of f(x) with respect to x is 2x.",
        "gt_answers": "x ^ { 2 } + 1 = t ^ { - 1 } ( x )\n",
        "image_path": "./data/HME100K/test_images/test_4418.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} & x^2 - 3x + 2 \\\\ & = (x - 1)(x + 2) \\end{aligned}$$\n\nThe formula is a quadratic equation, which can be factored as $(x - 1)(x + 2)$. The constant term in the formula is 2, which is added to the equation after the terms involving x.\n\nTo solve the equation, you can use the quadratic formula:\n\n$$\\begin{aligned} x = \\frac{-",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, you can use the following code:\n\n\\begin{equation}\na = \\frac{100 \\* (x^2 + y^2)}{(x^2 + 4y^2)}\n\\end{equation}\n\nIn this formula, a is the radius of the circle inscribed in the ellipse, x is the x-coordinate of the center of the circle, and y is the y-coordinate of the center of the circle. The numerator of the formula is the product of 100 and",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{a}{b} = \\frac{500\\ x 1000}{a \\times b}$\n\nNote: The formula is written in the form a:b = (a\u00d7b)a/b, which is equivalent to $\\frac{a}{b}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a circle is A = \u03c0r^2, where r is the radius of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{align\\*}\n\\text{Image Content} = \\frac{100}{200} \\times \\frac{50}{70} \\times \\frac{30}{60} \\times \\frac{20}{50}\n&= \\frac{100}{3500} \\times \\frac{50}{2100} \\times \\frac{30}{3500} \\times \\frac{20}{100}\n&= \\frac{1",
        "gt_answers": "\\overline { A B } \\cdot \\overline { O M } = 0\n",
        "image_path": "./data/HME100K/test_images/test_4424.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{3}{4}(x+5) + \\frac{1}{2}(y-3) = \\frac{3}{4}x + \\frac{1}{2}y + 5$.",
        "gt_answers": "\\frac { a } { 6 } = 1 . 3 3\n",
        "image_path": "./data/HME100K/test_images/test_4425.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression of the formula in the image:\n\n$$\\begin{align} A + B = C \\end{align}$$\n\nIn this equation, A, B, and C are variables.",
        "gt_answers": "P _ { 3 } ( 1 + \\sqrt { 3 } , 3 )\n",
        "image_path": "./data/HME100K/test_images/test_4426.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula for the expression of the image is:\n\n$$\\frac{a^2 - b^2}{a - b}$$\n\nwhere a and b are the coordinates of the two points in the image. To find the coordinates, we can use the Pythagorean theorem to calculate the length of each of the sides of the triangle formed by the two points and the center point. The coordinates of the two points are then given by:\n\n$$a = \\sqrt{\\frac{(x\\_c + x\\_1)^2 + (y\\_c + y\\_1)^2}{2}}",
        "gt_answers": "8 : \\frac { 2 } { 5 } = x : \\frac { 7 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4427.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n\\begin{center}\n$k = \\frac{d^2x}{dt^2} + \\omega\\_n^2 x$\n\\end{center}\n\nThis formula represents the second-order linear ordinary differential equation with constant coefficients. The solution to this equation is given by:\n\n\\begin{center}\n$x(t) = e^{\\omega\\_n t} \\left( A \\sin (\\omega\\_n t) + B \\cos (\\omega\\_n t) \\right)$\n\\end{center}",
        "gt_answers": "x \\cdot ( 1 0 0 - 2 0 ( x - 2 5 ) ) = 2 7 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_4428.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$y = \\frac{x^2}{a^2 + x^2}$$\n\nwhere $a$ is the length of the hypotenuse of the right triangle in the image.",
        "gt_answers": "N Q = \\frac { 1 } { 2 } C Q\n",
        "image_path": "./data/HME100K/test_images/test_4429.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is: 2x^2 + 3x - 4.",
        "gt_answers": "y _ { B Q } = - \\frac { 1 } { 2 } x + 2\n",
        "image_path": "./data/HME100K/test_images/test_4430.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} \\text{Image Content} = \\frac{a}{b} \\end{aligned}$$\n\nThis formula shows the formula in the image with a and b representing the variables shown in the image.",
        "gt_answers": "x ^ { 2 } - \\frac { 4 } { 3 } x - \\frac { 4 } { 3 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_4431.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$m = \\frac{3\\times 2}{5 + 2}$$\n\nwhere $m$ is the final mass of the substance produced when a 100 g sample of a substance is mixed with 50 g of water.",
        "gt_answers": "0 . 9 m = 9 0 0 m m\n",
        "image_path": "./data/HME100K/test_images/test_4432.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{x + 4y}{2x - 3y}$.\n\nThe denominator, $2x - 3y$, is the difference between $2x$ and $3y$, which can be written as $2x - 3(x + y)$.\n\nThe numerator, $x + 4y$, is the sum of $x$ and $4y$, which can be written as $x + 4(x + y)$.\n\nSo the formula can be written as $\\frac{x + 4",
        "gt_answers": "\\frac { 2 x - 1 } { 5 } + \\frac { x + 1 } { 2 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_4433.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned} \\text{Number of beans in the jar} &= 60\\ \\text{beans} \\\\ &= 5\\ \\text{groups of 12 beans each} \\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n\\begin{center}\n&#x2208;&#x2202;&#x2202;x = 1\" role=\"presentation\">dmdududx=1dmdududx=1\\frac{d}{dx} \\left(\\frac{d}{dx}u(x)\\right) = 1\n\\end{center}\n\nwhere $u(x)$ is the height of the water surface at time $t$. This is a characteristic equation of the wave equation.",
        "gt_answers": "7 . ( 1 ) a m + 4 b\n",
        "image_path": "./data/HME100K/test_images/test_4437.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\nwhere A and B are constants representing the parameters of the problem, r is the radius of the circular trajectory, and v is the velocity of the car at the starting point.",
        "gt_answers": "\\angle - \\frac { 3 } { 4 } < \\frac { 2 } { 3 } < \\frac { 5 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4438.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\text{sin}(x) + \\frac{3\\sqrt{5}}{2}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ E = mc^2 $$\n\nwhere E represents the energy of the system, m represents the mass of the object, c represents the speed of light, and ^2 represents the square of the speed of light.",
        "gt_answers": "C a C O _ { 3 } + 2 H C l =\n",
        "image_path": "./data/HME100K/test_images/test_4441.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$ \\text{T} = \\text{c} \\cdot \\sqrt{ \\frac{\\text{t}}{\\text{t}+\\text{b}} } $$\n\nwhere\n\n$$\\text{T}$$ is the time it takes to double the concentration of a drug in the body,\n\n$$\\text{c}$$ is a constant that depends on the drug and the body,\n\n$$\\text{t}$$ is the time elapsed since the drug was administered, and\n\n$$\\text{b}$$ is the half-life of the drug",
        "gt_answers": "A B = 1 0 \\div \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4443.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$\\frac{5+3\\times2}{2-2}=\\frac{11}{-4}=\\frac{5}{2}=\\frac{5}{2}=\\frac{2.5}{1}=\\frac{2.5}{1}=\\frac{2.5}{1}=\\frac{2.5}{1}=\\frac{2.5}{1}=\\frac{2.5}{1}=\\frac{2.5}{1}=\\frac{2.5}{1}=\\frac{2.5}{1}=\\frac{2.5}{1}=\\frac{2.",
        "gt_answers": "\\cdot \\frac { 2 5 } { 4 } + 5 b + c = 0\n",
        "image_path": "./data/HME100K/test_images/test_4444.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$\\text{Let } x\\text{ and } y\\text{ be the real numbers with } x > 0\\text{ and } y < 0\\text{. Then, the distance between } x\\text{ and } y\\text{ is given by }$$\n$$\\text{d}(x, y) = \\sqrt{(x - y)^2 + (x + y)^2} = \\sqrt{4x^2 + 4y^2}$$\n$$\\text{The expression } d(x, y)\\text{ is the distance between } x\\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$y=\\frac{1}{4}(3x+5)$$where x is the number of people in the room and y is the number of chairs in the room.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![Formula](https://latex.codecogs.com/svg.image?%5B%5BImg%5D%5D%5B%5D%5BImageContent%5D%5B%5D)\n\n![Formula](https://latex.codecogs.com/svg.image?%5B%5BImg%5D%5D%5B%5D%5BImageContent%5D%5B%5D)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n\\text{Image Content} &= \\frac{a}{b} \\times \\sqrt{2ab} \\times \\frac{c}{d} \\times \\sqrt{cd} \\times \\frac{e}{f} \\times \\sqrt{ef} \\times \\frac{g}{h} \\times \\sqrt{gh} \\times \\frac{i}{j} \\times \\sqrt{ij} \\times \\frac{k}{l} \\times \\sqrt{kl} \\times",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is pi \\* r^2, where r is the radius of the circle.\n\nThe area of the circle in the image is pi \\* r^2, where r is the radius of the circle. The radius of the circle can be calculated using the formula r = d / 2, where d is the diameter of the circle. In the image, the diameter of the circle is 3 cm, so the radius is 1.5 cm.\n\nThe area of the circle is therefore pi \\* 1.5^2 = 0.785",
        "gt_answers": "\\because A B / / C D\n",
        "image_path": "./data/HME100K/test_images/test_4451.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ \\text{Number of people} = \\frac{3000 \\times 2}{5 \\times 4} $$This formula is derived from the given information in the image that there are 3000 people in five cities with a population of 4 each. The formula calculates the number of people in each city by dividing the total number of people by the number of cities.\n\nThe formula can be represented using LaTeX as follows:$$\\text{Number of people} = \\frac{3000 \\times 2}{5",
        "gt_answers": "x = 3 1\n",
        "image_path": "./data/HME100K/test_images/test_4454.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\\begin{equation}\n\nx^2 + 2x - 5 = 0\n\n\" role=\"presentation\">x2+2x\u22125=0x^2 + 2x - 5 = 0x2+2x\u22125=0 \\end{equation}\n\nThis is a quadratic equation in the form of a polynomial of degree 2. The solutions to this equation are the values of x that make the equation true. One way to solve this equation is by using the quadratic formula:\n\nx = (-b \u00b1 sqrt(b^2 - 4ac",
        "gt_answers": "M g ( O H ) _ { 2 } + 2 H C l = M g C l _ { 2 } + 2 H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_4456.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length 3 and width 2 is $\\text{A} = \\text{L} \\times \\text{W}$, where $\\text{L}$ is the length and $\\text{W}$ is the width. In this case, $\\text{L} = 3$ and $\\text{W} = 2$, so the area is $\\text{A} = 3 \\times 2 = 6$.",
        "gt_answers": "( x + 1 ) ( x - 2 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_4457.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: x = (2 + 3) \\* 4 + 5.\n\nIn LaTeX format, it would be:\n\n$$x = \\left(2 + 3\\right) \\times 4 + 5$$\n\nThe LaTeX format displays the mathematical expression more clearly and accurately, with proper spacing and alignment of the symbols and operators.",
        "gt_answers": "5 x - 2 x = 2 4\n",
        "image_path": "./data/HME100K/test_images/test_4458.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n![Image of a right triangle with a square on the hypotenuse](https://latex.codecogs.com/svg.image?%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by A = \u03c0r^2, where r is the radius of the circle.\n\nGiven the image of a circle with a radius of 5 cm, we can find its area using the formula A = \u03c0r^2.\n\nA = \u03c0(5 cm)^2 = 78.53 cm^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{s+3}{s-5}$\n\nNote: The image does not contain enough information to determine the formula. Please provide more details or context for the formula.",
        "gt_answers": "S _ { 3 } = 9 = 3 ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4462.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is: $\\frac{dV}{dt} = -\\frac{V^2}{2a}$",
        "gt_answers": "S = 4 + \\frac { 1 } { 2 } \\times 6 - 1 = 4 + 3 -\n",
        "image_path": "./data/HME100K/test_images/test_4463.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am unable to see the image you provided. Can you please provide a different image or text that I can work with?",
        "gt_answers": "x - \\frac { 1 } { 2 } ( 4 x - 6 ) < 2\n",
        "image_path": "./data/HME100K/test_images/test_4464.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$ 3x^2 - 3 = 2x $$\nThis formula can be used to solve for x in the equation $3x^2 - 3 = 2x$.",
        "gt_answers": "( 4 5 + 1 ) \\times \\frac { 1 } { 5 0 0 } = 0 0 1 1 ( m )\n",
        "image_path": "./data/HME100K/test_images/test_4465.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\frac{50000000 + 40000000 + 30000000 + 20000000 + 10000000 + 4000000 + 5000000 - 1000000}{1000000000000000000000000000000",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:$$\\frac{4x^2 - 16x + 12}{x^2 - 4x + 6}$$Note: This expression is obtained by dividing the numerator by the denominator, after expanding the expression with the distributive property.",
        "gt_answers": "y _ { 3 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_4467.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{(x + 1)^2 - 4x^2}{x - 1}$$",
        "gt_answers": "\\frac { - 5 } { 2 } + a = - 1 5 + 8\n",
        "image_path": "./data/HME100K/test_images/test_4468.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression:\n\n$$\\frac{1}{4 \\cdot 3}+\\frac{1}{2 \\cdot 4}+\\frac{1}{5 \\cdot 3}+\\frac{1}{6 \\cdot 4}+\\frac{1}{7 \\cdot 3}+\\frac{1}{8 \\cdot 4}+\\frac{1}{9 \\cdot 3}+\\frac{1}{10 \\cdot 4}+\\frac{1}{11 \\cdot 3}+\\frac{1}{12 \\cdot 4}+\\frac{1}{13 \\cdot",
        "gt_answers": "x _ { 1 } = \\frac { 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4470.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}\nb &= 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}{204",
        "gt_answers": "B C = 1 O C = 1\n",
        "image_path": "./data/HME100K/test_images/test_4471.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the exponential function y = 2x. The derivative of this function is y' = 2x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the expression of the formula in the image using LaTeX format:\n\n\\begin{align\\*}\nx^2 - 2x + 1 &= 0 \\quad (\\text{factoring out }x) \\\n&= (x-1)^2 \\\\\n&= x^2 - 2x + 1\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written out in LaTeX format for the expression in the image is:\n\n$$\\begin{align\\*}\nx &= 2(3-x) \\\ny &= 3(x+y)\\\nz &= 2(x+z)\\\nw &= 2(y+w) \\\nt &= 3(t+w)\\\nu &= 2(u+v)\\\nv &= 3(u+v)\\\n\\end{align\\*}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the image:\n\n$$\\frac{a}{b}=\\frac{c^2}{d^2}$$\n\nThis is a proportion formula that relates two ratios. The numerator (a) is the ratio of the width of the image to the height, and the denominator (b) is the ratio of the area of the image to the perimeter of the image.",
        "gt_answers": "V = \\frac { B C } { \\frac { 2 } { 3 } } = 1 5 \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4476.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is written as:\n\n$$\\text{V} = \\frac{P \\cdot A}{3600}$$\nwhere V is the volume of the cylinder, P is the pressure of the gas and A is the cross-sectional area of the cylinder.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$ f(x) = \\frac{x^2}{x+4}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the image you provided:\n\n\\begin{center}\n\\begin{minipage}{0.4\\textwidth}\n\\begin{center}\n\\begin{tabular}{c}\n\\begin{center}\n\\begin{tabular}{cc}\n1 & 2\\\n\\end{tabular}\n\\end{center}\n\\end{center}\n\\end{minipage}\n\\end{center}\n\\end{center}\n\\end{center}\n\\end{center}\n\\end{center}\n\\end{center}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed as: A = \u03c0r^2, where r is the radius of the circle. In the image, the radius is given as 6 cm. Therefore, the area of the circle is A = \u03c0(6 cm)^2 = 36\u03c0 cm^2.",
        "gt_answers": "( b ^ { 2 } + 4 ) y ^ { 2 } =\n",
        "image_path": "./data/HME100K/test_images/test_4480.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n$$ 3x^2 + 4x + 5 = 0 $$",
        "gt_answers": "\\frac { 4 } { 5 } : x = \\frac { 1 } { 2 } : \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4481.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{x^2+3x-5}{x-3}$. This can be written as $\\frac{x^2 + 3x - 5}{x - 3}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center} $\\frac{3000-0.455x}{0.455x+3000}$ \\end{center}\n\nThis formula is used to determine the maximum number of people that can be seated in a movie theater with fixed seats and a maximum capacity of 3000 people. The formula takes into account the number of seats available and the number of people already seated to determine the maximum number of people that can be seated. The variable x represents the number of",
        "gt_answers": "3 0 \\times 3 0 = 9 0 0 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_4483.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$e^{i\\theta}=\\cos(\\theta)+i\\sin(\\theta)$$\n\nwhere $e$ is the base of the natural logarithm, $i$ is the imaginary unit, $\\theta$ is the angle in radians, and $\\cos$ and $\\sin$ are the trigonometric functions of an angle.",
        "gt_answers": "E C = \\frac { 1 3 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4484.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is A = l x w, where l is the length and w is the width. For example, the area of a rectangle with a length of 5 units and a width of 3 units is 5 x 3 = 15.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula for calculating the volume of a sphere. The formula is written as:\n\n$$V = \\frac{4}{3} \\pi r^3$$\n\nwhere $r$ is the radius of the sphere.",
        "gt_answers": "0 = k + \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4486.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\documentclass{article}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->,blue] (0,0) -- (3,0) node[midway,below]{$x$};\n\\draw[->,red] (0,0) -- (0,2) node[midway,right]{$y$};\n\\filldraw (1,0) circle (2pt) node[left]{$(1,0)$};\n\\filldraw (2,0",
        "gt_answers": "( x - 1 ) ^ { 2 } = \\frac { 7 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4487.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in LaTeX format is:\n\nm = \\frac{m\\_0}{1-\\frac{v\\_0^2}{2c^2}}\n\nwhere\nm\\_0 is the mass of the object at rest\nv\\_0 is the velocity of the object at rest\nc is the speed of light",
        "gt_answers": "m > - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4488.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 100 - \\frac{100}{40} \\cdot \\frac{40}{100} $$\n\nThis formula calculates the percentage of the original value that is left after subtracting a percentage of that value. The percentage of the original value that is left is calculated as:\n\n$$ 100 - \\frac{100}{40} \\cdot \\frac{40}{100} $$\n\nAnd the percentage of the original value that is left after subtracting",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\sum\\_{i=1}^n i^2\\_{i=1}^n$.",
        "gt_answers": "6 1 4 \\approx 6 0 0\n",
        "image_path": "./data/HME100K/test_images/test_4490.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius 5cm is given by:\n\narea = \u03c0r^2\n\nwhere r is the radius of the circle.\n\nThe formula for the area of a circle with radius 3cm is given by:\n\narea = \u03c0r^2\n\nwhere r is the radius of the circle.\n\nThe formula for the area of a circle with radius 4cm is given by:\n\narea = \u03c0r^2\n\nwhere r is the radius of the circle.\n\nThe formula for the area of a circle with radius",
        "gt_answers": "3 x ^ { 2 \\times 1 . 5 - 2 } - 4 = 0\n",
        "image_path": "./data/HME100K/test_images/test_4492.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression for the formula in the image using LaTeX format:\n\n$$\\text{Yield = \\frac{5000 \\* 30}{120 \\* 1.30}} \\times \\text{5000 \\* 300}$$\n\nwhere $\\frac{5000 \\* 30}{120 \\* 1.30}$ represents the yield per acre of wheat, calculated by dividing the total yield of 5000 bushels by the number of acres (120",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 5x^2 + 3x - 4 $$",
        "gt_answers": "- \\frac { 8 } { 3 } - \\frac { 3 } { 3 } = - \\frac { 1 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4494.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\text{ImageContent}$$",
        "gt_answers": "A H = B H = \\frac { 1 } { 2 } A B\n",
        "image_path": "./data/HME100K/test_images/test_4495.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n$$\\begin{aligned}\n\\text{x}^2 + y^2 = r^2\n\\end{aligned}$$\nwhere $\\text{x}$ and $\\text{y}$ are the coordinates of the image, and $r$ is the radius of the circle that is being drawn.",
        "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": "MiniGPT4"
    },
    {
        "question": "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: \\frac{a+b+c+d}{e+f+g+h} = \\frac{(a+b)+(c+d)}{(e+f)+(g+h)}{= (a+b+c+d)/(e+f+g+h)} = \\frac{(a+b)+(c+d)}{(e+f)+(g+h)} = \\frac{(a+b)+(c+d)}{(e+f)+(g+h)} = \\frac{(a+b+c",
        "gt_answers": "\\frac { 5 } { 6 } + \\frac { 1 } { 3 } = \\frac { 7 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_4497.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given as:\n\nx + 2y + 3z = 12x - 4y + 6z = 0x + 2y + 3z = 12x + 4y - 6z = 0x + 2y + 3z = 12x + 4y + 6z = 0x + 2y + 3z = 12x - 4y - 6z = 0x - 2y - 3z = - 12",
        "gt_answers": "x + \\frac { 1 } { 2 } x = 1 - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4498.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a mathematical expression that is used to calculate the average of a set of numbers. The expression is: ( n / N ) \\* 100.\n\nIn this formula, n represents the number of items in the set and N represents the total number of items in the set. The multiplication operator (\\*) is used to multiply the average of n by 100 to obtain the average of the set.",
        "gt_answers": "9 x = 4 ,\n",
        "image_path": "./data/HME100K/test_images/test_4499.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided as it is not available to me. Please provide a different image or text for me to work with.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n\\begin{center}\n\\begin{align}\n\\frac{d^2x}{dt^2} + \\frac{3}{2} \\omega\\_0^2 x = \\omega\\_0^2 x^3 - \\frac{2}{3} \\omega\\_0^2 x^2\n\\end{align}\n\\end{center}\n\nThis is a second-order ordinary differential equation with constant coefficients. The solution can be expressed in terms of the hypergeometric function.",
        "gt_answers": "\\angle 4 = \\frac { 1 } { 2 } \\angle D Q N\n",
        "image_path": "./data/HME100K/test_images/test_4501.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Can you please provide a different image or description of the formula?",
        "gt_answers": "y = - \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4503.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$x = \\frac{1}{2} \\left(\\frac{5}{8} + \\frac{7}{8}\\right) = \\frac{1}{2}\\left(\\frac{15}{8}\\right)$$",
        "gt_answers": "x = \\frac { 3 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4504.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is not provided. Please provide the image so that I can write out the formula using LaTeX format.",
        "gt_answers": "\\angle B A C = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4505.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{d^2 x}{dt^2} + \\frac{1}{2} \\times \\frac{d x}{dt} + \\frac{1}{4} x^2 - \\frac{1}{2} x = 0$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but there is no formula shown in the image. It appears to be a text message. Can you please provide a different image with a mathematical formula?",
        "gt_answers": "( 3 ) y _ { 1 } < y _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4507.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:$$\\frac{3x^2+5x-6}{2x^2+4x-8}=\\frac{3(2x+3)^2+5(2x+3)-6}{2(2x+3)^2+4(2x+3)-8}=\\frac{3(2x+3)^2+5(2x+3)-6}{2(2x+3)^2+4(2x+3)-8}=\\frac{3\\left(\\frac{2x+3}{1}\\right)^",
        "gt_answers": "y = \\frac { \\sqrt { 1 1 } } { 1 1 } ( x + \\sqrt { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_4509.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is g(x) = x^4 + 6x^3 + 9x^2 + 15x + 20.\n\nThis can be written in LaTeX format as:\n\n$$g(x) = x^4 + 6x^3 + 9x^2 + 15x + 20$$\n\nNote that the equation is written in the standard form of y = mx + b, where m is the slope of the line and b is the y-intercept. The x^4 term represents the slope of the par",
        "gt_answers": "\\frac { 9 } { 1 1 } - \\frac { 4 } { 1 1 } = \\frac { 5 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4510.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n$$\\begin{aligned} \\frac{b\\_{1} + b\\_{2}}{2} + \\frac{a\\_{1} + a\\_{2}}{2} - \\frac{a\\_{1}b\\_{2} + a\\_{2}b\\_{1}}{2} &= \\frac{1}{2}(b\\_{1} + b\\_{2}) + \\frac{1}{2}(a\\_{1} + a\\_{2}) - \\frac{1}{2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{align\\*}\n\\text{Image Content}\\_\\_\\_\\_\\_n = \\frac{1}{n}\\sum\\_{i=1}^n x\\_i^2\n\\end{align\\*}$$",
        "gt_answers": "a > b c > d \\frac { a } { c }\n",
        "image_path": "./data/HME100K/test_images/test_4514.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX code for the image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=0.5]\n\\draw[thick] (0,0) -- (1,0) node[midway, below]{$\\text{k} \\cdot \\text{c} = \\text{k} \\cdot \\text{c} + \\text{k} \\cdot \\text{z}$};\n\\draw[thick] (1,0) -- (2,0) node[midway, below]{$\\text{",
        "gt_answers": "k \\cdot \\frac { \\pi } { 2 } \\pm \\alpha ( k \\in z )\n",
        "image_path": "./data/HME100K/test_images/test_4515.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: $\\frac{r}{r+2}$.\n\nTo write this out in LaTeX format, you would use the following code:\n\n$$\\frac{r}{r+2}$$\n\nThis formula calculates the ratio of the number of red dots (r) to the total number of red and blue dots (r+2).",
        "gt_answers": "R _ { 3 } = 2 R _ { 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4516.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format. It appears to be a handwritten expression with various mathematical symbols, including a derivative symbol, a sum symbol, a multiplication symbol, and an exponent symbol. It is difficult to determine the exact expression without additional information.",
        "gt_answers": "1 \\times 7 - 1 . 3 = 5 . 7 c m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4517.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation shown in the image is:\n\n$$\\frac{1}{x} + \\frac{1}{y} = \\frac{1}{xy}$$\n\nThis equation represents the equation of a line in slope-intercept form, with a slope of $\\frac{1}{1}$ and a y-intercept of $\\frac{1}{y}$.",
        "gt_answers": "x = 1 , y = 1\n",
        "image_path": "./data/HME100K/test_images/test_4518.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:\n\n$$ A = l \\times w $$\n\nwhere $l$ is the length and $w$ is the width of the rectangle.",
        "gt_answers": "A A ^ { \\prime } = 4 \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4519.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$\\text{Image Content} = \\frac{1}{2} \\cdot (\\text{left image} + \\text{right image})$$\n\n$$\\text{left image} = \\frac{1}{2} \\cdot (\\text{blue region} + \\text{yellow region})$$\n\n$$\\text{right image} = \\frac{1}{2} \\cdot (\\text{green region} + \\text{purple region})$$\n\n$$\\text{blue region} = \\frac{1}{4} \\cdot (\\text{circle} + \\text",
        "gt_answers": "x ^ { 2 } + 4 x + 4 = 9\n",
        "image_path": "./data/HME100K/test_images/test_4520.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n$$ \\frac{5}{7} + 3 = \\frac{14}{7} $$\n\nor, in LaTeX format,\n\n$$ \\frac{5}{7} + 3 = \\frac{14}{7} $$",
        "gt_answers": "\\frac { 2 } { 3 } + 1 1 y = 1 0 y - 7 \\frac { 1 } { 3 } .\n",
        "image_path": "./data/HME100K/test_images/test_4521.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a circle with radius r is:\n\n$$ r = \\sqrt{\\frac{4}{\\pi}} $$\n\nIn LaTeX format, this can be written as:\n\n$$ r = \\sqrt{\\frac{4}{\\pi}} $$\n\nThe formula for the area of a circle with radius r is:\n\n$$ A = \\pi r^2 $$\n\nIn LaTeX format, this can be written as:\n\n$$ A = \\pi r^2 $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\frac{x + 5}{x - 3} = \\frac{5}{2}\n```",
        "gt_answers": "\\frac { 5 . 8 5 g } { 1 . 7 g } = 5 \\%\n",
        "image_path": "./data/HME100K/test_images/test_4523.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x^2 + y^2}{2}$. The formula is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a, b, and c are constants. The solution to the equation is $(x, y) = \\left(\\frac{-b}{2a}, \\frac{c}{2a}\\right)$.",
        "gt_answers": "2 = \\frac { 1 } { 2 } x - x\n",
        "image_path": "./data/HME100K/test_images/test_4524.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression of the formula in the image using LaTeX format:\n\n\\begin{align\\*}\ny = \\frac{b}{2a} - \\frac{4b^2}{4a^3}\n\\end{align\\*}",
        "gt_answers": ". y = \\frac { 4 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4527.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in the image using LaTeX format, we can follow these steps:\n\n1. Convert the image to LaTeX format by writing the equation in the format of f(x) = mx + b, where m is the slope and b is the y-intercept.\n2. Write the equation using LaTeX format, which includes using the slope-intercept form of a line, writing the equation in parentheses, and using the variable x for the independent variable and the constant m for the slope.\n3. Evaluate the equation for the given values of x and y.\n\nUsing",
        "gt_answers": "x = \\frac { 1 2 0 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4528.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is 5x^2 + 10x - 5.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\n$$\\text{lab} + \\text{bc} = \\frac{\\text{d}}{\\text{c}}$$\n\nwhere $\\text{lab}$ represents the laboratory, $\\text{bc}$ represents the bacterial culture, and $\\frac{\\text{d}}{\\text{c}}$ represents the amount of dye added to the bacterial culture.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is:\n\nA = \u03c0r\u00b2\n\nwhere \u03c0 is the mathematical constant that is approximately equal to 3.14159. To find the area of the circle in the image, we can substitute the radius of the circle, 2.5 cm, into the formula:\n\nA = \u03c0(2.5 cm)\u00b2\n\nA = 3.14159 \u00d7 6.25 cm\u00b2\nA = 19.63 cm\u00b2\n\nTherefore, the area of the circle",
        "gt_answers": "\\therefore S = 2 1 c m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4532.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a trapezoid is given by:\n\nA = (b1 + b2)h / 2A = (b\\_1 + b\\_2)h/2A=((b1+b2)h)/2where b1b2b\\_1b\\_2 and h are the lengths of the parallel sides and the height of the trapezoid, respectively.",
        "gt_answers": "x = 4 \\frac { 2 5 } { 6 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4533.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\\begin{equation}\n\n\\end{equation}\nIn this equation, the variable $x$ represents the position of the car relative to the origin. The variable $v$ represents the velocity of the car relative to the origin. The variable $t$ represents time, which is measured in seconds. The equation represents the position of the car as a function of time, assuming constant acceleration.\n\nAs the car moves along the path, its position $x$ changes at a constant rate given by the constant acceleration $a$. The velocity $v$ also changes at a constant rate given by the acceleration $a$, but",
        "gt_answers": "\\because D E \\bot A B\n",
        "image_path": "./data/HME100K/test_images/test_4534.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{48}{6} = 8$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression in the image:\n\n\\begin{center}\n$\\frac{2000 - 50}{300 + 50} = \\frac{1500}{400} = \\boxed{3.75}$\n\\end{center}\n\nThis formula calculates the average of $2000 - 50$ and $300 + 50$, which are the values of the image. The average is then divided by $300 + 50$ to find the ratio of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{a}{b} \\cdot \\frac{c}{d}$$\n\nwhere a, b, c, and d are integers.",
        "gt_answers": "2 + 4 + 6 + \\cdots + 1 6 + 1 8 + 2 0 ( 2 + 2 0 ) \\times 5 = 1 1 0\n",
        "image_path": "./data/HME100K/test_images/test_4538.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:$$\\text{75}\\% \\times 4 = 3$$The image shows that the fraction 75% can be simplified to 3/4. The multiplication of these two fractions results in 3.",
        "gt_answers": "7 7 9 \\div 5 1 = 1 5 \\cdots 1 4\n",
        "image_path": "./data/HME100K/test_images/test_4539.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{100}{200 + \\frac{1}{3}}$",
        "gt_answers": "x = \\frac { 3 1 } { 1 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4540.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n$$\\frac{2\\times 4 + 3\\times 6}{5\\times 9} = \\boxed{\\frac{12 + 18}{45}}$$",
        "gt_answers": "\\frac { 1 } { 1 2 } = \\frac { 1 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4541.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:",
        "gt_answers": "\\frac { 5 } { 6 } = \\frac { ( 2 0 ) } { ( 2 4 ) }\n",
        "image_path": "./data/HME100K/test_images/test_4542.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:$$\\frac{1}{3}+\\frac{1}{4}+\\frac{1}{5}+\\frac{1}{6}+\\frac{1}{7}+\\frac{1}{8}=\\frac{1}{3}\\cdot\\frac{1}{4}\\cdot\\frac{1}{5}\\cdot\\frac{1}{6}\\cdot\\frac{1}{7}\\cdot\\frac{1}{8}=63\\frac{1}{3}\\cdot\\frac{1}{4}\\cdot\\frac{1}{5}\\cdot\\frac{1}{6}\\cdot\\frac",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n$$ \\begin{aligned} \\text{Image formula} \\ &= \\text{expression for image} \\ \\ \\ \\ \\ \\text{using LaTeX format} \\ \\ \\ \\ \\ \\ \\frac{\\text{equation}}{\\text{equation}} \\ \\ \\ \\ \\ \\ \\frac{\\text{expression}}{\\text{expression}} \\ \\ \\ \\_\\_\\_\\_\\_\\_\\_\\_\\_ \\ \\_\\_\\_\\_\\_\\_\\_\\_\\_ \\ \\_\\_\\_\\_\\_\\_\\_\\_\\_ \\ \\_\\_\\_\\_\\_\\_\\_\\_\\_ \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a diagram of an RC filter with a capacitor and resistor in series, and a capacitor in parallel with a resistor. The formula for the transfer function of this circuit is given by: H(s) = (b/(1 + (a/s))) \\* (1/(1 + (b/s))) \\* (c/(1 + (c/s))) \\* (1/(1 + (a + b)/s)) where a, b, and c are the values of the capacitor, resistor and capacitor respectively.",
        "gt_answers": "1 + ( a - 2 ) ^ { 2 } + 9 + ( a - 1 ) ^ { 2 } = 1 7\n",
        "image_path": "./data/HME100K/test_images/test_4545.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the expression for the formula in the image using LaTeX format:\n\n\\begin{equation}\ny = \\frac{2}{x+2}\n\\end{equation}\nThis is a quadratic equation with vertex at the origin and passing through the point (1,1). The solutions to this equation are the points where the parabola intersects the x-axis. These points can be found by solving the equation for x:\n\n\\begin{equation}\nx = \\frac{y-1}{2}\n\\end{equation}\nPlugging in the value of y",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is:\n\nArea = (1/2) \\* base \\* height\n\nThe base of the triangle is 4 and the height is 6, so the area is:\n\nArea = (1/2) \\* 4 \\* 6\nArea = (1/2) \\* 4 \\* 6\nArea = (1/2) \\* 24\nArea = 12\n\nTherefore, the area of the triangle is 12 square units.",
        "gt_answers": "c = 4 a\n",
        "image_path": "./data/HME100K/test_images/test_4547.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\begin{center}\n\\frac{3x^2 + 4xy + 5y^2}{x^2 + 2xy + y^2} = \\frac{3x^2 + 2xy + 5y^2}{x^2 + y^2} + \\frac{2xy}{x^2 + y^2}\n\\end{center}\n```\nIn this expression, we have a rational expression with the numerator 3x^2 + 4xy + 5y^2 and the denominator x^2 + 2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n\\begin{center}\n\\frac{3x^{2}+5x+1}{2x+3}\n\\end{center}\n\nThis formula is for a quadratic function in the form of y = ax^2 + bx + c, where a = 3, b = 5, and c = 1. The denominator is 2x + 3, which is the constant term in the function.",
        "gt_answers": "2 ( 5 - 3 m ) = m + 1\n",
        "image_path": "./data/HME100K/test_images/test_4551.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by A = l x w, where l is the length and w is the width. The length of the rectangle is 4 cm and the width is 5 cm. Therefore, the area of the rectangle is 4 cm x 5 cm = 20 cm^2.\n\nThe formula for the area of a circle is given by A = \u03c0r^2, where r is the radius of the circle. The radius of the circle is 5 cm. Therefore, the area of the circle is \u03c0(5 cm)^2 = 78.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```markdown\n\n$$\n\\text{Kirchhoff's Voltage Law}\n$$\n\nThe voltage drop across a resistor is proportional to the current passing through it, according to Kirchhoff's Voltage Law. The formula for the voltage drop is given by:\n\n$$ V = IR $$\n\nwhere V is the voltage drop, I is the current, and R is the resistance of the resistor.\n\nThe image shows a circuit with a voltage source (V) connected in series with a resistor (R) and a load (L). Kirchhoff's Vol",
        "gt_answers": "t ^ { 2 } - 1 6 t \\geq 2 7\n",
        "image_path": "./data/HME100K/test_images/test_4553.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that.\n\nHere's the LaTeX formula for the given expression:\n\n$$\\text{e}^{\\frac{b}{c}}$$\n\nIn this formula, the subscript b represents the base of the logarithm (e), c represents the exponent, and the coefficient e is omitted as it is the base of the logarithm.",
        "gt_answers": "E F = \\frac { 1 } { 2 } B D C\n",
        "image_path": "./data/HME100K/test_images/test_4554.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 2x^2 + 6x - 50 = 0 $$\n\nThis is a quadratic equation in standard form, with the variable x raised to the second power and a constant term of 6x. The coefficient of x squared is 2, the constant term is -50, and the constant term of x is 6.",
        "gt_answers": "1 2 \\times 6 5 = 7 0\n",
        "image_path": "./data/HME100K/test_images/test_4555.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:$$\\frac{a}{b}=\\frac{a+b}{2b}$$This formula states that the ratio of the area of the shaded region to the area of the whole rectangle is equal to the ratio of the sum of the areas of the shaded and unshaded regions to twice the area of the unshaded region.",
        "gt_answers": "\\frac { E D } { P D } / = \\frac { P C } { B C }\n",
        "image_path": "./data/HME100K/test_images/test_4557.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\nb d = 2sin&#x2212;1\" role=\"presentation\" style=\"position: relative;\">b d=2sin\u22121b d = 2sin\u22121\\frac{b\\_d}{2\\sin^{-1}}",
        "gt_answers": "B D = 2 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4558.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: 2x + 5 = 6x + 10. This can be represented as: 2x + 5 = 6x + 10.\n\nIn this formula, x is the variable and the expression on the left side is the equation that we want to solve. The expression on the right side is the equation that we want to substitute into the original equation to solve for x.\n\nTo solve for x, we simply substitute the expression on the right side into the original equation, like this: 2x + 5 =",
        "gt_answers": "1 - \\frac { 2 x - 5 } { 6 } = \\frac { 3 - x } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4559.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the triangle in the image is:\n\nA = 0.5 \u00d7 base \u00d7 heightA = 0.5bhwhere b is the base of the triangle and h is the height of the triangle.\n\nTo calculate the area of the triangle, we need to know the values of b and h. We can use the ruler in the image to measure the base and height of the triangle.\n\nFrom the image, we can see that the base of the triangle is approximately 10 cm and the height is approximately 15 cm.\n\nTherefore, the area",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX code for the given formula:\n\n$$\\text{ImageContent}=\\frac{1}{2} \\times 3 + 5 \\times 2 = \\frac{11}{2}$$\n\nThis formula calculates the sum of the areas of the triangles in the image, using the given measurements for the sides of each triangle. The formula uses the multiplication symbol ($\\times$) to indicate that each triangle's area is calculated by multiplying its base by its height. The division symbol ($\\div$) is used to indicate that the sum of the areas of all the triangles is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is A = l \\* w, where l is the length and w is the width. To find the area of the rectangle in the image, we can use the formula:\n\nA = 16 \\* 3 = 48\n\nTherefore, the area of the rectangle in the image is 48 square units.",
        "gt_answers": "2 = ( 3 - 2 \\sqrt { 2 } ) x\n",
        "image_path": "./data/HME100K/test_images/test_4563.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $sap{paa}^{3} $ s.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a diameter of 6.25 cm is:A=\u03c0r^2where r is the radius of the circle. Using the given radius, we have:A=\u03c0(6.25)^2=\u03c037.875 cm^2Therefore, the area of the circle is 37.875 cm^2.",
        "gt_answers": "\\therefore L _ { 1 } = 0 . 4 5 m\n",
        "image_path": "./data/HME100K/test_images/test_4565.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is written as follows:\n\n$$\\frac{33}{4}+\\frac{34}{5}+\\frac{35}{6}+\\frac{36}{7}+\\frac{37}{8}+\\frac{38}{9}+\\frac{39}{10}+\\frac{40}{11}+\\frac{41}{12}+\\frac{42}{13}+\\frac{43}{14}+\\frac{44}{15}+\\frac{45}{16}+\\frac{46}{17}+\\frac{47}{18}+\\frac{4",
        "gt_answers": "x = \\frac { 2 3 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4566.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{3}+\\frac{5}{6}=\\frac{13}{9}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is an image of a mathematical expression in LaTeX format:\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline\n$x$ & $y$ & $z$ \\tabularnewline\n\\hline\n$1$ & $2$ & $3$ \\tabularnewline\n\\hline\n$4$ & $5$ & $6$ \\tabularnewline\n\\hline\n$7$ & $8$ & $9$ \\tabularnewline\n\\hline\n\\end{tabular}\n\\end{center}\n\nThis table shows",
        "gt_answers": "\\frac { 2 x } { x - 1 } + \\frac { 3 } { 1 - x } = 1\n",
        "image_path": "./data/HME100K/test_images/test_4568.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n3x + 2y = 12 \\\\\nx + y = 4z\n\\end{align\\*}\n\nThis formula is a system of two equations with three unknowns, x, y, and z. The first equation is a linear equation in x and y, while the second equation is a linear equation in x and y. The solution to the system is found by solving both equations simultaneously for x, y, and z, subject to the constraint that x + y = 4z.",
        "gt_answers": "\\rightarrow 1 . 5 \\times 1 0 ^ { 4 } P a\n",
        "image_path": "./data/HME100K/test_images/test_4569.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows an algebraic expression for the derivative of a function f(x) with respect to x. The expression is given by:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given image:\n\n\\begin{center}\\begin{tikzpicture}\\node[draw,circle,fill=black] at (0,0) {b};\\end{tikzpicture}\\end{center}\n\nThis expression represents a binary operation in which the left operand is the element 'b' and the right operand is anything else. The operation is to perform the binary operation and return the result.",
        "gt_answers": "b = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4572.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ 3x^2 + 2x - 5 = 0 $$\n\nTo find the roots of the equation, we can use the quadratic formula:\n\n$$ x = {-b \u00b1 \u221a(b^2 - 4ac)} / 2a $$\n\nSubstituting the values of a, b, and c from the given formula, we get:\n\n$$ x = {-(-5) \u00b1 \u221a((-5)^2 - 4(1)(3))] / 2(1)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n(3x^2 + 2x - 5) / (x^2 + 2x - 3) = 2(x + 3) / (x + 1) = 2x + 3 - x = 2x = 5\n\nTherefore, the image represents the equation y = 2x + 3, with x = 0, 1, 2, 3, and 4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I cannot see the image as it is not provided. Can you please provide the image so that I can assist you with the LaTeX format?",
        "gt_answers": "\\angle A B = \\angle C = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4578.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I cannot see the image as it is not provided. Can you please provide the image so that I can assist you?",
        "gt_answers": ": 1 2 x = 0 . 7 5 \\times 9\n",
        "image_path": "./data/HME100K/test_images/test_4579.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n  $\\frac{a+b}{c+d}$\n\n```",
        "gt_answers": "x = \\frac { 3 b + a } { 2 a - 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4581.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in the image using LaTeX format, we can use the following steps:\n\n1. Write the formula using LaTeX notation:\n\n$$ \\begin{aligned} \\frac{5x - 7y}{2} + 3 &= 11 \\end{aligned} $$\n\n2. Simplify the formula using algebra:\n\n$$ \\begin{aligned} 5x - 7y + 6 &= 11 \\end{aligned} $$\n\n3. Rewrite the simplified formula using LaTeX notation:\n\n$$ \\begin{aligned} 5x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{center}\n$ \\frac{x+2y}{x-y} = 4 $\\\\\n\\end{center}\n\nExplanation: The given image represents a rational function with a numerator of $ x+2y $ and a denominator of $ x-y $. The value of the image is $ 4 $.",
        "gt_answers": "\\frac { 8 } { 4 } = 8 \\div 4 = 2\n",
        "image_path": "./data/HME100K/test_images/test_4584.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x3 + 2x2 - x + 5.",
        "gt_answers": "x = \\frac { 2 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_4586.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b(\u22121)d(x2+x2)dx=\u221212\u222b\u222b(\u22121)dx2\\int\\_{-\\frac{1}{2}}^{\\frac{1}{2}} \\left(x^2+x^2\\right) dx = -\\frac{1}{2}\\int\\_{-\\frac{1}{2}}^{\\frac{1}{2}} dx^2\u222b\u222b\u222b(\u22121)d(x2+x2)dx=\u221212\u222b\u222b(\u22121)dx2",
        "gt_answers": "b _ { n + 1 } = 1 + \\frac { b _ { n } } { a _ { n } }\n",
        "image_path": "./data/HME100K/test_images/test_4587.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the equation in the image is x = (3y + 2) / (y - 4).\n\nTo write out the equation in LaTeX format, we can use the following code:\n\n$$\\begin{aligned} x & = \\frac{(3y + 2)}{(y - 4)} \\end{aligned}$$\n\nThis will produce the equation in the format shown in the image.",
        "gt_answers": "x - y = 2\n",
        "image_path": "./data/HME100K/test_images/test_4589.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a chemical formula for nitrate, represented as NO3-.\n\nThe formula can be written using LaTeX as:\n\n\\ce{NO3-}\\_\\_",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\frac{c^2}{2g}=\\frac{v^2}{2r}$$\n\nThis formula relates the speed of an object to its distance from the center of gravity. The left side of the equation is the square of the velocity of the object, divided by two times its distance from the center of gravity. The right side of the equation is the square of the acceleration due to gravity, also divided by two times the distance from the center of gravity. The equation is derived from the principle of equivalence, which states that the acceleration of an",
        "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": "MiniGPT4"
    },
    {
        "question": "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$$ x = \\frac{1}{2}\\left(\\sqrt{y^2 + z^2} + y\\right)$$",
        "gt_answers": "t = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4592.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: $ $\\frac{a+b}{c+d}$ $\\frac{a+b}{c+d} = \\frac{a}{c} + \\frac{b}{d}$ $\\frac{a}{c} + \\frac{b}{d} = \\frac{a+b}{c+d}$ $\\frac{a+b}{c+d} = \\frac{a+b}{c+d}$ $\\frac{a+b}{c+d} = \\frac{a+b}{c+d}$ $\\frac{a+b}{c+",
        "gt_answers": "\\frac { 1 } { 2 } \\rho \\cos A - \\frac { \\sqrt { 3 } } { 2 } \\rho \\sin A = 8\n",
        "image_path": "./data/HME100K/test_images/test_4593.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation for the number of integers that are factors of a given integer. To write the equation in LaTeX format, we can use the following code:\n\n\\begin{align}\nn &= 2, 3, 4, \\ldots, \\infty \\notag \\\\\n&= \\prod\\_{i=2}^{\\infty} \\left(10 - i\\right) \\notag \\\\\n&= \\frac{10!}{2! (10-2)! (10-3)! (10-4)! \\ldots} \\notag \\\\\n&= \\frac{",
        "gt_answers": "x = \\vert y \\vert = 2 . 5\n",
        "image_path": "./data/HME100K/test_images/test_4594.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n\\begin{center}\n$k\\_i=\\frac{P\\_i}{\\sum\\_{j=1}^n P\\_j}$\n\\end{center}\n\nWhere $k\\_i$ is the priority score of the $i^{th}$ task, $P\\_i$ is the processing time of the $i^{th}$ task, and $\\sum\\_{j=1}^n P\\_j$ is the sum of the processing times of all the tasks.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a right triangle with one leg labeled x and the other two legs labeled y and z. The hypotenuse is labeled with the number 1. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longer side. Using this theorem, we can find the length of the hypotenuse of the triangle:\n\nx^2 + y^2 = z^2\nx^2 = z^2 - y^2\nx = \u00b1\u221az^2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression in the image:\n\n$$\\frac{\\frac{100}{x} - 50}{\\frac{x}{2} + 10}$$",
        "gt_answers": "\\tan 3 0 ^ { \\circ } = \\frac { O A } { O C }\n",
        "image_path": "./data/HME100K/test_images/test_4597.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, follow these steps:\n\n1. Write the number 4 in the formula using the letter sigma (\u2211) and the variable x, like this: \u2211x2.\n2. Write the number 5 in the formula using the letter pi (\u03c0) and the variable y, like this: \u03c0y.\n3. Write the number 3 in the formula using the letter sigma (\u2211) and the variable z, like this: \u2211z3.\n4. Write the number 4 in the formula using the letter s",
        "gt_answers": "9 . 3 \\div 5 = \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4598.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:$$M = \\frac{1}{2}m\\_1v\\_1^2 + \\frac{1}{2}m\\_2v\\_2^2 - \\frac{1}{2}m\\_3v\\_3^2$$This formula is the momentum principle equation, which relates the momentum of an object to the force acting on it. The left-hand side of the equation represents the change in momentum of the system, while the right-hand side represents the net force acting on the system.\n\nThe variables in the equation are:\n\n* $",
        "gt_answers": "A B = E D = 1 . 5 m\n",
        "image_path": "./data/HME100K/test_images/test_4599.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression is: $\\frac{1}{2}x^2 + \\frac{1}{4}x - \\frac{1}{8}x^4$",
        "gt_answers": "x = \\frac { 1 0 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_4600.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n$$T=-\\frac{mgh}{\\sqrt{2g^2+2gh^2}}$$\n\nThis is the formula for the kinetic energy of an object that is falling under the influence of gravity. The variable `T` represents the kinetic energy, `m` represents the mass of the object, `g` represents the acceleration due to gravity, and `h` represents the height of the object from its initial position.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Please provide a different image for me to work with.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a linear equation with coefficients of 2 and 1, and constant term 4.\n\n$$2x + 4 = 6$$",
        "gt_answers": "2 . 4 \\times 2 . 0 6 = 4 . 9 4 4\n",
        "image_path": "./data/HME100K/test_images/test_4604.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{1}{2}(x + y) = \\frac{1}{4} $$",
        "gt_answers": "1 1 - 9 = 2 1 7 - 8 = 9\n",
        "image_path": "./data/HME100K/test_images/test_4605.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is given by the formula:\n\n$$x + 2y = 10$$\n\nwhere $x$ and $y$ are variables. This equation represents a line in the $xy$-plane that passes through the point $(0, 1)$ and has a slope of $2$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\narea = length x width\n\nIn the image, the length and width of the rectangle are not given. Therefore, we cannot calculate its area.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: r + 3r - 6 = 0.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, you can use the following LaTeX code:\n\n\\begin{center}\n\\begin{align\\*}\nf(x) &= \\sqrt{2} \\times 3 - 4 \\times \\frac{1}{2} \\times x^2 + 5x + 3 \\times \\sqrt{2} \\\n&= \\sqrt{2} \\times 3 - \\frac{2}{2} \\times x^2 + 5x + 3 \\times \\sqrt{2} \\\n&= 3 - \\",
        "gt_answers": ". 7 5 t : 6 t = 0 . 6 2 5\n",
        "image_path": "./data/HME100K/test_images/test_4612.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{x + 1}$.\n\nThe numerator is $\\frac{1}{x + 1}$ which is equal to 1 when $x + 1 = 1$, which is the condition for a closed loop with no flow in it. The denominator is $x + 1$, which is equal to 2 when $x = 1$. Therefore, the closed loop equation becomes: $\\frac{1}{2} = 1$, which is satisfied when $x = 1$.",
        "gt_answers": "m = - \\frac { 3 7 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4614.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot access the image you have provided as it is not available. Can you please provide a different image for me to work with?",
        "gt_answers": "x _ { 2 } = \\frac { 1 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4615.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{32\\sqrt{21}}{4}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I can't see the image. Can you please provide the image?",
        "gt_answers": "a ( 3 m - a ) = 2 m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4618.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This image is a mathematical expression that represents the derivative of the function f(x) = 3x + 4 with respect to x. The expression is written as d/dx [3x + 4].",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I don't see any image in your message. Could you please provide the image?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: \u222b\\_0^af(x)dx. Here, f(x) is the given function, a is the upper limit of integration and 0 is the lower limit of integration.",
        "gt_answers": "5 4 \\times \\frac { 1 } { 6 } = 9 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_4621.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{2x + 4y}{x + y} = \\frac{2(2x) + 4(2y)}{2x + 2y} = \\frac{4x + 8y}{2x + 2y} = \\frac{4}{2} = 2$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is not clear from the image provided. Please provide a clear and legible image for me to write the equation.",
        "gt_answers": "x = \\frac { 2 7 8 0 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4623.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:x2+1=2x2.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is x2=1.\\nThe solution is",
        "gt_answers": "x _ { 1 } = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4624.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$ \\frac{1}{4} x^2 + \\frac{1}{2} x + \\frac{1}{8} $$\n\nThis is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 1$, $b = \\frac{1}{4}$, and $c = \\frac{1}{8}$. The solutions to this equation are the values of $x$ that make the equation true. These solutions can be found by solving the equation using the quadratic formula:\n\n$$ x =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, you can use the following code:\n\n\\begin{equation} \\frac{5x^2+3x-2}{x+2}=\\frac{5(x+2)(x+1)^2-3(x+2)+2}{(x+2)^2}\\end{equation}\nThis formula can be derived by using the distributive property of multiplication over addition, as follows:\n\n\\begin{equation} \\frac{a(b+c)}{d}+\\frac{b(c+d)}{a}+\\frac{c",
        "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": "MiniGPT4"
    },
    {
        "question": "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 + 3x - 4x2 + 5x3 - 6x4 + 7x5 - 8x6 - 9x7 + 10x8 - 11x9 + 12x10 - 13x11 + 14x12 - 15x13 + 16x14 - 17x15 + 18x16 - 19x17 + 20x18 - 21x19",
        "gt_answers": "x : \\frac { 3 } { 1 6 } = \\frac { 1 } { 3 } : 2\n",
        "image_path": "./data/HME100K/test_images/test_4628.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n![ImageContent](https://www.mathworks.com/help/images/ref/imagelist/gr37f9c9d7282b424b797b62d5629524e.png)\n\n![ImageContent](https://www.mathworks.com/help/images/ref/imagelist/gr37f9c9d7282b424b797b62d56295",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: $\\frac{1}{2}x^2 + \\frac{1}{4}x - \\frac{1}{8}x^4$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression shown in the image is given by:\n\n![](https://i.imgur.com/0d0m9QW.png)\n\nwhere x and y are variables, and a, b, and c are constants.",
        "gt_answers": "A B = \\frac { \\sqrt { 2 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4631.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is showing a mathematical expression that can be written as follows:\n\n$$ \\frac{(x+y-3)}{(2x-5)} = \\frac{y+z-4}{2z-9} $$",
        "gt_answers": "x < - \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4633.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{equation}\nA = \\frac{m}{M}\n\\end{equation}\n\\end{center}\n\nThis formula represents the ratio of mass of an object (A) to the mass of the Earth (M). The variable m represents the mass of the object.",
        "gt_answers": "\\angle A B O = \\angle B A O = 1 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4634.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the equation 4x^2 + 12x + 8 = 0.",
        "gt_answers": "\\frac { b } { 4 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4636.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the number of seconds is:t=2sint2t=(2sin60)t=2sin60t=60sin2t=\\frac{2}{t}\\sin\\left(\\frac{t}{2}\\right)\\frac{t}{2}\\sin\\left(\\frac{t}{2}\\right)=60\\sin2t=60sin2t=\\frac{2}{t}\\sin\\left(\\frac{t}{2}\\right)\\frac{t}{2}\\sin\\left(\\frac{t}{2}\\right)=60\\sin2t=",
        "gt_answers": "1 4 . 1 3 \\div 2 . 5 \\approx 5 . 7 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_4638.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{1}{\\sqrt{2}} - \\frac{1}{\\sqrt{2}}$$\n\nThis is because the image shows two negative signs, each with a line below it, which can be represented as a fraction with a denominator of 2. The numerator of the fraction is 1, which is the coefficient of the variable x in the formula.",
        "gt_answers": "c p ^ { 2 } = ( 4 - x ) ^ { 2 } + ( - x + 6 ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4640.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$$\\text{mass}\\_{total}=\\sum\\_{i=1}^{n}m\\_i$$\n\nwhere $m\\_i$ is the mass of the $i$th atom in the compound. The summation symbol $\\sum$ indicates that the sum of all the masses of the atoms is taken.",
        "gt_answers": "C M : y = \\frac { \\sqrt { 3 } } { 3 } x + m\n",
        "image_path": "./data/HME100K/test_images/test_4641.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you have provided as the message is incomplete. Can you please provide the full message?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n5 + 4i + 3j + 2k = 12\n\n5 + 4i + 3j + 2k + 1 = 12\n\n5 + 4i + 3j + 2k + 1 = 12",
        "gt_answers": "4 \\sqrt { 2 } = \\sqrt { 2 } \\cdot \\sqrt { 4 + 8 b }\n",
        "image_path": "./data/HME100K/test_images/test_4643.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the following LaTeX expression: $\\frac{3x^2 + 4x - 5}{2x + 2}$. This is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 3$, $b = 2$, and $c = 5$.",
        "gt_answers": "\\frac { a } { c } < \\frac { b } { d }\n",
        "image_path": "./data/HME100K/test_images/test_4644.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{60}{56} = \\frac{5}{4}$",
        "gt_answers": "\\frac { 5 } { 3 } = \\frac { - ( 1 0 ) } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_4645.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image using LaTeX format is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "1. Write out the equation for the given image: x + 5 = 10.\n\n2. Simplify the equation: x = 5.\n\n3. Evaluate the equation for x = 2: 2 + 5 = 7.\n\n4. Plot the equation on the number line: 5, 2, 7, 10.",
        "gt_answers": "x = 1 0 \\times \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4647.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression written in LaTeX format. The expression is given below:\n\n\u222b0\u222b 0f(t)dt\u222b 0\u222b 0f(t)dt\u222b 0\u222b 0f(t)dt\u222b 0\u222b 0f(t)dt\u222b 0\u222b 0f(t)dt\u222b 0\u222b 0f(t)dt\u222b 0\u222b 0f(t)dt\u222b 0\u222b 0f(t)dt\u222b 0\u222b 0f(t)dt\u222b 0\u222b 0f(t)dt",
        "gt_answers": "a + b + c = 0 .\n",
        "image_path": "./data/HME100K/test_images/test_4648.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the formula in the image is: \\frac{5}{4}\\frac{2}{3}x^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the given expression:\n\n$$\\begin{aligned} x^2 + 2x + 1 &= 0 \\Rightarrow x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} \\ &= \\frac{-(2) \\pm \\sqrt{(2)^2 - 4(1)(1)}}{2(1)} \\ &= \\frac{1 \\pm \\sqrt{5}}{2} \\ &= \\frac{2 \\pm \\sqrt{5}}{4} \\ &= \\frac{1}{2} \\pm \\",
        "gt_answers": "x _ { 1 } = 3 , x _ { 2 } = 6\n",
        "image_path": "./data/HME100K/test_images/test_4650.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{m}{t} $$\n\nwhere $m$ is the mass of the object and $t$ is the time it takes for the object to fall to the ground.",
        "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": "MiniGPT4"
    },
    {
        "question": "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 = sqrt( (y - b)^2 + (x - d)^2 )",
        "gt_answers": "\\frac { A B } { B E } = \\frac { A D } { D F }\n",
        "image_path": "./data/HME100K/test_images/test_4652.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length 8 cm and width 6 cm is:\n\nA = l \\* w\n\nA = 8 cm \\* 6 cm\n\nA = 48 cm\u00b2\n\nTherefore, the area of the rectangle is 48 cm\u00b2.",
        "gt_answers": "x _ { 1 } = - \\sqrt { 6 } , x _ { 2 } = \\frac { \\sqrt { 6 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4653.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n$$\\begin{aligned}a^2+b^2=c^2\\end{aligned}$$\n\nwhere a, b, and c are the side lengths of the triangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ \\frac{1}{2} \\left( \\frac{a^2 + b^2}{c^2} + \\frac{b^2 + c^2}{a^2} + \\frac{c^2 + a^2}{b^2} \\right) = \\frac{1}{2} \\left( \\frac{(1)^2 + (3)^2}{4^2} + \\frac{(3)^2 + (4)^2}{(1)^2} + \\frac{(4)^2 +",
        "gt_answers": "x = \\frac { 1 + \\sqrt { 3 3 } } { 4 } ; x = \\frac { 1 - \\sqrt { 3 3 } } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4655.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:$$ \\frac{a+b}{c-d}$$This is a basic algebra expression that shows how to find the sum of two numbers, a and b, by subtracting another number, c, from another number, d.",
        "gt_answers": "b ^ { 2 } + c ^ { 2 } - 2 b c = a ^ { 2 } - b c\n",
        "image_path": "./data/HME100K/test_images/test_4656.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is:\n\nx + 2y = 11\n\nThis equation can be solved using the substitution method, by solving for one of the variables in terms of the other. Let's solve for y in terms of x:\n\ny = (11 - x) / 2\n\nNow we can substitute this expression into the equation to solve for x:\n\nx + 2((11 - x) / 2) = 11\n\nSimplifying the right side:\n\n2x + 2((11 - x) / 2) =",
        "gt_answers": "x _ { 2 } = - \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4657.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\begin{aligned}x^2 + 3x - 2\\end{aligned}$$",
        "gt_answers": "\\frac { 4 } { 9 } x \\div \\frac { 4 } { 9 } = \\frac { 8 } { 1 5 } \\div \\frac { 4 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_4658.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression in LaTeX format.\n\nso, b=a\u22c5c\u22c5d\u22c5f\u22c5g\u22c5h\u22c5i\u22c5j\u22c5k\u22c5l\u22c5m\u22c5n\u22c5o\u22c5p\u22c5q\u22c5r\u22c5s\u22c5t\u22c5u\u22c5v\u22c5w\u22c5x\u22c5y\u22c5z.",
        "gt_answers": "S _ { \\Delta } B D C = \\frac { 1 } { 2 } B C \\cdot A F .\n",
        "image_path": "./data/HME100K/test_images/test_4661.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```scss\n\nThe formula for the sum of the series is given by:\n\n$$S\\_n = \\frac{1}{1 - r}$$\n\nwhere r is the common ratio of the geometric series. The formula can be derived by summing the infinite series, which is given by:\n\n$$\\sum\\_{n=0}^{\\infty} r^n = \\frac{1}{1 - r}$$\n\nThe value of r is given by the formula:\n\n$$r = \\frac{a}{b}$$\n\nwhere a and b are the first two terms of the geometric series",
        "gt_answers": "\\sqrt { x } = 5\n",
        "image_path": "./data/HME100K/test_images/test_4662.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $6 \\times 2 - 4$\n\nHere is the LaTeX code for the formula:\n\n\\begin{align}\n6 \\times 2 - 4 &= 12 - 4 \\\n&= 8 \\\n&= 8 \\\n\\end{align}\n\nSo the result of the formula is 8.",
        "gt_answers": "t = 6 \\div 0 . 1 = 6 0 \\min\n",
        "image_path": "./data/HME100K/test_images/test_4663.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{equation}\n2 + 2 = 4\n\\end{equation}\n```\nIn the image, the formula is written in the LaTeX format, which represents mathematical expressions and equations using special characters and symbols.",
        "gt_answers": "2 4 - 1 2 = 1 2 ( m L )\n",
        "image_path": "./data/HME100K/test_images/test_4664.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\text{f}=\\frac{a}{b}\\left(\\frac{c}{d}\\right)^{\\frac{e}{f}}$$\n\nIn this formula, the variables $a, b, c, d, e, and f$ are given in terms of the given numbers:\n\n$$a=49, b=26, c=1, d=14, e=6, f=14$$\n\nThus, the formula becomes:\n\n$$\\text{f}=\\frac{49",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{x^2 + 3x - 20}{x - 3}$.",
        "gt_answers": "d = - 7\n",
        "image_path": "./data/HME100K/test_images/test_4667.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\nx + 1 = 3x - 2\n\nTo write this in LaTeX format, we can use the following code:\n\n$x + 1 = 3x - 2$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format. It is written in a handwritten notation.\n\nHowever, assuming the formula is written in LaTeX format, we can express it as:\n\n$$\\text{Image Content} = \\frac{a}{b}$$\n\nwhere `a` and `b` are constants that determine the size and shape of the image content.",
        "gt_answers": "x = v t\n",
        "image_path": "./data/HME100K/test_images/test_4669.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{sin}^{2}\\theta + \\cos^{2}\\theta = 1$$\n\nwhere $\\theta$ is the angle between the vectors $\\mathbf{a}$ and $\\mathbf{b}$.",
        "gt_answers": "x = - 1 \\pm \\frac { 1 1 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4670.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle is given by A = l \\* w, where l is the length and w is the width. The equation for the perimeter of a rectangle is given by P = 2l + 2w, where l is the length and w is the width. The equation for the volume of a rectangular prism is given by V = l \\* w \\* h, where l is the length, w is the width, and h is the height. The equation for the surface area of a rectangular prism is given by S = 2l + 2w +",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is given as:\n\n$$ (x + 3)(x - 5) = x^2 - 8x + 15 $$\n\nThe image shows the formula with the variables replaced by specific numbers, which can be used to solve the equation. The formula is used to find the value of the expression for any given values of x and y.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression for the given formula:\n\n$$ 6444 + \\frac{656}{26} = 701 $$\n\nNote: In LaTeX, we use the fraction bar (/) to denote division, and the multiplication symbol (\u00d7) is used for multiplication.",
        "gt_answers": "6 = - 2 1 c + b\n",
        "image_path": "./data/HME100K/test_images/test_4674.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a rectangle with a width of 6 inches and a height of 10 inches is:\n\nA = l \\* w + h = 6 \\* 10 + 10 = 60 + 10 = 70 square inches\n\nThe formula for the area of a rectangle is:\n\nA = l \\* w + h\nWhere l is the length and w is the width.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\nA = \\frac{B\\*C+C\\*D}{2}\n\\end{align\\*}\n\nThis formula calculates the average of two numbers, B and C, and another number, D. It adds the product of B and C, and the product of C and D, then divides the sum by 2 to find the average.",
        "gt_answers": "3 a + 3 a + 2 a = 2\n",
        "image_path": "./data/HME100K/test_images/test_4676.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\frac{k\\_{1}}{k\\_{2}}=\\frac{k\\_{2}}{k\\_{1}}=\\frac{\\frac{1}{2}\\left(\\frac{a\\_{1}}{b\\_{1}}-\\frac{a\\_{2}}{b\\_{2}}\\right)}{\\frac{1}{2}\\left(\\frac{a\\_{1}}{b\\_{1}}-\\frac{a\\_{2}}{b\\_{2}}\\right)}=\\frac{\\frac{1}{2}b\\_{1}}{k\\_{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the equation of a circle with a radius of 10 cm. It can be written in LaTeX format as:\n\n\\[ r = \\sqrt{10} \\]\n\nwhere $r$ is the radius of the circle and $\\sqrt{10}$ is the square root of 10.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$x = \\frac{2y+1}{y-2}$$\n\nThis formula can be derived by solving the equation $y^2 - 2y - 1 = 0$ for $y$. Substituting $y = \\frac{x+1}{x-1}$ into the equation gives $x = \\frac{2x+1}{x-2}$.",
        "gt_answers": "\\frac { 1 } { 2 } x = - 2\n",
        "image_path": "./data/HME100K/test_images/test_4679.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: $\\frac{a}{b^2 + c^2}$.\n\nIn LaTeX format, the expression would be written as: $\\frac{a}{b^2 + c^2}$",
        "gt_answers": "A O = 6 , B O = 8 A D = 6\n",
        "image_path": "./data/HME100K/test_images/test_4680.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of a circle with a diameter of 2.2 cm is given by:\n\nA = (r^2)\u03c0 = (2.2^2) \\* 3.14 = 11.46 cm^2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle with radius r can be written as: A = \u03c0r^2. In LaTeX format, this would be written as:\n\nA = \\pi r^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the volume of a rectangular solid can be represented using LaTeX as follows:\n\nV = lwh, where l is the length, w is the width, and h is the height.\n\nHere is the LaTeX code for the formula:\n\n$V = lwh$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is $\\frac{1}{2}$.\n\nHere's how to write it in LaTeX format:\n\n\\frac{1}{2}",
        "gt_answers": "< - 5 \\sim 5\n",
        "image_path": "./data/HME100K/test_images/test_4685.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is an image of the number 3 in LaTeX format:\n\n\\begin{center} $\\frac{3}{5}$ \\end{center}\n\nThis expression represents the fraction 3 divided by 5. The fraction bar is used to indicate the division.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n`$k = \\frac{P}{t^2 + (4/3)\\*a^2 - (2/5)\\*b^2}$`",
        "gt_answers": "2 a _ { 3 } = 6 a _ { 1 } + a _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4687.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n\\begin{center}\n\\frac{2}{3} + \\frac{25}{2} - \\frac{1}{4}\n\\end{center}\n\nwhere the fractions are written in standard notation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the sum of two numbers is:\n\n5 + 7 = 12\n\nThis can also be expressed as:\n\n(5 + 7) = 12\n\nAlternatively, the formula can be written as a fraction:\n\n5 / 2 + 7 / 2 = 12 / 2\n\nThis can be simplified further as:\n\n5 / 2 + 7 / 2 = 7 / 2\n\nTherefore, the sum of 5 and 7 is 12.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image you provided does not contain any mathematical expression. It appears to be a graphical representation of a mathematical equation, but without the equation itself, I am unable to write out the expression in LaTeX format. Please provide the mathematical expression in the image so I can help you.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the given image:\n\n$$\\begin{aligned} x &= \\frac{3}{5} \\\\ y &= \\frac{4}{7} \\end{aligned}$$\n\nIn this equation, x represents the number of students in a class with 30 desks, and y represents the number of desks in a class with 40 students.",
        "gt_answers": "\\pm \\sqrt { c - 2 } = \\pm \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4693.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $ $ $\\frac{x}{2}$x$ $ $ $2x$ $\\frac{x}{4}$ $\\frac{x}{4}$ $ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{4}$ $\\frac{x}{",
        "gt_answers": "y = \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4694.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is:\n\nx + 5y = 10\n\nThis equation represents a linear equation with two variables, x and y. The right-hand side of the equation is a constant value of 10.\n\nTo solve this equation, we can use the method of substitution to isolate one variable. Let's start by substituting x with the expression on the left-hand side of the equation:\n\ny = (10 - x) / 5\n\nNow we can substitute this expression for y in the equation:\n\ny = (10",
        "gt_answers": "x + 1 . 8 \\% x = 1 5 2 7\n",
        "image_path": "./data/HME100K/test_images/test_4695.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$\\text{sin}\\left(\\text{x}\\right) + \\text{cos}\\left(\\text{x}\\right) = \\frac{\\text{sin}\\left(\\text{x}\\right) + \\text{cos}\\left(\\text{x}\\right)}{\\sqrt{\\text{1 - (\\text{sin}\\left(\\text{x}\\right)^2 + \\text{cos}\\left(\\text{x}\\right)^2)}}}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX formula for the given image:\n\n\\begin{align\\*}\nS &= 5 + 4 \\times 2 \\div (2 - 1) \\times 3 \\div (3 + 1) \\div (3 + 4) \\div (4 + 5) \\div (5 - 3) \\div (5 + 2) \\div (2 + 1) \\div (2 + 2) \\div (2 + 3) \\div (3 + 2) \\div (3",
        "gt_answers": "S _ { 5 } = 5 ^ { 2 } = 2 5\n",
        "image_path": "./data/HME100K/test_images/test_4697.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the equation in LaTeX format, we need to first define the variables and constants. Let's assume that the length of the rectangle is $ a $ and its width is $ b $. The perimeter of the rectangle is the sum of its sides, which are $ 2a $ and $ 2b $.\n\nThe area of the rectangle is the product of its width and height, which are $ b $ and $ h $.\n\nWe can substitute these values into the formula for perimeter and area:\n\nPerimeter = 2(a + b) = 2a + 2b =",
        "gt_answers": "x = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4698.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: $\\text{sin}\\left( \\frac{\\text{x}}{\\text{h}} \\right) = \\frac{\\text{sin}\\left( \\frac{\\text{h}}{\\text{x}} \\right)}{\\text{cos}\\left( \\frac{\\text{h}}{\\text{x}} \\right)}$",
        "gt_answers": "S _ { \\Delta B D A } =\n",
        "image_path": "./data/HME100K/test_images/test_4700.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n\u222b \u222b y = a sin x + b cos x dx\n\u222b \u222b x = c t + d\n\u222b \u222b t = \u222b \u222b x = c t + d\n\u222b \u222b y = a sin x + b cos x + C\n\u222b \u222b x = c t + d + E\n\u222b \u222b t = \u222b \u222b x = c t + d + E\n\u222b \u222b y = a sin x + b cos x + C + E",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\node[draw, circle, minimum size=2cm] at (0,0) {$$$\\prod$};\n\\end{tikzpicture}\n\\end{center}\n\nThe expression for the formula in the image is $\\prod$.",
        "gt_answers": "x ^ { 2 } = \\frac { 3 } { a + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4703.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: $\\frac{x^2 + 3x - 5}{x - 2}$.",
        "gt_answers": "\\frac { 1 } { x - y } = V\n",
        "image_path": "./data/HME100K/test_images/test_4704.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{4} - \\frac{1}{4} = \\frac{1}{4}$",
        "gt_answers": "y = 1 1 x = 2\n",
        "image_path": "./data/HME100K/test_images/test_4705.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:$\\text{x} = \\frac{5+6\\sqrt{4}}{3\\sqrt{2}}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2(x + 1) = 10x. This can be written as: 2x + 2 = 10x.",
        "gt_answers": "3 . 2 , - 1 0 0\n",
        "image_path": "./data/HME100K/test_images/test_4707.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle is given by:\n\nA = \u03c0r^2\n\nwhere r is the radius of the circle. To find the area of the circle in the image, we can use the formula above and plug in the given values:\n\nA = \u03c0(3.5 + 0.25)^2\nA = \u03c0(3.5^2 + 0.25^2)\nA = 3.52\u03c0 + 0.0625\u03c0\nA = 3.58\u03c0\n\nTherefore, the area",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: x 2 + 4x - 3y + 2z 3.",
        "gt_answers": "a = 3 b = 5 c = - 2\n",
        "image_path": "./data/HME100K/test_images/test_4709.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ f = \\frac{m}{t}$$where $m$ is the mass of the object and $t$ is the time it takes to fall from rest to the ground.",
        "gt_answers": "c = 0\n",
        "image_path": "./data/HME100K/test_images/test_4710.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ 5x + 4y - 3z = 10 $$",
        "gt_answers": "l _ { 2 } : 2 = 2 k _ { 2 } + 4 .\n",
        "image_path": "./data/HME100K/test_images/test_4711.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is $\\text{SIN(A+B+C)+D}$.\n\nHere's how to derive it:\n\n1. Replace the letter A in the formula with $\\frac{1}{2}$: $\\frac{1}{2}\\cdot \\sin \\left(\\frac{1}{2}\\right) + \\frac{1}{2}\\cdot \\sin \\left(\\frac{1}{2}\\right) + \\frac{1}{2}\\cdot \\sin \\left(\\frac{1}{2}\\right) + \\frac{1}{2}\\cdot \\",
        "gt_answers": "\\textcircled { 1 } 1 . 5 \\times 1 0 ^ { 2 } P a\n",
        "image_path": "./data/HME100K/test_images/test_4712.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as follows:\n\n![](https://i.imgur.com/image.png)x(y) = x2y2 + xy2where x and y are the variables in the equation. The equation represents the slope of the tangent line to the graph of y = x2 at the point (1, 1).",
        "gt_answers": "( 1 - \\frac { 2 } { 3 } ) x = 9 0\n",
        "image_path": "./data/HME100K/test_images/test_4713.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{image}(x, y) = \\text{black} + \\text{white} - \\frac{1}{2}\\text{black} - \\frac{1}{2}\\text{white} + \\frac{1}{4}\\text{black} + \\frac{1}{4}\\text{white} - \\frac{1}{8}\\text{black} - \\frac{1}{8}\\text{white} + \\frac{1}{16}\\text{black} + \\frac{1}{16}\\",
        "gt_answers": "2 0 = 5 x\n",
        "image_path": "./data/HME100K/test_images/test_4716.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not clear without the image.",
        "gt_answers": "3 \\div 1 1 = \\frac { 3 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4717.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{100}{4} + \\frac{100}{4} = \\frac{200}{4} $$\n\nThe expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{100}{4} + \\frac{100}{4} = \\frac{200}{4} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2}\\cdot (6 + 2) - 3 = \\frac{1}{2}(8 - 3) = \\frac{1}{2}(5)$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the sum of the numbers 1, 3, 5, and 7 can be written as:1 + 3 + 5 + 7 = 151 + 3 + 5 + 7 = 151 + 3 + 5 + 7 = 151 + 3 + 5 + 7 = 151 + 3 + 5 + 7 = 151 + 3 + 5 + 7 = 151 + 3 + 5 + 7 = 151 + 3 +",
        "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": "MiniGPT4"
    },
    {
        "question": "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: 2x^2 + 5x + 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written in the image using LaTeX format is:\n\n$$\\frac{1}{1+x^2}=\\frac{1}{2}\\cdot\\frac{1}{1-\\frac{1}{2x^2}}=\\frac{1}{2x}\\cdot\\frac{1}{1-\\frac{1}{2x^2}}=\\frac{1}{2x}\\cdot\\frac{1}{1-x^2}=\\frac{1}{x}\\cdot\\frac{1}{1-x^2}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be represented as follows:\n\n\\begin{aligned}\nf(x) &= \\frac{1}{2}\\left(\\frac{x+2}{x-1}\\right)^2 + 5x^2 - 10x + C\\\n&= \\frac{1}{2}\\left(\\frac{x+2}{x-1}\\right)^2 + 5x^2 - 10x + 12\\\n&= \\frac{1}{2}\\left(\\frac{x+2}{x-1}\\right)^2 + 5",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as follows:\n\n$$f(x) = \\frac{1}{1 + \\sin(x)}$$",
        "gt_answers": "> F e > H > C u\n",
        "image_path": "./data/HME100K/test_images/test_4727.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX formula for the expression in the image:$$\\frac{1000}{500+300}$$This formula represents the probability that a person has a blood pressure of 150 mmHg or higher, given that they have a heart rate of 80 bpm. The numerator is the number of people with a blood pressure of 150 mmHg or higher (1000), and the denominator is the number of people with a heart rate of 80 bpm and a blood pressure of 150 mmHg",
        "gt_answers": "m = 0 , n = 1\n",
        "image_path": "./data/HME100K/test_images/test_4728.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image can be written as follows:\n\n$$ \\frac{(45)(16500) + (35)(32500) + (20)(25000) + (10)(5000)}{4} = \\frac{167,500 + 33,500 + 25,000 + 5,000}{4} = 95,000 $$\n\nThis formula calculates the average of the numbers in the image. The numerator is the sum",
        "gt_answers": "n = 1 4 + 1 4 + 2 + 2 = 3 2\n",
        "image_path": "./data/HME100K/test_images/test_4729.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$\\frac{a+b-c}{d-e}$\n\nwhere $a, b, c, d,$ and $e$ are all integers. This is a variation of the formula for the sum or difference of two fractions.",
        "gt_answers": "x - 3 + 6 x = \\frac { 9 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4730.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:$$40 - 2 \\times 6 + 12 = 38$$This equation can be rewritten as follows:$$40 - 2 \\times 6 + 12 = 38$$In this equation, the variable x is 40, and the variable y is 2. The operator - is used to subtract x from y, and the operator \\* is used to multiply y by 6. The constant value 12 is added to the result of the subtraction and multiplication. This results in the equation 38",
        "gt_answers": "4 9 2 \\div 8 0 = 6 \\cdots 1 2\n",
        "image_path": "./data/HME100K/test_images/test_4732.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:$$\\frac{2x}{x+4}$$where x is the variable representing the width of the rectangle.",
        "gt_answers": "3 x ^ { 2 } y ( 4 2 - 3 y )\n",
        "image_path": "./data/HME100K/test_images/test_4733.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a right triangular prism is given by:A= (1/2)bh,where b is the base of the prism, h is the height of the prism, and A is the area of the prism. The base of the prism is given by:b=l2sin&#x2212;&#x2212;60&#x2212;180&#x2212;90&#x2212;180&#x2212;&#x2212",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2} x^2 - \\frac{1}{4} x^4 + \\frac{1}{8} x^6 - \\frac{1}{16} x^8 + \\frac{1}{32} x^{10}$\n\nNote: This formula is a polynomial equation of degree 10 with variable x. The coefficients are given by the numbers inside the parentheses.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}$\n\nNote: The image is not available for me to view or process.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula using LaTeX format is:\n\n\\begin{center}\n\\frac{3(x^2+3x-5)}{(x-2)(x+1)}\n\\end{center}\n\nThe red ink appears to be written on the top of the paper and the number 502 appears to be written on the right side of the paper.",
        "gt_answers": "n = 5 0 e\n",
        "image_path": "./data/HME100K/test_images/test_4737.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given below using LaTeX format.\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick] (0,0) -- (4,0) node[midway, right]{$x$};\n\\draw[thick] (0,0) -- (0,4) node[midway, above]{$y$};\n\\filldraw (2,2) circle [radius=2pt];\n\\end{tikzpicture}\n\\end{center}\n\nIn this expression, the coordinates of the point P are given by (2,2",
        "gt_answers": "\\sqrt [ 3 ] { - 4 } a = \\sqrt [ 3 ] { - 6 4 } = - 4\n",
        "image_path": "./data/HME100K/test_images/test_4739.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a mathematical formula written in LaTeX format.\n\n$$\\frac{20}{3} + \\frac{35}{5} = \\frac{32}{5}$$\n\nThe formula shows the sum of two fractions, $\\frac{20}{3}$ and $\\frac{35}{5}$, and the result is $\\frac{32}{5}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows:$$ f(x) = \\frac{1}{2}(3x - 2)$$This is a linear function with a slope of $\\frac{1}{2}$ and a y-intercept of $3x - 2$. The domain of the function is all real numbers, as the equation does not involve any imaginary numbers. The range of the function is all real numbers, as the equation does not involve any negative numbers.",
        "gt_answers": "a ( C - x ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4741.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: f(x) = 1 + x2, where x is a variable.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\text{Area} = \\frac{1}{2} \\cdot \\text{Base} \\cdot \\text{Height}$$\n\nwhere $\\text{Area}$ is the area of the image, $\\text{Base}$ is the base of the image, and $\\text{Height}$ is the height of the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\frac{1}{\\sqrt{2}} + \\frac{1}{2} = \\frac{1 + \\sqrt{2}}{2} = \\frac{1 + 1}{2} = \\frac{2}{2} = 1$$\n\nIn words, the expression is the sum of $\\frac{1}{\\sqrt{2}}$ and $\\frac{1}{2}$, which simplifies to $\\frac{1 + \\sqrt{2}}{2}$, and then simplifies further to $\\frac{1 + 1}{2} =",
        "gt_answers": "1 1 \\div 1 0 = \\frac { 1 1 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4744.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{sin}\\left(\\frac{x}{2}\\right) = \\frac{1}{2} $$\n\nThis formula states that the sine of half of a value is equal to half of that value.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n$\\textstyle 2x^2 - 3x - 1 = 0$\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n\u222b\u222b \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is: ( x^2 + 3x + 1)/ (x - 1) = x^2 + 3x.",
        "gt_answers": "S _ { n } - n ( 2 n - 1 ) a _ { n }\n",
        "image_path": "./data/HME100K/test_images/test_4748.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $ $\\frac{x+5}{x-3}=3$$.\n\nTo solve for x, we can divide both sides by $x-3$, giving us $\\frac{x+5}{x-3}=\\frac{3}{x-3}$$. Simplifying the right side, we get $\\frac{3}{x-3}=3$$.\n\nSubstituting this into the left side, we get $\\frac{x+5}{x-3}=3$$. Solving for x, we find that x=3, which is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 2 + 3x + 5y = 15, where x and y are variables.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\documentclass[a4paper, 12pt]{article}\n\n\\begin{document}\n\n\\begin{center}\n\\includegraphics[width=0.5\\textwidth]{image.png}\n\\end{center}\n\n\\end{document}\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{1}{2}(a + b)$ where a and b are the integers in the image.\n\nIn LaTeX format, the expression can be written as $\\frac{1}{2}(a + b)$.",
        "gt_answers": "y = - \\frac { 1 9 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4753.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is y = 5x + 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula in the image using LaTeX format, you can use the following LaTeX code:\n\n$$\\frac{1}{a + 2}$$\n\nwhere $a$ is the variable and 2 is the constant.\n\nThe formula represents the arithmetic mean of $a$ and 2.",
        "gt_answers": "a _ { 1 } = a _ { 3 } - 1 2\n",
        "image_path": "./data/HME100K/test_images/test_4755.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 5x + 3y = 10.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image:\n\n\\begin{center} $\\text{Image Content}$ \\end{center}\n\nThis is a LaTeX expression that represents the image content you provided, with the center alignment and the text \"Image Content\" in bold font.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation on the whiteboard in the image is:\n\n$$ (10 + 2) \\times (6 + 5) = 45$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "2 \\frac { 2 } { 4 } = a + \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4759.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression for the formula in the image:\n\n$$\\frac{1}{2} x^2 + \\frac{3}{4} x + \\frac{1}{8}$$\n\nThis formula is a quadratic equation with two variables, x and y. The constants 1/2, 3/4, and 1/8 represent the coefficients of the equation.\n\nI hope this helps! Let me know if you have any other questions.",
        "gt_answers": "x _ { 2 } = \\frac { 1 5 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4760.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the derivative of the function f(x) = x^3. The derivative is given by d/dx (x^3) = 3x^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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$x = \\frac{y - 3}{4} - \\frac{1}{3}$$\n\nThe variable x represents the width of the rectangle in the image and the variable y represents the height of the rectangle in the image. The numerator of the fraction is the difference between the height and 3, and the denominator is the difference between 4 and 3. This expression can be used to find the width of the rectangle in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 1 + 1 = 2.",
        "gt_answers": "P _ { A } = \\frac { F _ { A } } { 4 h ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_4763.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{1}{3} - \\frac{1}{5} = \\frac{1}{15}$$",
        "gt_answers": "\\frac { x + 1 } { 2 } - 1 = \\frac { 5 - x } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4764.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\text{200}\\times\\text{0.005} = \\text{10000}$$This formula is used to calculate the cost of goods sold in a company. It is calculated by multiplying the total cost of goods sold by the percentage of goods sold. The result is the cost of goods sold.",
        "gt_answers": "\\frac { 1 } { 8 } \\times 4 = \\frac { 4 } { 8 } \\frac { 2 } { 4 } \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4765.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$\\frac{x^2+y^2}{2xy}=\\frac{a^2+b^2}{2ab}$\n\\end{center}\n\nwhere x and y are the lengths of the two sides of a right triangle and a and b are the lengths of the hypotenuse and one of the other sides, respectively.",
        "gt_answers": "C P _ { 2 } = 5 , C P = 4\n",
        "image_path": "./data/HME100K/test_images/test_4768.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a multiplication of 5 and 7 with the result of 35.\n\nTo calculate this in LaTeX format, you can use the following expression:\n\n$ 5 \\times 7 = 35 $\n\nThis can be written in LaTeX as:\n\n$ 5 \\times 7 = 35 $\n\nNote that the multiplication symbol is represented by the letter \"x\" in LaTeX. The equal sign is represented by the letter \"=\".",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{1}{x} - \\frac{1}{x+1}$\n\nNote: The above expression is written using LaTeX format, where $x$ is the variable and $+$ is used for addition.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\frac{100 \\times 3}{100 + 25} = \\frac{300}{125} $$\n\nAlternatively, we can use the following LaTeX code to write the expression:\n\n$$ \\frac{100 \\times 3}{100 + 25} = \\frac{300}{125} $$",
        "gt_answers": "\\frac { x } { x - 1 } = y\n",
        "image_path": "./data/HME100K/test_images/test_4771.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n\\begin{center} $\\frac{1}{a+2b+4c+8d+16e+32f}$ \\end{center}\n\nNote: The variable names are a, b, c, d, e, and f.",
        "gt_answers": "1 1 . a \\div 1 2 , c \\times 1 2\n",
        "image_path": "./data/HME100K/test_images/test_4772.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ \\frac{1}{2}(2x + 3y) - 5$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you can follow these steps:\n\n1. Write the formula in LaTeX format: $\\frac{1}{2} \\times \\left(\\frac{3}{4}\\right)$\n2. Replace the variables with their numerical values: $\\frac{1}{2} \\times \\left(\\frac{3}{4}\\right)$\n3. Write the formula with the variable values: $\\frac{1}{2} \\times \\left(\\frac{3}{4}\\right)$\n\nSo the formula in LaTeX format is: $\\frac{1",
        "gt_answers": "x = \\frac { 3 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4774.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given as follows:\n\n&#x03BC;=&#x2212;(A&#x2212;B)+(C&#x2212;D)+&#x03D0;&#x2212;2(E&#x2212;F)+&#x03D0;&#x2212;3(G&#x2212;H)+&#x03C3;&#x2212;2(I&#x2212;J)+&#x03C",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: \\frac{x^2+x-5}{x+2}.",
        "gt_answers": "2 x = 1 \\frac { 1 } { 6 } - \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_4776.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2} - \\frac{1}{4}$.",
        "gt_answers": "2 \\sqrt { y + 5 } = y - 1 0\n",
        "image_path": "./data/HME100K/test_images/test_4777.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX format for the expression of the formula in the image:\n\n$$\\frac{2400 \\times 1.5 + 3600 \\times 0.8}{600 + 2400 \\times 0.3} = 1200$$\n\nIn this equation, the numerator is the product of two terms: 2400 \\* 1.5 and 3600 \\* 0.8. The denominator is the sum of two terms: 6",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows:\n\n\\begin{align\\*}\n\\frac{4\\times 3}{5\\times 2} &= \\frac{12}{10} \\\n&= \\frac{1}{1} \\\n&= 1\n\\end{align\\*}\n\nThis formula is derived by dividing the numerator (4\\*3) by the denominator (5\\*2), and then simplifying the fraction to its lowest terms. The final result is 1, indicating that the numerator is equal to the denominator.",
        "gt_answers": "C H _ { 3 } - C - C H _ { 2 } - C H _ { 3 } .\n",
        "image_path": "./data/HME100K/test_images/test_4779.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that.\n\nHere is the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\n& b = \\frac{a \\times (1 - a)}{1 - 2a}\\\\\n& c = \\frac{b \\times (1 - b)}{1 - 2b}\\\\\n& d = \\frac{c \\times (1 - c)}{1 - 2c}\n\\end{align\\*}\n\nIn words, this formula is saying that the values of b, c, and d can be calculated using the following steps:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$4x + 2y = 24$\n\\end{center}\n\nThis is a linear equation in two variables, with a constant term of 24. The equation represents a line in two dimensions, with a slope of 4x and an intercept of 2y. The solution to the equation is the set of points that satisfy the equation, which can be found by substituting the values of x and y into the equation and solving for x and y. For example, if x =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\text{The sum of the infinite geometric series } \\sum\\_{n=0}^{\\infty} \\frac{(-1)^n}{4^n}$$\n\nThe formula in the image is the infinite sum of the geometric series with the first term as $1$, common ratio as $-1$, and the index starting from $0$.\n\nNote: The image is not visible to me, as I am an AI language model and do not have the capability to view images.",
        "gt_answers": "\\Delta E C F \\sim \\Delta O F N\n",
        "image_path": "./data/HME100K/test_images/test_4783.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the slope of the line passing through the points (x1, y1) and (x2, y2) can be written as:\n\nm = (y2 - y1) / (x2 - x1)\n\nwhere m is the slope of the line, (x1, y1) is the first point and (x2, y2) is the second point.",
        "gt_answers": "m - 2 = ( 2 - m ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4785.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\frac{1}{2} x^2 + \\frac{1}{2} xy + \\frac{1}{2} y^2 = \\frac{1}{2} x^2 + \\frac{1}{2} xy + \\frac{1}{2} y^2$$\n\nThis is a quadratic formula with the variable x representing the width and y representing the height. The coefficients are 1/2 for both the square of x and the square of y.",
        "gt_answers": "2 N a O H + C O _ { 2 } = N a _ { 2 } C O _ { 3 } + H _ { 2 } O\n",
        "image_path": "./data/HME100K/test_images/test_4786.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the formula in the image using LaTeX format is:\n\n$$\\text{f(x) = \\frac{a}{b} \\sin^c x + \\frac{d}{e} \\cos^d x}$$\n\nwhere `a`, `b`, `c`, `d`, `e` and `f(x)` are constants. The formula represents a nonlinear differential equation of order 2 with constant coefficients.",
        "gt_answers": "x = \\frac { 8 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4787.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$$ m = \\frac{50 \\%}{5} $$\n\nThe expression represents a percentage of a given quantity. The numerator is $50$% of the quantity, while the denominator is $5$%. The percentage value can be expressed as a decimal, fraction or ratio.",
        "gt_answers": "4 . 0 5 m ^ { 3 } = ( 4 ) m ^ { 3 } ( 5 0 ) d m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4788.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The expression for the given image is: $\\frac{x^{2}}{2x+1}$.",
        "gt_answers": "S _ { n } = n ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4789.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$\\frac{x+3}{2x-1}$$\n\nwhere x is any variable.",
        "gt_answers": "x = \\frac { 4 5 } { 5 4 } - \\frac { 4 2 } { 5 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4790.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 5 + 3 + 5 + 5 + 5 + 5 + 2 + 5 + 2 + 2 = 30.",
        "gt_answers": "S _ { 5 } = 5 ^ { 2 } = 2 5 .\n",
        "image_path": "./data/HME100K/test_images/test_4791.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{E} = \\frac{1}{2}mv^2 $$\n\nwhere E is the energy, m is the mass, and v is the velocity of the object.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the volume of a cylinder is:\n\nV = (\u03c0r\u00b2h) / 4\n\nWhere r is the radius of the cylinder and h is its height. The formula gives the volume of a cylinder with a radius of 5cm and a height of 10cm.\n\nUsing the given values for r and h in the formula:\n\nV = (\u03c0 \\* 5\u00b2 \\* 10) / 4\n\nV = \u03c0 \\* 25 \\* 10\n\nV = 500\u03c0\n\nThe",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: $ (m + 2) \\times (n - 1) + 4 = m \\times n - 3 $",
        "gt_answers": "( \\frac { 1 } { m } + \\frac { 1 } { 1 - m } ) ( m + 1 - m )\n",
        "image_path": "./data/HME100K/test_images/test_4794.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the given expression:\n\n\\frac{5y+3}{2y-1} = \\frac{3}{2}\n\nThe expression is a rational expression, which means it can be simplified by dividing both numerator and denominator by a common factor. In this case, the common factor is 2y-1.\n\nSo, the simplified expression is:\n\n\\frac{5y+3}{2y-1} = \\frac{3}{2} = 1.5 + \\frac{3}{2y-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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is \\frac{sin(x)}{x^2} - \\frac{2cos(x)}{x^2}. The numerator is the product of the sine and cosine of x raised to the first power, and the denominator is the square of x raised to the first power. The formula is derived from the identity \\frac{d}{dx} \\sin(x) = \\cos(x) and the chain rule of differentiation.\n\nIn LaTeX format, the formula would be written as:\n\n$$\\frac{\\sin(x)}{x^2} - \\",
        "gt_answers": "x = 7 \\div \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4796.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is written as:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "O E = \\frac { 6 \\sqrt { 3 } . } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4798.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle is given by:\n\nA = l x w\n\nwhere l is the length and w is the width. The length and width of a rectangle are given by:\n\nl = 4/3 \\* 3\nw = 4/3 \\* 2\n\nTherefore, the area of the rectangle is:\n\nA = l x w = (4/3 \\* 3) x (4/3 \\* 2) = 4/9 \\* 8/3 = 4/3\n\nSo, the area of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written as follows:\n\nlatex format\n\n$$ \\frac{dV}{dt} = \\frac{Q}{C} $$\n\nwhere $V$ is the volume of the capacitor, $Q$ is the charge stored in the capacitor, and $C$ is the capacitance of the capacitor.\n\nThe expression represents the rate of change of volume with respect to time, which is equal to the ratio of the charge stored in the capacitor to its capacitance. This is a basic formula in capacitor physics and electrical engineering.",
        "gt_answers": "a ^ { 2 } + b ^ { 2 } > c ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4802.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for finding the missing number in the image is 2x4+5=14. The missing number is 5.",
        "gt_answers": "\\frac { 5 } { - 1 } = \\frac { x + 4 } { x + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4803.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is $\\frac{4}{3}$.\n\nThe expression for the image is:$$\\frac{4}{3}$$",
        "gt_answers": "\\frac { x - 4 } { 2 x } = 0\n",
        "image_path": "./data/HME100K/test_images/test_4804.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: x + 4y - 3z = 12x + 3y - 5z = 12x + 3y + 2z = 14x + 2y + 3z = 14x + 3y + 4z = 16x + 3y + 5z = 16x + 5y + 4z = 20x + 5y + 6z = 20x + 6y + 6z = 26x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX format of the expression:$$\\text{0.45}\\times\\left(\\frac{1}{2}\\right) + \\text{0.03}\\times\\left(\\frac{1}{2}\\right) - \\text{0.05}\\times\\left(\\frac{1}{2}\\right) = \\frac{3.60}{2}$$In this expression, the term on the left is multiplied by 0.45 and 0.03, and then added to the term on the right,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$\\text{2a + 5b = 8}$$\n$$\\text{2x + 5y = 8}$$\n$$\\text{2(a + b) + 5(x + y) = 8}$$\n$$\\text{2a + 2b + 5x + 5y = 8}$$\n$$\\text{2(a + b) + 5(x + y) = 8}$$\n$$\\text{2a + 2b + 5x + 5y = 8}$$\n$$\\text",
        "gt_answers": "\\angle 1 + \\angle 3 = \\angle B C A = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4808.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the given formula in LaTeX format, we can use the following syntax:\n\n$$\\text{hp} = \\frac{3.545 \\times 10^7 \\text{N}}{5.34 \\times 10^3 \\text{kg}\\times \\frac{1}{2}} = \\frac{6.89 \\times 10^4 \\text{N}\\text{s}}{5.34 \\times 10^3 \\text{kg}}$$\n\nwhere $\\text{hp}$ represents the power in horsepower,",
        "gt_answers": "H P = A P = x , C P = 1 0 - 7\n",
        "image_path": "./data/HME100K/test_images/test_4809.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given by the equation: (x + y) / (x - y) = 2x.\n\nThis formula can be read as \"two times the sum of x and y, divided by the difference of x and y, is equal to two times x\". The equation represents the slope of a line between two points in the Cartesian plane.",
        "gt_answers": "\\frac { 3 } { 4 . } - \\frac { 1 } { 4 } = \\frac { 2 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4810.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "\\angle A = \\angle C = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4811.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a formula for the number of integers from 1 to 10 that are multiples of 3. To write it out using LaTeX format, we can use the following equation:\n\n$$\\sum\\_{i=1}^{10} (i\\ mod 3) = 1+2+3+4+5+6+7+8+9+10 = 45$$\n\nThis equation uses the modulus operator (``%``) to find the remainder of each integer from 1 to 10 when divided by 3, and then adds",
        "gt_answers": "B H = 1 + \\frac { \\sqrt { 3 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4813.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b(\u222b",
        "gt_answers": "a _ { n } = n a _ { n + 1 } - n a _ { n }\n",
        "image_path": "./data/HME100K/test_images/test_4814.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{a+b}{c-d}$.",
        "gt_answers": "\\cos A = \\frac { \\sqrt { 3 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4815.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, you would need to write the equation as follows:\n\nLet the image be denoted by $x$. Then, the sum of the areas of the two triangles is given by:\n\n$$\\begin{aligned}x&=500\\\ny&=200\\\nz&=100\\\nArea(x)+Area(y)+Area(z)&=500+200+100&=1000\\end{aligned}$$\nTherefore, the sum of the areas of the two triangles",
        "gt_answers": "( 5 . 4 - 3 . 6 ) x + 6 \\cdot \\frac { 1 5 2 0 } { 8 } - 3 . 6 x \\geq 1 0 5 0\n",
        "image_path": "./data/HME100K/test_images/test_4817.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$x = \\frac{4+3i}{2-1i}$$\n\nwhere $x$ is the variable, $4+3i$ is the numerator and $2-1i$ is the denominator.",
        "gt_answers": "5 4 - x = \\frac { 1 } { 3 } ( 6 6 - x )\n",
        "image_path": "./data/HME100K/test_images/test_4819.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a leaf is given by the equation 1. The equation can be written in LaTeX format as:$$E = \\frac{A}{V}$$where E is the energy stored in the leaf, A is the area of the leaf, and V is the volume of the leaf. The formula shows that the energy stored in a leaf is directly proportional to its area and inversely proportional to its volume. This means that a larger leaf has more energy stored in it than a smaller leaf, but it takes up more space.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a derivative of the exponential function y = a^x with respect to x. The derivative is expressed as: dy/dx = a^x \\* ln(a) dx/dx = x \\* a^(x - 1).",
        "gt_answers": "1 y = 5\n",
        "image_path": "./data/HME100K/test_images/test_4821.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by the formula $\\ A = \\pi r^2$, where r is the radius of the circle. The area of the circle in the image is given by the formula $\\ A = 3.14 \\* 0.5^2 = 0.785$ square inches.",
        "gt_answers": "a + \\sqrt { a ^ { 2 } + 1 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_4822.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a width of 5 inches and a height of 7 inches is A = (5 in x 7 in) = 35 in^2.",
        "gt_answers": "u = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4824.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\nx2+y2=r22+y2\u2212x2x2+y2=r22+y2\u2212x2x^2 + y^2 = r^2 - \\frac{x^2}{y^2} + y^2 - \\frac{x^2}{y^2}x2\u200b+y2\u200b=r2\u200b2+y2\u200b\u2212x2\u200b\\frac{x^2}{y^2} + y^2 - \\frac{x^2}{y^",
        "gt_answers": "x = - 2\n",
        "image_path": "./data/HME100K/test_images/test_4828.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression for the integral of the Gaussian distribution. The expression is written as follows:\n\n\u222b(x - \u03bc)2dx, where \u03bc is the mean of the Gaussian distribution and x is the variable of integration.",
        "gt_answers": "x - 3 x = 6 x = 2 - 3 + 1 0 J .\n",
        "image_path": "./data/HME100K/test_images/test_4829.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: a = (b/d) \u00d7 (c/d).",
        "gt_answers": "\\frac { A B } { P D } = \\frac { B D } { C D }\n",
        "image_path": "./data/HME100K/test_images/test_4830.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $\\frac{a^2 + b^2}{2a} + 2b$ where $a$ and $b$ are the lengths of the sides of the rectangle.",
        "gt_answers": "\\angle E C F = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4831.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I can't see any image in the text provided. Can you please provide the image?",
        "gt_answers": "F \\bot B P\n",
        "image_path": "./data/HME100K/test_images/test_4832.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as:$\\frac{1}{2}+\\frac{3}{4}=\\frac{7}{8}$\n\nThis equation shows that the sum of $\\frac{1}{2}$ and $\\frac{3}{4}$ is equal to $\\frac{7}{8}$",
        "gt_answers": "a > \\frac { 6 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4833.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle can be written as:\n\nA = (1/2)bh, where b is the base of the triangle and h is the height.\n\nIn the given image, the base of the triangle is 30 cm and the height is 15 cm. Therefore, the area of the triangle is:\n\nA = (1/2) \\* 30 cm \\* 15 cm = 150 square cm.\n\nSo the area of the triangle is 150 square cm.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\frac{a+b+c}{5}\n```",
        "gt_answers": "a + b = \\frac { 5 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_4835.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is:\n\nA = \u03c0r^2, where r is the radius of the circle.\n\nIn this image, the radius of the circle is 2cm. To find the area of the circle, we would divide the circumference of the circle by \u03c0:\n\nA = \u03c0r^2\n= \u03c0(2)^2\n= 8\u03c0\n\nTherefore, the area of the circle is 8\u03c0 square units.",
        "gt_answers": "x _ { 1 } < x _ { 2 } < x _ { 3 } - : a > 0 , b < 0 .\n",
        "image_path": "./data/HME100K/test_images/test_4836.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the derivative of the exponential function f(x) = 4ex. It can be written as follows:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression for the formula in the image:\n\n\\begin{align}\n6000 &x; 4 \\u m \\\n\n= 6000\\u m \\\n\n= 6000 \\* 10^4 \\\n\n= 6,000,000 \\\n\n= 6,000,000 \\* 1 \\\n\n= 6,000,001 \\\n\n= 6,000,001 \\* 1 \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{100}{250}+\\frac{250}{500}=\\frac{150}{500}$$This formula calculates the sum of two fractions, with the numerator being 100 and the denominator being 250, and the second fraction having a numerator of 250 and a denominator of 500. The result is the sum of the two fractions, which is 150/500.",
        "gt_answers": "x > \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4839.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222babf(x)dx\u222bcdf(x)dx=\u222babf(x)dx\u222bcdf(x)dx=\u222bc(a, b)\u222bc(a, b)f(x)dx+\u222bc(b, c)\u222bc(b, c)f(x)dx+\u222bc(c, d)\u222bc(c, d)f(x)dx\\int\\_a^b f(x)dx\\int\\_c^d f(x)dx = \\",
        "gt_answers": "B D = O D = O C = O B = O C\n",
        "image_path": "./data/HME100K/test_images/test_4840.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image you provided does not contain any mathematical expression or formula. It appears to be a blackboard with some writing on it, but there is no mathematical content to work with.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is 2x^2 - 6x + 8.",
        "gt_answers": "y = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4842.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format.\n\nThe image shows a formula for a rectangular coordinate system with three axes: x, y, and z. The formula is written in a mathematical notation that includes the coordinates of each point, the distance between each point, and the angle between each pair of points.\n\nThe formula is as follows:\n\n(x1, y1, z1) = (0, 0, 0)\n(x2, y2, z2) = (1, 1, 1)\n(x3",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\text{p} = \\frac{1}{2}(3x + 4y)$",
        "gt_answers": "\\vert t \\vert t = 2 k \\pi + \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4847.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am unable to see the image as it is not provided. Please provide the image so I can assist you with the LaTeX format.",
        "gt_answers": "9 6 + 1 6 = 1 1 2 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_4848.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is given by:\n\n![](https://www.mathworks.com/help/matlab/ref/imread-function.html)\n\nwhere the image path is specified as an array of characters separated by forward slashes, and the output image is returned as a two-dimensional array.\n\n![](https://www.mathworks.com/help/matlab/ref/imread-function.html)\n\nwhere the image path is specified as an array of characters separated by forward slashes, and the output image is returned as a two-dimensional",
        "gt_answers": "\\frac { x } { 4 } = 1 2\n",
        "image_path": "./data/HME100K/test_images/test_4849.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{ImageContent} = \\frac{a+b}{c+d} $$\n\nwhere `a`, `b`, `c`, and `d` are constants.",
        "gt_answers": "V = I _ { 1 } R _ { 1 } = 3 A \\times 4 W = 1 2 V\n",
        "image_path": "./data/HME100K/test_images/test_4850.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{1}{2}$$\n\nwhich is the formula for the sum of the angles in a triangle.",
        "gt_answers": "k = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4851.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{4}\\left(5 + \\frac{3}{5}\\right) = \\frac{5}{12}$. This formula can be rearranged as $\\frac{1}{4}\\left(5 + \\frac{3}{5}\\right) = \\frac{5}{12}$ using the distributive property of multiplication and addition, where $\\frac{1}{4}$ is the common denominator for both terms.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the number of moles in a sample of a compound is given by:\n\nn = V / Vm\n\nwhere V is the volume of the sample and Vm is the molar volume of the compound.\n\nUsing the given volume of 0.25 L and molar mass of 120 g/mol for C6H12O6, we can calculate the number of moles of glucose in the sample:\n\nn = 0.25 L / 180.16 g/mol = 1.3",
        "gt_answers": "\\vert a \\vert + 1 = 2\n",
        "image_path": "./data/HME100K/test_images/test_4854.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as:A=\u03c0r^2where A is the area, r is the radius, and \u03c0 is the constant value of 3.14. In LaTeX format, the formula can be written as:A=\u03c0r^2A = \\frac{\\pi}{r^2}where A is the area, r is the radius, and \u03c0 is the constant value of 3.14.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:4x + 3y = 5. The variable values are x = 4 and y = 3.\n\nThe formula is a linear equation in two variables. The slope of the line is m = 4/3, and the y-intercept is b = 5. The equation can be written in slope-intercept form as:y = mx + b.\n\nTo find the value of the variable b, we substitute x = 0 into the equation and solve for y. This gives us y = 5/3. Therefore,",
        "gt_answers": "x _ { 4 } = - \\frac { 9 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4856.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n$$\\frac{5+6+8+9+10}{5\\times 6\\times 7\\times 8\\times 9}$$\n\nwhich simplifies to:\n\n$$\\frac{35}{35\\times 35\\times 35\\times 35}$$\n\nwhich simplifies further to:\n\n$$\\frac{1}{35\\times 35\\times 35\\times 35}$$\n\nwhich is equal to:\n\n$$\\frac{1}{122",
        "gt_answers": "x = \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4857.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{1}{5}+\\frac{2}{7}+\\frac{3}{9}+\\frac{4}{11}+\\frac{5}{13}+\\frac{6}{15}+\\frac{7}{17}+\\frac{8}{19}+\\frac{9}{21}+\\frac{10}{23}+\\frac{11}{25}+\\frac{12}{27}+\\frac{13}{29}+\\frac{14}{31}+\\frac{15}{33}+\\frac{16}{35}+\\frac{",
        "gt_answers": "1 . 3 7 5 x = - 2 . 7 5\n",
        "image_path": "./data/HME100K/test_images/test_4858.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed as follows in LaTeX format:\n\n\\begin{center}\n$A = \\pi r^2$\n\\end{center}\n\nwhere $A$ is the area of the circle and $r$ is its radius.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as:\n\nA = pi \\* r^2,\n\nwhere A is the area, pi is a constant equal to 3.14, and r is the radius of the circle.",
        "gt_answers": "D E = 2 \\sqrt { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4860.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$\\frac{3x + 5y - 7z}{2x + 4y - 6z}$$This formula can be read as the ratio of the sum of the coefficients of the equation to the sum of the coefficients of the denominator, with the coefficients of the numerator and denominator being multiplied by 2 and 4, respectively.",
        "gt_answers": "R = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4861.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the given formula using LaTeX format, we need to use the syntax for multiplication and addition.\n\nFor multiplication, we use the multiplication symbol \"x\" and the exponents of the variables involved. For example, if we want to write out the expression for 2x^2 + 4x + 6, we would use the following syntax:\n\n2x^2 + 4x + 6\n\nFor addition, we use the plus symbol \"+\". For example, if we want to write out the expression for 3 + 4x + 5, we would use",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $ 2x + 3 = 7x + 5 $\n\nTo solve for x, we can simplify the equation by dividing both sides by 2:\n\n$$ \\frac{2x + 3}{2} = \\frac{7x + 5}{2} $$\n\n$$ \\boxed{x + \\frac{3}{2} = \\frac{7}{2}x + \\frac{5}{2}} $$\n\nSubstituting $u = x + \\frac{3}{2}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula for the expression in the image is:\n\n$$ \\text{Image Content} = \\frac{1}{2} \\left( \\frac{1}{3} x^2 + \\frac{1}{2} x - \\frac{1}{6}\\right) $$\n\nThis formula represents the image content of a rectangular box with width $x$ and height $3x$. The expression inside the parentheses represents the area of the box, which is $\\frac{1}{3}x^2$ for the top half of the box and $\\frac{1}{2}x$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{align}\nA = \\frac{B}{C}\n\\end{align}\n\\end{center}\n\nwhere A, B, and C are the lengths of the three sides of the triangle.",
        "gt_answers": "\\frac { 7 x } { 2 0 } = \\frac { x } { 5 } + 3\n",
        "image_path": "./data/HME100K/test_images/test_4865.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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\\begin{align}\n&x + 2y - 3z = 12 \\\n\\end{align}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 1+1=2.",
        "gt_answers": "x = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4867.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{center}\n$\\frac{1}{\\sqrt{4m^2+h^2}}$\n\\end{center}\n\nThis formula represents the time it takes for an object to fall from rest to the ground, assuming a constant acceleration due to gravity.",
        "gt_answers": "( 5 + 1 ) \\times 2 = 1 2 c m\n",
        "image_path": "./data/HME100K/test_images/test_4868.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is $1 + 2x - 3y$.",
        "gt_answers": "x = - \\frac { 1 5 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4869.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: $\\frac{4}{x} = \\frac{2\\times 5}{3}$. This can be rewritten in LaTeX format as: $\\frac{4}{x} = \\frac{2\\times 5}{3}$.\n\nThis formula can be used to solve the problem shown in the image. To use it, we first find the value of $x$ that satisfies the equation. This is done by multiplying both sides of the equation by $x$ and simplifying: $\\frac{4x}{x} = \\frac{2x\\times 5}{3",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is an expression of the formula using LaTeX format:\n\n\\begin{equation}\n(x + 2y) \\cdot (3x + y) = 3(x + y)^2 + 2xy + y^2\n\\end{equation}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a line segment AB with endpoints A and B, and a point C on the line segment AB such that the distance from C to A is equal to the distance from C to B. The equation for the distance from C to A is given by AB^2 + AC^2 = AB^2 + BC^2, which simplifies to AC = AB/sqrt(2). The equation for the distance from C to B is given by BC^2 = AC^2 + AB^2, which simplifies to BC = AB/sqrt(2).\n\nThe line segment AB is defined by the point",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in the image using LaTeX format, you can use the following steps:\n\n1. Open a LaTeX editor, such as TeXstudio or Overleaf.\n2. Paste the image into the editor.\n3. Select the equation in the image that you want to write in LaTeX format.\n4. Click on the equation to highlight it.\n5. In the editor, replace the equation with the LaTeX code that corresponds to the equation.\n6. Press enter to generate the LaTeX code for the equation.\n\nThe LaTeX code for the formula in the image would be:",
        "gt_answers": "\\frac { 3 + x + a } { x - a - 2 } = \\frac { 7 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4875.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with base length l and height h is A = lh.\n\nUsing LaTeX format, we can write the formula as:\n\n$$A = lh$$\n\nwhere l is the base length and h is the height of the rectangle.",
        "gt_answers": "\\cos B = \\frac { 4 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4877.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\nsin(x) = tan(x)cos(x)cos(x)tan(x)cos(x)sin(x)",
        "gt_answers": ": V = ( \\pi r ^ { 2 } ) h\n",
        "image_path": "./data/HME100K/test_images/test_4878.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$x = \\frac{5a}{b}$$where $a$ and $b$ are integers.",
        "gt_answers": "\\frac { x } { 1 5 } = \\frac { 1 . 5 } { 0 . 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4879.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x2 + 2x + 3.",
        "gt_answers": "x = 2 a - 3 = a\n",
        "image_path": "./data/HME100K/test_images/test_4880.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{4b} + \\frac{300}{40} = \\frac{360}{40}$$\n\nThe above equation is a statement of the formula in the image, where the variable `b' is the height of the image and the variable `40' is the width of the image. The expression calculates the area of the image, which is the product of the width and height of the image.",
        "gt_answers": "\\angle B = 1 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4881.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$s\\_x = \\frac{4x^2 + 9x - 8}{2x + 4}$$",
        "gt_answers": "S _ { 8 } = [ ( - 4 ) + ( - 1 8 ) ] \\times 4 = - 8 8\n",
        "image_path": "./data/HME100K/test_images/test_4882.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the expression in the image:\n\n$$ \\frac{10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "gt_answers": ": 2 0 0 \\times 1 0 0 = 2 0 0 0 0 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_4883.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle is given by:\n\nA = \u03c0r^2\n\nwhere A is the area of the circle, r is the radius of the circle, and \u03c0 is the mathematical constant approximately equal to 3.14159.",
        "gt_answers": "a \\neq \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_4884.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is written as: $\\frac{dv}{dt} = \\frac{k}{m}$ where v is the velocity of the object, k is the spring constant, and m is the mass of the object.",
        "gt_answers": "\\angle B O D = \\angle D O C : 6 0\n",
        "image_path": "./data/HME100K/test_images/test_4886.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula: 1 - ( 1 - x )^2 + x.\n\nThe expression can be written in LaTeX format as follows:\n\n$$\\left(1 - \\frac{1}{x}\\right)^2 + x$$\n\nThe variable x is used in the formula to represent the current time period. The formula calculates the expected value of the time period based on the previous time period's value, using the formula 1 - ( 1 - x )^2 + x. This formula is commonly used in finance to calculate the present value of an investment.##",
        "gt_answers": "x + y - 3 = 0\n",
        "image_path": "./data/HME100K/test_images/test_4887.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the expression:$$\\frac{60000 - 12000}{5000} = \\frac{100000 - 12000}{5000} = 10000$$This means that the number obtained by subtracting 12000 from 60000 is divided by 5000 to obtain 10000.",
        "gt_answers": "0 . 0 6 = \\frac { 6 0 } { 1 0 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4888.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: (2x + 5) / (x + 3) = 5x - 7.",
        "gt_answers": "x - 1 = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4889.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image using LaTeX format is: 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + 1 / 32 + 1 / 64 + 1 / 128 = 1/128.\n\nThe formula can be written in LaTeX format as: $\\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} + \\frac{1}{32} + \\frac{1}{64",
        "gt_answers": "D E = \\frac { 1 } { 2 } B C\n",
        "image_path": "./data/HME100K/test_images/test_4890.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$ 3x^2 - (2x - 3)^2 = 9 $\n\nThis can be derived by applying the formula for the square of a binomial, which is given by:\n\n$ a^2 = a(a+b) $\n\nwhere a and b are the terms of the binomial. Applying this formula to the binomial expression $3x^2 - (2x - 3)^2$, we get:\n\n$ 3x^2 - (2x - 3)^2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{\\frac{2\\pi^2}{3}-\\sqrt{5}}{\\sqrt{15}-\\sqrt{2}}$$",
        "gt_answers": "\\frac { D C } { D E } = \\frac { D O } { D B }\n",
        "image_path": "./data/HME100K/test_images/test_4892.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{mass of } \\ce{CH3CH2OH} = \\frac{moles\\_{water} \\times molar\\_{mass\\_{water}}}{moles\\_{alcohol} \\times molar\\_{mass\\_{alcohol}}}$$\n\nwhere $\\ce{CH3CH2OH}$ is the solution containing alcohol and water, and $\\ce{molar\\_{mass\\_{water}}}$ and $\\ce{moles\\_{water}}$ are the molar mass and number of moles of",
        "gt_answers": "n _ { o 2 } = \\frac { m _ { o 2 } } { M _ { o 2 } } = \\frac { 3 . 2 g } { 3 2 g / m o l } = 0 . 1 m o l\n",
        "image_path": "./data/HME100K/test_images/test_4894.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the number 7 in the image is:\n\n7/5 = 14/10 = 1 1/2\n\nThis is a fraction that represents the quotient of dividing 7 by 5. The numerator is 7 and the denominator is 5. When this fraction is reduced to its lowest terms, it becomes 1 1/2.",
        "gt_answers": "\\frac { 7 } { 9 } - \\frac { 5 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_4895.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} \\text{a} + \\text{bc} = \\frac{\\text{a}}{\\text{b} + \\text{c}} \\end{aligned}$$\n\nThis formula represents the addition of the numbers a, b, and c, with the result being the ratio of a to the sum of b and c.",
        "gt_answers": "A C \\bot B C\n",
        "image_path": "./data/HME100K/test_images/test_4896.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is not shown in the image, so it cannot be written in LaTeX format.\n\nHowever, assuming that the formula in the image is a^2 + b^2 = c^2, where a, b, and c are variables, we can write it in LaTeX format as follows:\n\n$$ a^2 + b^2 = c^2 $$\n\nIn this formula, the variables a, b, and c are used to represent the squared values of the sides of a right triangle, and the equation states that the sum of the squares of the sides is equal to the square",
        "gt_answers": "A E = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4897.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$$ \\text{diameter} = \\sqrt{\\left(\\frac{a}{2}\\right)^2 + \\left(\\frac{b}{2}\\right)^2}$$\n\nwhere a and b are the length of the two sides of the square.",
        "gt_answers": "\\angle C P A = 9 0 ^ { \\circ } \\therefore \\Delta A B C \\sim \\Delta A C D\n",
        "image_path": "./data/HME100K/test_images/test_4898.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image using LaTeX format is:\n\n$$\\sin(x) = \\frac{e^x - e^{-x}}{2}$$\n\nwhere $x$ is the angle whose sine is being computed.",
        "gt_answers": "\\sin x = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4899.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "( b - 2 ) ( b - 5 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_4900.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the number of integers in the image, we can write the equation as:$$3x^2+2x+1=0$$This equation represents a quadratic equation with three terms, where the coefficients are $3$, $2$, and $1$. The solutions to the equation are the integers that satisfy it, which are $-3$, $-2$, and $-1$.\n\nTo solve the equation, we can use the quadratic formula:$$x = -\\frac{b\\pm\\sqrt{b^2-4ac}}{2a}$$where $a=3$, $b=2$, and $c",
        "gt_answers": "\\frac { 3 } { 4 } \\times 1 . 2 = \\frac { 9 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4901.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 64x^4 + 32x^3 + 8x^2 + 2x + 1 $$\n\nwhere x is the variable and the coefficient 64, 32, 8, 2 and 1 are the constants.",
        "gt_answers": "x = \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_4903.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by A = l \u00d7 w, where l is the length and w is the width.\n\nThe area of the rectangle in the image can be calculated as follows:\n\nA = 10 \u00d7 5 = 50 cm\u00b2\nTherefore, the area of the rectangle in the image is 50 cm\u00b2.",
        "gt_answers": "y _ { 1 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4904.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a function of x, which is represented by the variable x. The function has three solutions, x=0, x=3, and x=4. The function is a quadratic function with a constant value of 3 and a leading coefficient of 2. The solutions can be found by solving the quadratic equation: 2x^2 - 5x + 3 = 0.\n\nThe solutions to the equation are x = 3 and x = 4. The solutions can be found by using the quadratic formula: x = (-b +/- sqrt(b^2 -",
        "gt_answers": "\\frac { 3 } { 4 } : \\frac { 3 } { 5 } = \\frac { 5 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4905.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = \\frac{c^2}{d^2}$ where $x$ and $y$ are the coordinates of the image and $a$, $b$, $c$, and $d$ are the sides of the image.",
        "gt_answers": "\\frac { 3 } { 2 } \\vert m \\vert + 3\n",
        "image_path": "./data/HME100K/test_images/test_4906.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as follows: A = \u03c0r^2, where r is the radius of the circle. The area of the circle in the image is \u03c0(3 - 2)^2 = \u03c0(5 - 2)^2 = \u03c0(3 - 2)^2 = \u03c0(5 - 2)^2 = \u03c0(3 - 2)^2 = \u03c0r^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear, so it cannot be written in LaTeX format.\n\nHowever, assuming that the formula is in the form of `a = b + c`, we can write it in LaTeX format as follows:\n\n`a = b + c`\n\nwhere `a`, `b`, and `c` are variables or expressions representing the quantities in the formula.",
        "gt_answers": "x _ { 1 } = 4 x _ { 2 } = - 3\n",
        "image_path": "./data/HME100K/test_images/test_4910.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image provided is not a mathematical expression, it's just a blackboard with some mathematical formulas written on it. If you could provide a mathematical expression, I would be happy to write it out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by A = l \\* w, where l is the length and w is the width. The area of the rectangle in the image is A = 4 \\* 2 = 8 cm^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{4}{5}x^2 + \\frac{1}{5}x - \\frac{4}{5}$.",
        "gt_answers": "y _ { 4 } = - \\frac { 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4913.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle with sides of 5 and 6 is:\n\nA = (1/2) \\* (5^2 + 6^2)\n= (1/2) \\* (25 + 36)\n= (1/2) \\* 61\n= 30.5\n\nTherefore, the area of the triangle is 30.5 square units.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{center}\n\\frac{4x + 3y - 5z}{x + y - z} = \\frac{4}{x + y - z}\n\\end{center}\n\nThis expression represents the equation of the line passing through the points A(1, 0, 0), B(4, 3, 5), and C(1, 3, 0) in the three-dimensional Cartesian coordinate system. The equation is in the form of a ratio of polynomials with a common denominator",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX format for the given formula:\n\n\\begin{equation}\n\\frac{1}{3}\\left(4x^2+4x+1\\right) = \\frac{1}{3}(12x^2+12x+3)\n\\end{equation}",
        "gt_answers": "x ^ { 2 } - x = \\frac { 9 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_4917.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$ \\frac{1}{2} \\left( x^2 + y^2 \\right) + \\frac{1}{4} \\left( 3x^2 - 4xy + y^2 \\right) + \\frac{1}{4} \\left( 3y^2 - 4xy + x^2 \\right) $$\n\nThis formula represents the expression in the image as a function of the variables x and y. The expression can be interpreted as the sum of the areas of the two rectangles with base (x",
        "gt_answers": "A E \\bot B C\n",
        "image_path": "./data/HME100K/test_images/test_4918.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I don't have access to the image you provided. Without the image, I am unable to complete this task. Can you please provide the image so I can assist you?",
        "gt_answers": "\\frac { 1 5 } { 1 0 0 } x - \\frac { 9 } { 1 0 0 } = \\frac { 7 } { 1 0 0 } x + \\frac { 3 1 } { 1 0 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4919.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n$$\\text{f(x) = \\frac{1}{2} x^2 + 4$$}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\n<latex>a^2 + b^2 = (a + b)^2</latex>\n\nThe variables a and b are defined as the coordinates of the points at which the line intersects the x-axis and y-axis, respectively. The equation represents the distance between the two points on the line.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2x + 3y = 7. This can be written as: 2x + 3y = 7, or 2x + 3y = 7.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image can be represented as follows:\n\n$A = \\frac{B}{C}$\n\nwhere A, B, and C are constants. The expression represents a proportional relationship between A, B, and C, where the value of A is proportional to the values of B and C.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that! Here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}a&=\\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",
        "gt_answers": "x _ { 1 } , - 2 8 x _ { 2 } ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4924.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```",
        "gt_answers": "\\angle A = 4 6 ^ { \\circ } , \\angle B = 4 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4925.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: \\frac{245 - 144}{356 - 224}\n\nExplanation:\n\nThe given expression is a formula to calculate the average of two sets of numbers. The two sets of numbers are given by the two fractions in the formula:\n\n\\frac{a}{b} and \\frac{c}{d}\n\nThe average of these two sets of numbers can be calculated by finding the sum of the numerators and denominators, and then dividing by the sum of the denominators:",
        "gt_answers": "[ 2 ( x + 3 ) - 3 ( x - 3 ) ] = 9\n",
        "image_path": "./data/HME100K/test_images/test_4927.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is: $\\frac{1}{2}\\cdot\\frac{1}{4}\\cdot\\frac{1}{8}\\cdot\\frac{1}{16}\\cdot\\frac{1}{32}$ or $\\frac{1}{8}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the volume of a cone with radius $r$ and height $h$ can be expressed as:\n\nV = $\\frac{1}{3}$\u03c0r^2h\n\nwhere $V$ is the volume of the cone and $\\frac{1}{3}$\u03c0 is the volume of a sphere with the same radius $r$.\n\nThe formula for the volume of a sphere with radius $r$ can be expressed as:\n\nV = $4\\pi$r^3\n\nwhere $V$ is the volume of the sphere.\n\nTherefore, the formula for the volume",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I'm unable to see the image as there's no image provided. Can you please provide the image so that I can help you?",
        "gt_answers": "x - \\frac { 1 } { 3 } x = \\frac { 2 } { 3 } x\n",
        "image_path": "./data/HME100K/test_images/test_4931.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{aligned}\nf(x) &= x^2 + 4x - 8 \\\n&= (x + 2)^2 - 8 \\\n&= (x + 2 + 2)(x + 2 - 4) \\\n&= x^2 + 6x + 4 - 8 \\\n&= x^2 + 6x - 4\n\\end{aligned}\n```",
        "gt_answers": "f ( - x ) = f ( x )\n",
        "image_path": "./data/HME100K/test_images/test_4932.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ x = \\frac{3}{4} $$\n\nTo write this expression in LaTeX format, we can use the following code:\n\n$$ x = \\frac{3}{4} $$\nIn LaTeX, we use the fraction bar (/) to denote the fraction and the division operator (/) to separate the numerator and denominator. The numerator and denominator are enclosed in parentheses to denote the order of operations.\n\nNote that the variable x is defined as the numerator of the fraction, while the constant value 3 is defined",
        "gt_answers": "y _ { 1 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4933.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n$\\frac{d^2 x}{dt^2} + \\frac{2g}{m} \\frac{dx}{dt} + \\frac{g^2}{m^2} x = \\frac{k}{m} x^2$\n```",
        "gt_answers": "D F = F C = \\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_4934.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 3x - 2y = 5 $$",
        "gt_answers": "x _ { 1 } = - \\frac { 2 } { 3 } x _ { 2 } = - 4\n",
        "image_path": "./data/HME100K/test_images/test_4935.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 16x + 8y - 4x^2 - 8y^2 + 4x - 4y.",
        "gt_answers": "B D \\bot A C \\cong A O = C 0\n",
        "image_path": "./data/HME100K/test_images/test_4936.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the area of the triangle, we can use the formula for the area of a triangle:\n\nA = (1/2) \\* base \\* height\n\nwhere base is the length of the base of the triangle and height is the height of the triangle.\n\nFor this triangle, the base is 5 cm and the height is 6 cm. So, the area is:\n\nA = (1/2) \\* 5 cm \\* 6 cm\n= 15 cm^2\n\nTherefore, the area of the triangle is 15 cm^2.",
        "gt_answers": "r = 2 5 c m = 2 . 5 d m\n",
        "image_path": "./data/HME100K/test_images/test_4938.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{3}{4}+\\frac{1}{5}+\\frac{2}{6}=\\frac{13}{15}$$\n\nThis expression can be read as, `the sum of 3/4, 1/5, and 2/6 is equal to 13/15'.",
        "gt_answers": "\\angle 2 = \\angle D E C\n",
        "image_path": "./data/HME100K/test_images/test_4939.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align}\nf(x) &= 100 - \\frac{x^2}{16} \\\n\\end{align}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\text{cubic } x^2 + 3x - 2$.",
        "gt_answers": "\\angle A E B = 4 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4941.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$y = \\frac{1}{4} x^2 + \\frac{9}{8} x - \\frac{1}{2}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{3n^2+4n}{5n^3+4n^2+2n}$$This is a quadratic equation in the form of $\\frac{ax^2+bx+c}{dx^3+ex^2+fx}$. The numerator is $(3n^2+4n)$, and the denominator is $5n^3+4n^2+2n$.",
        "gt_answers": "( n = 3 , 4 , 5 \\cdots )\n",
        "image_path": "./data/HME100K/test_images/test_4943.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Could you please provide a different image that I can work with?",
        "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_4944.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is $\\frac{100\\times x}{x + 5}$, where x is any real number.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the expression of the formula, which is represented by the equation: y4 = 4x3 - 9x2 + 6x - 3. The image shows the y-coordinate of the point on the parabola at the vertex. The x-coordinate of the vertex is x = -3. The equation of the parabola is given by y = ax^2 + bx + c, where a = 4, b = -9, and c = 6.",
        "gt_answers": "y _ { 4 } = - \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4946.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the image:\n\n$$\\frac{325}{204} + \\frac{54}{204} + \\frac{52}{204} + \\frac{27}{204} = \\frac{356}{204}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a piece of notebook paper with a drawing of a cube. The cube is drawn in black ink with the numbers 1, 2, and 3 written on each of its faces. The cube is labeled as a three-dimensional figure and has a red arrow pointing to it. The image appears to be a diagram or illustration of a cube.",
        "gt_answers": "\\frac { 1 } { 2 } + \\frac { 2 } { 5 } = \\frac { 9 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_4948.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format of the expression of the formula in the image:\n\n\\begin{center}\n$\\frac{dV}{dt} = \\frac{Q}{C}$\n\\end{center}\n\nwhere $V$ is the voltage of the capacitor, $Q$ is the charge flowing into or out of the capacitor, and $C$ is the capacitance of the capacitor.",
        "gt_answers": "F _ { 3 } ( 1 + \\sqrt { 5 } , 2 \\sqrt { 5 } ) .\n",
        "image_path": "./data/HME100K/test_images/test_4950.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ 1 + 3x^2 + 4x - 5 $$\n\nThis expression can be derived by identifying the coefficients and exponents of the terms in the polynomial function given in the image.",
        "gt_answers": "6 ( 2 x - 1 ) - 5 ( x - 1 ) = 6 0\n",
        "image_path": "./data/HME100K/test_images/test_4952.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nLaTeX code for the image:\n\n\\frac{4x^2 - 9x + 3}{2x^2 - 3x + 1}\n```\nThe denominator is $2x^2 - 3x + 1$, which is a quadratic equation with a leading coefficient of $2$. The numerator is $\\frac{4x^2 - 9x + 3}{2x^2 - 3x + 1}$, which is also a quadratic equation with a leading coefficient of $4$.\n\nThe image shows the graph of the function pl",
        "gt_answers": "2 - \\frac { 1 } { 3 } ( k + 1 ) = 2\n",
        "image_path": "./data/HME100K/test_images/test_4953.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by the equation:2x^2+2x-1=0, which can be written as2x^2+2x\u22121=02x^2+2x\u22121=02x^2+2x\u22121=02x^2+2x\u22121=0This equation represents the quadratic equation with a constant term of 1 and coefficients of 2x^2 and 2x.\n\nTo factor the polynomial, we can use the quadratic formula, which gives the roots of the equation as follows:x=\u2212b\u00b1b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression for the formula in the image using LaTeX format:\n\n$$\\begin{aligned} r = \\frac{d}{t}\\end{aligned}$$\n\nwhere $r$ is the radius of the circular path, $d$ is the diameter of the circular path, and $t$ is the time taken to travel around the circular path.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is x + 2y = 10. The variable x represents the number of apples, and the variable y represents the number of oranges.\n\nThe equation can be solved by substituting x = 3 and y = 5 into the equation, as follows:\n\n10 = x + 2y\n10 = 3 + 5\n10 = 8\n\nTherefore, the solution to the equation is x = 3 and y = 5, which represents a total of 8 apples and oranges.",
        "gt_answers": "x _ { 2 } = \\frac { 3 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_4956.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 2x^2 + 4x + 3.\n\nTo derive this formula, we start with the given pattern, which shows the coefficients and variables of the polynomial:\n\n[2, 1, 3] \\* x^2 + [4, 1] \\* x + [3]\n\nWe can then use the distributive property of multiplication over addition to expand the polynomial:\n\n[2, 1, 3] \\* x^2 + [4, 1] \\* x + [3] = 2x^2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 1 / 2 (x + 3) + 1 / 4 (y - 4) + 3 / 8 (z - 2) = 5 / 8 (x + 3 + y - 4 + z - 2) = 5 / 8 (x + y + 3 + 2z) = (5 / 8) \\* (x + y + 3 + 2z) = 5 / 8 \\* (x + y + 3 + 2z",
        "gt_answers": "m > 2 o r m = - 3\n",
        "image_path": "./data/HME100K/test_images/test_4959.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is written as:\n\n$ $ $\\frac{\\text{number of students in the class}}{\\text{total number of students in the school}}$\n\nThis formula can be used to calculate the percentage of students in a particular class out of the total number of students in the school. The numerator is the number of students in the class, and the denominator is the total number of students in the school.",
        "gt_answers": "\\Delta P B D \\sim \\Delta E C D\n",
        "image_path": "./data/HME100K/test_images/test_4960.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image appears to be written in black ink on a white surface. The writing appears to be a series of letters and numbers written in a circular pattern, with a small circle in the center. It is difficult to make out the exact expression of the formula, but it appears to be written in a circular pattern with the numbers 3, 4, 5, 6, 7, 8, and 9.\n\nThere is also a small circle in the center of the writing, which may indicate that this is the starting point or center of the formula. However, without more context or information, it is",
        "gt_answers": "\\angle E D B = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4962.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\nH2O + CO2 \u2192 H2CO3\n\nThe balanced chemical equation shows the reactants on the left side and the products on the right side. In this equation, the reactant is water (H2O) and the product is carbonic acid (H2CO3). The reactant is written on the left side of the equation and the product is written on the right side.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression in LaTeX format:$$\\frac{p}{q} = \\frac{r}{s} \\cdot \\frac{t}{u}$$This expression represents the proportion of p to q, where p and q are two quantities with different units, and r, s, t, and u are conversion factors used to convert one unit to another.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by: 4x2+2x+1=0.\n\nThe solution is given by: x=\u221222.2222222.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write out the expression of the formula in the image using LaTeX format.\n\nHere is the LaTeX format of the expression:\n\n$$\\frac{2x + 5}{x - 3} = \\frac{2(x + 5)}{(x - 3)}$$\n\nIn words, the formula is the ratio of two fractions, where the numerator of the first fraction is 2x plus 5, and the denominator is x minus 3. The numerator of the second fraction is x plus 5, and the denominator is x minus",
        "gt_answers": "x - 2 = \\pm 5\n",
        "image_path": "./data/HME100K/test_images/test_4967.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression of the formula in the image using LaTeX format:\n\n\\begin{aligned} \\frac{2x + 2y - x^2 - y^2}{2x + y - 2xy - y^2} \\ &= \\ \\frac{2x + 2y - x^2 - y^2}{(2x + y - 2xy - y^2)(2x + y - 2xy - y^2)} \\ &= \\ \\frac{x + 2y - x^2 - y^2}{2x + y - 2xy -",
        "gt_answers": "\\vert - 2 . 2 \\vert = 2 . 2\n",
        "image_path": "./data/HME100K/test_images/test_4968.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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 below using LaTeX format:\n\n$$\\frac{3}{4}x^2 + \\frac{1}{2}x - 1 = 0$$\n\nwhere x is the variable.",
        "gt_answers": "2 x \\epsilon [ 0 , \\frac { \\pi } { 6 } ]\n",
        "image_path": "./data/HME100K/test_images/test_4969.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is $\\pi$r$^2$.",
        "gt_answers": "x _ { 1 } = \\sqrt { 7 - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4973.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ r = \\frac{x^2 + y^2}{x + y} $$\n\nwhere x and y are the lengths of the sides of the rectangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{\\frac{x^2+y^2}{r^2}}{\\frac{x^2+y^2}{r^2}+1}$$",
        "gt_answers": "x _ { 4 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4975.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```scss\n\n$\\alpha = \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5}$\n\n```",
        "gt_answers": "A O = C O = D O = B O\n",
        "image_path": "./data/HME100K/test_images/test_4976.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following code:\n\n\\begin{align\\*}\nE = mc^2\n\\end{align\\*}\n\nwhere E is the energy of the object, m is its mass, and c is the speed of light in a vacuum. This equation is derived from the theory of special relativity, which states that the total energy of an object is equal to the sum of its rest mass and its kinetic energy.\n\nIt is important to note that the constant c is the speed of light in a vac",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the expression shown in the image:\n\n$$\\frac{a + b}{c}$$\n\nwhere $a, b, and c are integers.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = (l x w) / 2\n\nwhere l is the length of the rectangle and w is the width of the rectangle. To find the area of the rectangle in the image, we can use the formula above.\n\nFirst, we need to find the length and width of the rectangle. We can do this by measuring the distance between the two diagonal corners of the rectangle. This distance is given by the equation:\n\nd = sqrt(l^2 + w^2)\n\nwhere l is the length of the rectangle and w",
        "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",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```scss\n\nThe expression is 2x + 3y - 4xy + 5y^2.\n```",
        "gt_answers": "S y = 2\n",
        "image_path": "./data/HME100K/test_images/test_4980.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clearly visible as it is written in a different language. Can you provide more information or the formula in English?",
        "gt_answers": "y = 3 1 \\times \\frac { 1 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_4982.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula using LaTeX format is: $\\text{m} = \\text{F} \\cdot \\text{v}^{2}$.",
        "gt_answers": "w = P t\n",
        "image_path": "./data/HME100K/test_images/test_4983.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression in the image:\n\n\\begin{align\\*}\nx^2 + 2x + 1 &= x^2 + 2x + 1\\\n&= (x + 1)^2\\\n&= (x + 1)^2\\\n&= (2x + 1)^2\\\n&= 4x^2 + 4x + 1\\\n&= 4x^2 + 4x + 1\n\\end{align\\*}.",
        "gt_answers": "a < - b < 0 < b < - a\n",
        "image_path": "./data/HME100K/test_images/test_4984.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\nx4+3x3+2x2+x+14\n\nThis can be written in LaTeX format as:\n\n$$x^{4} + 3x^{3} + 2x^{2} + x + 14$$",
        "gt_answers": "\\angle 4 = \\frac { 1 } { 2 } \\angle A B D\n",
        "image_path": "./data/HME100K/test_images/test_4985.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Image content} = \\text{Image}$$",
        "gt_answers": "O A = O D , \\angle A = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4986.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n4x^2 + 4y^2 = 200\n\nThis equation represents a parabolic shape with the vertex at the center of the image. The vertex is the point where the parabolic shape changes direction, from increasing to decreasing, or vice versa.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\frac{1}{3}(3x + 5) + \\frac{1}{2}(2x - 1) = 13$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->] (0,0) -- (1,0) node[right] {$ x $};\n\\draw[->] (0,0) -- (0,1) node[above] {$ y $};\n\\filldraw (0.5, 0.5) circle[radius=2pt];\n\\node at (0.5, 0.5) {$ (x,y) = (0.5, 0.5)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the expression in LaTeX format:\n\n\\begin{align}\nx + 3 &= 4 \\\n\\begin{aligned}\nx &= 4 - 3 \\\n\\end{aligned}\nx &= 1\n\\end{align}\n\nThis equation is solving for the value of x when added to 3 is equal to 4. The equation is set up as an equation in two variables, x and y, where x is the variable that we're trying to find and y is the variable that we're given. We can substitute the value of y (",
        "gt_answers": "4 . 8 \\times \\frac { 2 } { 3 } = 3 . 2 k m\n",
        "image_path": "./data/HME100K/test_images/test_4990.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is as follows:\n\n$$\\text{L=} \\frac{1}{2}(x\\_1^2 + x\\_2^2 + \\cdots + x\\_n^2)$$\n\nwhere L is the sum of the squares of the coordinates of the points in the image and n is the number of points in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression of the formula in the image using LaTeX format:\n\n$$x = \\frac{3y + 5z - 2w}{4}$$",
        "gt_answers": "x _ { 2 } = \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_4992.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$$\\begin{aligned}\n\\frac{2x^2+5x-8}{x+3} &= \\frac{2(x+1)(x+3) - 8}{x+3} \\\\\n&= \\frac{(x+1)(x+2) - 8}{x+3} \\\\\n&= (x+1)\\left( \\frac{x+2}{x+3} \\right) - 8\n\\end",
        "gt_answers": "x _ { 1 } = \\frac { \\sqrt { 1 0 } } { 2 } + \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4993.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{aligned}\n&\\frac{2x+4y}{x+y-2x(y+2)}& \\text{for } x \\geq 0, y \\geq 0\\\n\\end{aligned}\n\nThis formula is derived from the geometric series and is used to find the sum of the infinite geometric series with initial terms $x$ and $y$.",
        "gt_answers": "4 + 4 = 8 8 > 4\n",
        "image_path": "./data/HME100K/test_images/test_4995.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n$$\\text{Area} = \\frac{1}{2} \\cdot \\text{Base} \\cdot \\text{Height}$$\n\nwhere $\\text{Base}$ is the length of the rectangle's base, $\\text{Height}$ is the height of the rectangle, and $\\frac{1}{2}$ is a constant value representing half of the rectangle's area.",
        "gt_answers": "\\angle 1 = 1 8 0 ^ { \\circ } - \\angle B = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_4996.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{ImageContent}\\times\\left(\\frac{1}{2}\\right)^2$$",
        "gt_answers": "a x ^ { 2 } + 5 x + c = 0\n",
        "image_path": "./data/HME100K/test_images/test_4997.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{equation}\n    x^2 + y^2 = r^2\n\\end{equation}\n```",
        "gt_answers": "( y + 3 ) ( y - 2 )\n",
        "image_path": "./data/HME100K/test_images/test_4998.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 1 - 3x + 6y.",
        "gt_answers": "x = \\frac { 6 } { k - 2 }\n",
        "image_path": "./data/HME100K/test_images/test_4999.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{equation}\n2x + 5y = 12\n\\end{equation}",
        "gt_answers": "- 5 k = - 5\n",
        "image_path": "./data/HME100K/test_images/test_5001.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I'd be happy to help you with that! Here's the LaTeX formula for the expression shown in the image:\n\n\\begin{center}x^2 + 3x + 2 = 0\\end{center}\n\nThe expression in the image is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = 3, and c = 2. To write it in LaTeX format, we simply need to enclose the expression in the quadratic formula, which looks like this:\n\n\\begin{center}\\",
        "gt_answers": "1 \\times 2 2 2 2 = 2 2 2 2\n",
        "image_path": "./data/HME100K/test_images/test_5002.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is A = l x w, where l is the length and w is the width. The formula for the perimeter of a rectangle is P = 2l + 2w, where l is the length and w is the width. The formula for the area of a triangle is A = (1/2)bh, where b is the base and h is the height. The formula for the perimeter of a triangle is P = b + h, where b is the base and h is the height. The formula for the volume of a cube is V = (length)",
        "gt_answers": "\\frac { I } { I _ { 2 } } = \\frac { I _ { 1 } + I _ { 2 } } { I _ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_5003.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in LaTeX format.\n\nThe expression for the image given is:\n\n\\begin{center}\n\\frac{3x^2 + 10x + 5}{2x^2 + 5x + 3}\n\\end{center}\n\nHere, the numerator is given as $3x^2 + 10x + 5$ and the denominator is given as $2x^2 + 5x + 3$. To evaluate the expression, we first simplify the numerator and denominator using the distrib",
        "gt_answers": "\\frac { 1 0 x - 2 0 } { 2 } - \\frac { 1 0 x + 1 0 } { 5 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_5004.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression of the formula in the image using LaTeX format:\n\n\\begin{center}\n\\begin{minipage}{0.4\\textwidth}\n\\centering\n\\begin{equation}\ny = \\frac{x^2 - 4x + 5}{2x - 3}\n\\end{equation}\n\\end{minipage}\n\\end{center}\n\nThis formula is a quadratic equation of the form $y = ax^2 + bx + c$, where $a = 1$, $b = -4$, and $c = 5",
        "gt_answers": "D C = 2 \\times ( 8 - 4 \\sqrt { 3 } ) = 1 6 - 8 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5006.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $ x = 400 \\div 0.4 $.",
        "gt_answers": "0 . 4 0 = 0 . 4 0 0\n",
        "image_path": "./data/HME100K/test_images/test_5007.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as:\n\n$$ \\text{A} + \\text{B} = \\text{C} $$\n\nwhere A, B, and C are mathematical expressions that represent the values shown in the image.",
        "gt_answers": "= \\frac { D G } { A G } = \\frac { 8 } { 4 \\sqrt { 5 } }\n",
        "image_path": "./data/HME100K/test_images/test_5008.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is not provided. However, if you provide the image, I can write out the expression using LaTeX format.",
        "gt_answers": ": \\sqrt { x + 5 } = 4 - \\sqrt { x - 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5009.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n5 3 2 1 4 5 3 2 1 4 5 3 2 1 4 5 3 2 1 4 5 3 2 1 4 5 3 2 1 4 5 3 2 1 4 5 3 2 1 4 5 3 2 1 4 5 3 2 1 4 5 3 2 1 4 5 3 2",
        "gt_answers": "5 + \\frac { 3 } { 4 } - \\frac { 1 } { 2 } = 0 . 7 5\n",
        "image_path": "./data/HME100K/test_images/test_5010.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the formula in the image is:La = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc + 2cLa = Lc +",
        "gt_answers": "\\angle A = \\angle C = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5011.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is 2x^2 - 4x + 3.",
        "gt_answers": "\\frac { 3 } { 5 } : x = \\frac { 3 } { 8 } : \\frac { 5 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_5012.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b(\u222b(x^2)dx)\\*\u222b(1dx)\n\n\u222b(\u222b(x^2)dx)\\*1\n\u222b(x^2)dx)\n\u222b(x^2)dx\n\u222b(x^2)dx\n\u222b(x^2)dx\n\u222b(x^2)dx\n\u222b(x^2)dx\n\u222b(x^2)dx\n\u222b(x^2)dx\n\u222b(x^2)dx\n\u222b(x^2)dx\n\u222b(x^",
        "gt_answers": "\\frac { 3 } { 2 } < c < \\frac { 5 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5013.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\ny = 3x\u00b2 + 4x + 1\n\nwhere x is the input variable and y is the output variable.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression of the formula in LaTeX format:\n\n$$\\text{I = \\frac{V^2}{R + \\sqrt{R^2 - (V^2/R) + 1}}$$} \\text{where I is the current in amperes, V is the voltage in volts, and R is the resistance in ohms.}$$\n\nThis formula is known as Ohm's law for DC circuits. It relates the current, voltage, and resistance in a DC circuit and can be used to calculate the current in a circuit given the voltage and",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$ \\frac{b}{2} = \\frac{1}{2}(x + y) - \\frac{1}{2}xy$$",
        "gt_answers": "O B = O A = \\frac { A B } { 2 } = 8\n",
        "image_path": "./data/HME100K/test_images/test_5017.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$$\\text{ImageContent}\\_{n+1}=\\frac{\\text{ImageContent}\\_n}{\\text{Slope}\\_n}+\\text{Noise}\\_{n+1}$$\n\nwhere $\\text{ImageContent}\\_{n+1}$ is the intensity of the pixel at the top right corner of the image, $\\text{ImageContent}\\_n$ is the intensity of the pixel at the bottom left corner of the image in the previous iteration, $\\text{Slope}\\_n$ is the slope",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a diagram with two overlapping circles, one labeled \"x\" and the other labeled \"y\". There is also an equation written in LaTeX format: $ x^{2} + y^{2} = r^{2} $. This equation is known as the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two sides is equal to the square of the length of the hypotenuse.",
        "gt_answers": "2 x ^ { 2 } + x = 2 ( x ^ { 2 } + 1 + 2 x )\n",
        "image_path": "./data/HME100K/test_images/test_5019.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{3x^2 + 2x - 5}{x^3 - 4x^2 + 6x - 7}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows an equation for the volume of a cylinder. The formula for the volume of a cylinder is given by:\n\nV = \u03c0r^2h\n\nwhere V is the volume, r is the radius of the cylinder, and h is the height of the cylinder. To find the volume of the cylinder in the image, we need to measure the radius and height of the cylinder.\n\nFirst, we can see that the radius of the cylinder is 4 cm. This is because the diameter of the cylinder is 8 cm, and the radius is half of the",
        "gt_answers": "( b + 2 ) ( b - 1 ) = 0 .\n",
        "image_path": "./data/HME100K/test_images/test_5021.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression for the formula in the image using LaTeX format:\n\n$$\\begin{aligned} \\text{Image Content} = \\frac{2 \\times 4 \\times 3 \\times 5 \\times 7 \\times 8}{3 \\times 5 \\times 7} \\end{aligned}$$\n\nThis is a formula for calculating the image content. It involves multiplying several numbers together and dividing by a certain number of factors. The result is the image content.",
        "gt_answers": "( 1 - 1 ) x ^ { 2 } + ( 4 + 3 ) x + 3 - 5 = 0\n",
        "image_path": "./data/HME100K/test_images/test_5022.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n<latex code>$$ \\left(\\frac{m}{n}\\right)^2 + \\left(\\frac{m}{n}\\right)^4 = \\left(\\frac{m^2}{n^2}\\right) + \\left(\\frac{m^4}{n^4}\\right)$$</latex code>\n\nAlternatively, you can use the LaTeX code to write the formula:\n\n<latex code>$$ \\left(\\frac{m}{n}\\right)^2 + \\left(\\frac{m}{n}\\right)^4 =",
        "gt_answers": "\\angle E D B = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5023.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:\n\n\\begin{align}\n3x^2 + 4x - 5 &= 0 \\\\\\\nx^2 + 2x - 5 &= 0 \\\n\\end{align}\n\nThese are two equivalent ways of writing the same equation, which represents a quadratic equation in standard form. The first equation uses the quadratic formula, while the second equation factorizes the quadratic expression into two linear factors.",
        "gt_answers": "3 . 1 4 \\times 2 ^ { 2 } = 1 2 . 5 6 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5024.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\n$$ \\text{y} = \\frac{1}{3}x^3 + \\frac{2}{3}x^2 + \\frac{1}{3}x + 1 $$\n\nwhere $\\text{y}$ is the dependent variable, and $x$ is the independent variable.",
        "gt_answers": "( x + 1 ) ^ { 2 } > 4\n",
        "image_path": "./data/HME100K/test_images/test_5025.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image you provided is:\n\n$$\\frac{486 + 492}{700 - 162} = \\frac{988}{538}$$\n\nThis is a ratio of two fractions, where the numerator is the sum of the two numbers and the denominator is the difference between the two numbers.",
        "gt_answers": "\\frac { 1 0 6 } { 7 5 } = \\frac { x } { 7 . 3 g }\n",
        "image_path": "./data/HME100K/test_images/test_5026.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \u2211 i=1^n (x\\_i - \u03bc)2.\n\nHere, x\\_i is the i-th observation of the data set, \u03bc is the population mean, and n is the sample size. The summation is taken over all i-th observations, from 1 to n. The formula calculates the sum of the squared differences between each observation and the population mean. This formula can be used to calculate the sample variance, which is an estimate of the population variance.",
        "gt_answers": "7 8 - 7 8 \\textcircled { < } 7 8 \\div 7 8\n",
        "image_path": "./data/HME100K/test_images/test_5027.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you would use the following equation:$$P = \\frac{mgh}{L^2}$$where:P is the pressure of the gas in the cylinderm is the mass of the gasg is the acceleration due to gravityh is the height of the cylinderL is the length of the piston.",
        "gt_answers": "S _ { n } \\cdot \\frac { 2 } { n + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5028.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be written as:\n\nA = \u03c0r^2,\n\nwhere A is the area, \u03c0 is the mathematical constant pi, and r is the radius of the circle. The value of \u03c0 is approximately 3.14159, so the area of a circle with a radius of 2 would be:\n\nA = \u03c0(2)^2\n= 8.2599335",
        "gt_answers": "x = \\frac { 5 0 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5029.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image can be written as follows:\n\n$$\\frac{2}{5}x + \\frac{3}{4}y = \\frac{1}{2}$$\n\nThis is a system of linear equations in two variables that can be solved using substitution, elimination, or cross-multiplication methods.",
        "gt_answers": "D E \\bot A B\n",
        "image_path": "./data/HME100K/test_images/test_5030.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To represent the expression using LaTeX format, you can use the following code:\n\n$$\\frac{a^2 + b^2}{c^2}$$\n\nwhere $a$, $b$, and $c$ are variables. The expression represents the ratio of the sum of the squares of $a$ and $b$ to the square of $c$.",
        "gt_answers": "4 2 \\rightarrow 2 4 \\rightarrow 1 8\n",
        "image_path": "./data/HME100K/test_images/test_5031.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in LaTeX format for the given image is:\n\n$$\\frac{1}{2}x^2 + \\frac{1}{4}x - \\frac{1}{8}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format expression for the formula in the image:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "1 2 \\times 6 = 7 2 ( d m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5033.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{5x^2 + 2x + 1}{x^2 + 5x + 4}$",
        "gt_answers": "4 = \\frac { 4 } { 9 } ( x - 3 + m ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5034.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I am unable to see the image as it appears to be broken. Can you please provide the image or a different method of describing the expression?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, the equation for the expression in the image is given by:\n\n$$\\frac{a+b}{c+d} = \\frac{ad+bc}{bd+ac}$$\n\nThis can be derived from the distributive property of multiplication over addition, as follows:\n\n$$\\frac{a+b}{c+d} = \\frac{a(c+d)+b}{c(d+a)+b}$$\n\nSimplifying the numerator and denominator:\n\n$$\\frac{a+b}{c+d} = \\frac{ac+ad+bc",
        "gt_answers": "\\frac { x - a - b } { c } + \\frac { x - b - c } { a }\n",
        "image_path": "./data/HME100K/test_images/test_5036.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x^2 + y^2 = x^2 + y^2.",
        "gt_answers": "x _ { 1 } = 2 , x _ { 2 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_5037.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ f(x) = 2x^2 + 4x - 3 $$\n\nThis can be derived by using the given formula and substituting the values given in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows an equation written in LaTeX format. The equation is shown as follows:\n\n$$\\text{Image Content}$$\n\nwhere the red arrow points to the formula in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick, red] (0,0) -- (1,0) node[midway, below] {$30''$};\n\\draw[thick, blue] (1,0) -- (2,0) node[midway, below] {$45''$};\n\\draw[thick, green] (2,0) -- (3,0) node[midway, below] {$60''$};\n\\draw[thick, purple] (3,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b \u222b \u222b (x + 4y + 2z) dx dy dz = \u222b \u222b \u222b (x + 4y + 2z) dx dy dz = \u222b \u222b \u222b \u222b (x + 4y + 2z) dx dy dz = \u222b \u222b \u222b \u222b (x + 4y + 2z) dx dy dz = \u222b \u222b \u222b \u222b (x + 4y + 2z) dx dy dz = \u222b \u222b \u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\begin{aligned} 2x^2 - 5x + 3 &= 0 \\ \\Rightarrow \\ x = 2 - \\frac{5}{2} \\\\ &= 1 - \\frac{5}{4} \\end{aligned} $$\n\nAlternatively, we can factor the polynomial:\n\n$$ \\begin{aligned} 2x^2 - 5x + 3 &= 0 \\ \\Rightarrow (2x - 1)(x + \\frac{1}{2}) = 0 \\",
        "gt_answers": "x - \\frac { 1 } { 5 } = 0 . 2 \\times 1 0\n",
        "image_path": "./data/HME100K/test_images/test_5043.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression written in LaTeX format. The expression is:\n\n$$\\frac{1000+1000}{2000}=0.5$$\n\nThis expression represents the average of 1000 and 1000, which is 1000, divided by 2, which results in 0.5.",
        "gt_answers": "1 0 0 0 \\div 1 0 0 = 1 0 ( k g )\n",
        "image_path": "./data/HME100K/test_images/test_5044.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$3x + 2y = 5$$The variable x represents the number of red beans and the variable y represents the number of blue beans. The equation says that the sum of the red beans and the blue beans is equal to 5.",
        "gt_answers": "\\frac { 4 } { 1 5 } \\div \\frac { 2 } { 3 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5045.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the equation for the sum of 4 numbers, represented by x, y, z, and w. The formula is: x + y + z + w = 10x + y + z + w = 10The equation shows that the sum of the 4 numbers is equal to 10. This formula can be used to calculate the sum of any 4 numbers, regardless of their values.",
        "gt_answers": "x ^ { 3 } - 3 x ^ { 2 } - 3 x - 3 x ^ { 3 } +\n",
        "image_path": "./data/HME100K/test_images/test_5046.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the equation for the sum of two numbers: 2 + 3 = 5.",
        "gt_answers": "P ( 2 + 2 \\sqrt { 2 } , - 2 \\sqrt { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5047.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the formula in the image can be written as:$$E=mgh$$where $E$ is the energy of the object being lifted, $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the height to which the object is lifted.",
        "gt_answers": "2 x ^ { 2 } + x = 2 ( x ^ { 2 } + 2 x + 1 )\n",
        "image_path": "./data/HME100K/test_images/test_5048.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ f(x) = \\frac{1}{2}\\left( \\frac{3x}{x+4} \\right) $$",
        "gt_answers": "5 0 0 7 5 \\times 1 0 \\div 1 0 0 \\times 1 0 0 0 0 = 5 0 0 7 5 0 0 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_5049.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is 1/3 + 1/4 + 1/5 + 1/6 = 1/3 + 1/5 + 1/6.",
        "gt_answers": "\\vert 3 - 0 \\vert = 3\n",
        "image_path": "./data/HME100K/test_images/test_5050.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is A = (pi)r^2, where r is the radius of the circle.\n\nIn LaTeX format, this formula can be written as:\n\n\\frac{A}{\\pi} = r^2\n\nwhere A is the area of the circle and r is the radius of the circle.",
        "gt_answers": "x _ { 1 } = - \\sqrt [ 4 ] { 1 2 8 } - 1\n",
        "image_path": "./data/HME100K/test_images/test_5052.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows:\n\n$$w = \\frac{5 \\times 4}{3 \\times 5 + 4 \\times 3} = \\frac{20}{17} = 1.176$$\n\nThe equation in the image is a line with slope 1 and y-intercept 17. To find the equation, we can use the point-slope form of a line, which has the form:\n\ny = mx + b\n\nwhere m is the slope and b is the y-intercept. To",
        "gt_answers": "W = - ( x - 3 . 5 ) ^ { 2 } + 6 0 . 2 5\n",
        "image_path": "./data/HME100K/test_images/test_5053.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a triangle with base b and height h is given by:\n\nA = (1/2)bhA = (1/2)bhA = (1/2)bhA = (1/2)bhA = (1/2)bhA = (1/2)bhA = (1/2)bhA = (1/2)bhA = (1/2)bhA = (1/2)bhA = (1/2)bhA = (1/2)bh",
        "gt_answers": "x = - \\frac { 3 a } { a - 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5055.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is not provided. Please provide the expression for the formula in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is A = l x w, where l is the length and w is the width. Using the image provided, we can find the area of the rectangle as follows:\n\nA = 5 x 7\n\nA = 5 x 7\n\nThe area of the rectangle is 35 square units.",
        "gt_answers": "1 0 \\times 7 = 7 0 ( k m )\n",
        "image_path": "./data/HME100K/test_images/test_5057.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{a + b}{c + d} = \\frac{ab + cd}{ad + bc}$$",
        "gt_answers": "\\frac { \\frac { \\sqrt { 2 } } { 2 } } { b } = \\frac { \\sqrt { 1 0 } } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5058.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n\\begin{equation}\n5 + 3 \\times 7 + 2 \\times 4 = 5 + 21 + 8 = 34\n\\end{equation}",
        "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",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{2}(x + 3)(x - 2) = x^2 - 5x + 9$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be represented using the following LaTeX expression:\n\n\\begin{center}\nA = \u03c0r^2\n\\end{center}\n\nwhere A is the area of the circle, r is its radius, and \u03c0 is the mathematical constant approximately equal to 3.14.",
        "gt_answers": "l : x = - \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5064.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not provided. Please provide the image to get the formula.",
        "gt_answers": "\\frac { 1 } { S h } = 4 + 4 ( n - 1 ) = 4 n\n",
        "image_path": "./data/HME100K/test_images/test_5065.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle can be written as:\n\nA = l \\* w\n\nwhere l is the length of the rectangle and w is the width of the rectangle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n\\begin{equation}\nf(x) = \\frac{2}{x^2 + 1}\n\\end{equation}\n\nNote that the function has a hole at x = 0, which means that the function is undefined at that point.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=1.25]\n\\draw[step=1cm,thin, gray!50] (0,0) grid (2,2);\n\\draw[thick, fill=white] (0,0) rectangle (2,2);\n\\draw[thick, fill=black] (0,0) rectangle (1,1);\n\\draw[thick, fill=white] (1,1) rectangle (2,2);\n\\draw[thick, fill",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{minipage}{0.4\\textwidth}\n\\begin{center}\n$A = \\frac{P \\cdot I}{Q \\cdot E}$\n\\end{center}\n\\end{minipage}\n\\end{center}\n\nThis formula calculates the area of a rectangle given the perimeter, width, and height.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression in the image:\n\n$$\\frac{5 + 2\\sqrt{3}}{4} = \\frac{7 + \\sqrt{3}}{2}$$\n\nAlternatively, you can use the Pythagorean theorem to find the missing value:\n\n$$\\begin{aligned} x^2 + y^2 &= z^2 \\\\ 4^2 + 9^2 &= 16^2 \\end{aligned}$$\n\nSolving for x and y gives:\n\n$$x = 4 - \\sqrt{1",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, you can follow the steps below:\n\n1. First, open a LaTeX editor, such as TeXstudio or TeXworks.\n2. Type the following LaTeX code:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->] (0,0) -- (2,0) node[right] {$ x $};\n\\draw[->] (0,0) -- (0,2) node[above] {$ y $};\n\\draw[->] (2,0) -- (",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n<img>b = (a + 1)\\*2</img>\n\nNote: This answer assumes that the variable 'a' is already defined, which is not clear from the image.",
        "gt_answers": "B O = \\frac { 1 } { 2 } A B\n",
        "image_path": "./data/HME100K/test_images/test_5074.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\begin{aligned}\n\nE &= hf + \\frac{1}{2}mv^2 \\\\\nE &= \\frac{1}{2}mv^2 + hf\n\n\\end{aligned}$$The formula is the energy equation, which relates the energy of a system to the frequency of its oscillations and the mass and spring constant of its spring. In the formula, E represents the total energy of the system, hf represents the energy stored in the spring due to the force applied to it, and mv^2 represents the",
        "gt_answers": "M _ { y } > F e > C u\n",
        "image_path": "./data/HME100K/test_images/test_5075.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is given by: $\\text{sin}(x) = \\frac{\\text{sin}(\\text{sin}(x))}{\\cos(\\text{cos}(x))}$.",
        "gt_answers": "\\frac { 1 } { 4 } = 1 - 2 \\sin ( \\frac { 1 } { 2 } ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5076.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This formula is a mathematical expression that represents the energy of an object in motion. The expression is given by:E = 1/2mv^2where E is the energy of the object, m is its mass, and v is its velocity. The formula shows that the energy of an object depends on its mass and velocity.\n\nThe formula can be used to calculate the energy of different objects, such as a car, a ball, or a person running. For example, if we want to know the energy of a 1 kg ball moving at a velocity of 5 m/s, we can use the formula as",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format of the formula in the image:\n\n$$ \\frac{2\\left(\\frac{1}{2}\\right)+3}{4\\left(\\frac{1}{4}\\right)+5} $$\n\nThis is the expression of the formula in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! The formula for the given image using LaTeX format is:\n\n$$\\frac{\\text{d}x}{\\text{d}t} = \\frac{\\text{d}^2x}{\\text{d}t^2}$$\n\nwhere x is the position of the object, t is time, and the derivatives are taken with respect to time. This formula is known as the second derivative equation and is used to find the rate of change of position over time.",
        "gt_answers": "\\angle A E C = 1 1 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5079.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nc = (2c)(c\\_0 + c\\_1x + c\\_2x^2) = (2c)(4 + 2x + 4x^2) = 4c + 8x + 8x^2.",
        "gt_answers": "C E = \\frac { 5 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5080.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:$$\\frac{2}{4\\sqrt{5}}$$The image shows a blue line with the equation $y = 2x + 5$ written on it in white. The line starts at the origin and goes up to the point $(2, 5)$. The equation is in slope intercept form, with the slope being 2 and the y-intercept being 5. The expression evaluates to $\\frac{2}{4\\sqrt{5}}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write out the expression of the formula in the image using LaTeX format. Here is the formula:\n\n$$\\frac{x\\_1+x\\_2+x\\_3+x\\_4+x\\_5+x\\_6}{6}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$\\begin{align}\\text{Expression of the formula in the image:}\\quad & x^2 + 3x + 2 \\quad \\text{in LaTeX format}$$\n\nThis LaTeX code will display the formula as $\\text{x}^2 + 3\\text{x} + 2$.",
        "gt_answers": "x = \\frac { 5 } { 3 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5083.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n![image content](https://www.merriam-webster.com/dictionary/image%20content)\n\nThe formula is written in LaTeX format, which is a mathematical markup language used for expressing mathematical equations and symbols. The formula is written in blue ink on a white background with the words \"image content\" written in black ink above the formula. The formula is written in a text editor or word processor and then converted to an image format for display on the website.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed using LaTeX as follows:\n\n\\begin{align\\*}\nA = \\frac{\u03c0r^2}{4}\n\\end{align\\*}\n\nwhere r is the radius of the circle.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a mathematical expression for the derivative of a function. The derivative of a function is calculated by finding the slope of the tangent line at each point on the graph of the function. The slope of the tangent line is calculated by finding the limit of the ratio of the change in y to the change in x as x approaches a, where a is the value of the function at that point. This expression is often written in the form of dy/dx=0, indicating that the derivative is equal to zero at that point.",
        "gt_answers": "x = - \\frac { 1 5 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_5088.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the image:\n\n\\begin{center}\n\\begin{tabular}{|c|c|}\n\\hline\n$x$ & $2x$ \\\\\n\\hline\n$y$ & $x + 3$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nThe image shows a table with two columns and two rows, with the values $x$ and $y$ listed in each row. The first column lists the values of $x$, while the second column lists the values of $2x$. The first row lists the values of",
        "gt_answers": "2 \\sqrt { 1 3 } < x < 1 0\n",
        "image_path": "./data/HME100K/test_images/test_5089.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image can be written as:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "( 1 ) 4 \\div 1 7 = \\frac { 4 } { 1 7 }\n",
        "image_path": "./data/HME100K/test_images/test_5090.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{F}(x) = \\begin{cases} \\frac{1}{x} & \\text{if } x \\neq 0 \\\\ 0 & \\text{if } x = 0 \\end{cases} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is an equation in LaTeX format for the formula: \u03c0 \u2248 3.14. The equation is written using the ` ` character to represent the approximation symbol.\n\nThe equation can be read as follows: the value of pi (\u03c0) is approximately equal to 3.14.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows an algebraic expression with an unknown number of terms. The expression is given as follows:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as:\n\n$$ \\frac{a}{b} $$\n\nwhere $a$ and $b$ are the lengths of the two sides of the triangle. The image shows a right triangle with legs of length $a$ and $b$ and hypotenuse of length $c$, which can be calculated using the Pythagorean theorem as $c^2 = a^2 + b^2$. Solving for $c$, we have $c = \\sqrt{a^2 + b^2}$. Substituting this value into the formula for the",
        "gt_answers": "\\angle 1 + \\angle A C B = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5094.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b0a f(x) dx\n\u222b0a ( 2x + 3 ) dx\n\u222b0a ( x^2 + 5x + 7 ) dx\n\u222b0a ( e^x - 3x^2 ) dx\n\u222b0a ( sin(x) + cos(x) ) dx\n\u222b0a ( 2 sin(x) cos(x) + 3cos(x)^2 ) dx\n\u222b0a ( e^(x/2) + cos(x) ) dx",
        "gt_answers": "\\angle D O E = 7 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5095.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula using LaTeX format is:\n\n$$ \\frac{2x}{x^2+2x-3} $$",
        "gt_answers": "1 g c _ { 1 } + 1 g a m 9 = 0 ,\n",
        "image_path": "./data/HME100K/test_images/test_5096.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the formula for the given image using LaTeX format, we can use the following code:\n\n\\begin{align}\ny = \\frac{x^2}{4} - \\frac{x}{2} + C\n\\end{align}\n\nwhere $x$ is the input variable and $C$ is the constant of integration. This formula represents a parabolic function with a vertex at the origin and a minimum value of $-\\frac{x}{2}$ at $x=0$.",
        "gt_answers": "y = \\frac { 1 } { 3 } x - 1\n",
        "image_path": "./data/HME100K/test_images/test_5097.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is not shown in the image provided. Please provide a mathematical expression in LaTeX format for the image.",
        "gt_answers": "y = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5098.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} f(x) = \\frac{1}{2x^2 + 10x - 5}\\end{aligned}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that.\n\nHere is the LaTeX code for the image:\n```\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[->] (0,0) -- (4,0) node[below right] {$x$};\n\\draw[->] (0,0) -- (0,4) node[above left] {$y$};\n\\filldraw (2,2) circle [radius=2pt] node[above right] {$f(x,y)=x^2+y^2$};\n\\end{tikzpicture}",
        "gt_answers": "\\frac { P D } { B E } = \\frac { F P } { B F }\n",
        "image_path": "./data/HME100K/test_images/test_5100.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n&#x3BC; &#x3BC; 3&#x2212;2(x&#x2212;a)+a&#x2212;3(x&#x2212;b)+b&#x2212;2(x&#x2212;c)+c&#x3BC; 3&#x2212;2(x&#x2212;a)+a&#x2212;3(x&#x2",
        "gt_answers": "1 0 m = 1 0 0 0 c m\n",
        "image_path": "./data/HME100K/test_images/test_5102.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:$$\\begin{aligned} \\text{pdpp} + \\text{d} &= \\text{pdpp} + \\text{dd}\\end{aligned}$$This formula is a mathematical equation that represents the image given, which shows the addition of two terms pdpp and d.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is t&#x2061;&#x2062;&#x2061;&#x2060;&#x2061;&#x2062;&#x2060;&#x2061;&#x2061;&#x2061;&#x2061;&#x2061;&#x2061;&#x2061;&#x2061;&#x2061;&#x2061",
        "gt_answers": "E B = E C , O C = O B\n",
        "image_path": "./data/HME100K/test_images/test_5104.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "\\angle D _ { 1 } A _ { 1 } A = 1 5 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5105.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ \\frac{1}{2}x^2 + \\frac{1}{4}x + \\frac{1}{8}$$\nThis formula is a quadratic equation with a constant term of $\\frac{1}{2}$ and a coefficient of $x^2$ of $\\frac{1}{2}$, $x$ of $\\frac{1}{4}$, and $x^2$ of $\\frac{1}{8}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the area of a circle. The formula is:A= (pi\\*r^2)where A is the area, pi is the constant value of approximately 3.14, and r is the radius of the circle. The image shows the formula written out in chalk on a blackboard.\n\nThe area of a circle is calculated using the formula:A= (pi\\*r^2)where A is the area, pi is the constant value of approximately 3.14, and r is the radius of the circle. This formula can be used",
        "gt_answers": "e ^ { 2 } < 2\n",
        "image_path": "./data/HME100K/test_images/test_5108.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX code for the expression:\n\n$$\\text{sin}\\left(\\frac{x}{2}\\right) = \\frac{x^2}{2!}$$\n\nThis expression calculates the sine of half of the input value, x, and then divides it by 2! to get the squared value of x.",
        "gt_answers": "y = \\sqrt { 2 } \\sin ( x + \\frac { \\pi } { 4 } )\n",
        "image_path": "./data/HME100K/test_images/test_5109.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by: $\\frac{2}{x^2 + 4x - 8}$.",
        "gt_answers": "\\frac { 1 } { 3 } \\overrightarrow { b } - \\frac { 1 } { 3 } \\overrightarrow { a }\n",
        "image_path": "./data/HME100K/test_images/test_5110.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:$$\\begin{align\\*} \\text{The volume of the pyramid is given by } V = \\frac{1}{3}Bh^2, \\text{where } B \\text{ is the base area and } h \\text{ is the height of the pyramid}.\\end{align\\*}$$This formula calculates the volume of a pyramid by taking the base area and multiplying it by the height of the pyramid to the power of two, then dividing that result by three. The resulting value is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is not written in LaTeX format. LaTeX is a typesetting system for mathematical and scientific documents.\n\nHowever, the image appears to be a handwritten formula written in Japanese, which cannot be translated into LaTeX format.",
        "gt_answers": "y = \\frac { k } { x }\n",
        "image_path": "./data/HME100K/test_images/test_5112.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: $$ 10x + 5y + 4z = 20 $$\n\nThis is a linear equation in three variables x, y, and z, with the constant term 20. The coefficient of x is 10, the coefficient of y is 5, and the coefficient of z is 4.",
        "gt_answers": "a - c > b - c .\n",
        "image_path": "./data/HME100K/test_images/test_5113.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clearly written. However, it appears to be the formula for the average of three numbers, with each number represented by a letter in the alphabet. The average is calculated by adding the three numbers and dividing by three.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\text{sin}\\left(\\frac{\\pi}{6}\\right) = \\frac{\\text{sin}(\\pi)}{2}$$\n\nIn the formula, $\\text{sin}\\left(\\frac{\\pi}{6}\\right)$ is the sine of $\\frac{\\pi}{6}$ radians and $\\frac{\\text{sin}(\\pi)}{2}$ is the sine of $\\pi$ radians. The expression reduces to $\\frac{1}{2}$, which is the sine of $\\frac{\\pi}{3}$ radians",
        "gt_answers": "\\sqrt { 2 } \\sin a ( x - \\frac { \\pi } { 4 } )\n",
        "image_path": "./data/HME100K/test_images/test_5117.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is 4x + 3y = 11.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a length of 5 and a width of 4 is:\n\narea = length x width\narea = 5 x 4\narea = 20 square units\n\nIn LaTeX format:\n\n$\\text{area = } 5 \\times 4 \\text{ square units}$",
        "gt_answers": "x - 2 y = 0 , x + y = 0\n",
        "image_path": "./data/HME100K/test_images/test_5119.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \u222b\u222b[a, b] f(x) dx.",
        "gt_answers": "x = - 7 \\frac { 4 } { 5 } \\div [ - 3 \\frac { 1 } { 4 } ]\n",
        "image_path": "./data/HME100K/test_images/test_5120.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows:$$\\begin{aligned} y &= x^2 - 2x + 1 \\ \\ \\text{for} \\ x \\in \\left[-\\frac{1}{2},\\frac{3}{2}\\right] \\end{aligned}$$This equation represents a parabolic function with vertex at the origin and a maximum value of $2$ at $x=\\frac{1}{2}$ and a minimum value of $-1$ at $x=\\frac{3}{2}$. The domain of the function is $\\left[-\\frac{1",
        "gt_answers": "a ^ { 2 } - 6 = - 2\n",
        "image_path": "./data/HME100K/test_images/test_5122.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image can be represented using LaTeX format as follows:\n\n\\begin{center}\n$ \\frac{m}{m + n} $\n\\end{center}\n\nwhere m and n are positive integers. The expression represents the probability that a randomly chosen person is the president of a country where the probability of a randomly chosen person being a president is $\\frac{m}{m+n}$.",
        "gt_answers": "x _ { 1 } = 3 x _ { 2 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_5124.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a general quadratic function with leading coefficient a, constant term b, and constant term c is given by:\n\ny = ax^2 + bx + c\n\nwhere x is the independent variable and y is the dependent variable.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the probability that the sum of two dice is equal to 7.\n\nThe probability can be represented as follows:\n\n$$ P(\\text{sum of two dice is 7}) = \\frac{1}{6} $$\n\nThis can also be written as:\n$$ P(X + Y = 7) = \\frac{1}{6} $$\nwhere X and Y are the numbers that appear on the dice.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by the equation:\n\n$$ 2x^2 + 2y^2 = 25 $$\n\nwhere x and y are the variables representing the coordinates of the points on the curve. The curve is a parabola with its vertex at the origin. The equation can be derived from the formula for a parabola in the form $ y = ax^2 + bx + c $ by setting $ a = 1, b = 0, c = 1/4 $. The curve has a minimum value of 0 at the origin and its maximum value is",
        "gt_answers": "\\varphi ^ { \\prime } ( x ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_5127.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here is the LaTeX expression for the formula in the image:$$\\text{y} = \\frac{b}{a+b}$$This formula is known as the formula for the arithmetic mean of two numbers. It calculates the average of two numbers by adding them together and dividing by the sum. In this case, a is the first number and b is the second number. The result is the average of the two numbers. Let me know if you have any other questions.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n5x^2 + 9x + 5 &= 29 && x &= 4\\\n\\end{align\\*}\n\nwhere $x$ is the variable that satisfies the equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\frac{x - 3}{x + 2}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX representation of the expression in the image:\n\n$$\\begin{aligned} \\frac{100}{25} + \\frac{200}{25} + \\frac{300}{25} &= \\frac{100+200+300}{25} = 600\\end{aligned}$$",
        "gt_answers": "x = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5135.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given as x + 2y = 6.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is not clear as there is no equation given. Can you please provide the equation to calculate the expression?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the expression in the image:\n\n\\begin{center}\n$x^2+y^2=r^2$\n\\end{center}\n\nIn this formula, x and y are variables and r is a constant. The equation is a quadratic equation in x and y, which means that it can be solved using the quadratic formula:\n\n\\begin{center}\n$x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}$\n\\end{center}\n\nwhere a, b, and c are the coefficients",
        "gt_answers": "- 1 2 k ^ { 2 } + 4 = c\n",
        "image_path": "./data/HME100K/test_images/test_5138.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:126+678\\*\\*789+6478+5678+4567+3456+2345+1234\\*\\*5678+4567+3456+2345+1234\\*\\*6789+5678+4567+3456+2345+1234\\*\\*126.",
        "gt_answers": "x \\geq 4 8\n",
        "image_path": "./data/HME100K/test_images/test_5139.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written as:\n\n$$\\frac{a\\_{1}+a\\_{2}+...+a\\_n}{n}$$\n\nwhere $a\\_1, a\\_2,..., a\\_n$ are the lengths of the sides of the triangle and $n$ is the number of sides in the triangle. This formula calculates the average length of the sides of the triangle.",
        "gt_answers": "y _ { 1 } = \\frac { 1 } { 3 } , y _ { 2 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_5140.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n\\begin{align\\*}\n 2y + 3x &= 6 \\\n\\end{align\\*}",
        "gt_answers": "P A \\cdot P B = P C \\cdot P D\n",
        "image_path": "./data/HME100K/test_images/test_5141.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x2+ 3x + 2.\n\nTo derive this expression, we can use the following steps:\n\n1. Multiply the variable x by 2 to get x2\n2. Add 3x to get x2 + 3x\n3. Add 2 to get x2 + 3x + 2\n\nSo the formula in the image is x2 + 3x + 2.",
        "gt_answers": "x = - \\frac { 2 8 5 } { 0 . 6 }\n",
        "image_path": "./data/HME100K/test_images/test_5142.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the product of two binomials.\n\n5(x + 4) \\* (2x - 3) = 5x^2 + 20x - 15",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: x + 18 = y + 6. This is a linear equation in two variables with a constant term of 18 and a variable term of 6.",
        "gt_answers": "4 x - 1 . 8 = 1 6 \\div 1 0\n",
        "image_path": "./data/HME100K/test_images/test_5144.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image:\n\n\\begin{center}\n\\frac{m}{m+c}\n\\end{center}\n\nwhere m and c are constants.",
        "gt_answers": "\\angle K F C = \\angle D B C\n",
        "image_path": "./data/HME100K/test_images/test_5145.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n\\begin{align\\*}\ny &= 2x^2 + 4x - 6 \\\\\n&= 2(x^2 + 2x) - 6 \\\\\n&= 2x(x + 2) - 6 \\\\\n&= x^2 + 2x + 2x - 6 \\\\\n&= x^2 + 2x - 6 \\\\\n&= (x + 2)^2 - 6\n\\end{align\\*}",
        "gt_answers": "1 = \\frac { 6 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_5146.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is:\n\n(1) 2 + 3 = 5\n\n(2) 10 \u00d7 5 = 50\n\n(3) \u221a5 + 2 = 3\n\n(4) \u221a5 \u00d7 5 = 25\n\n(5) 5 / 2 = 2.5\n\n(6) 2 + 3 \u00d7 5 = 13\n\n(7) \u221a5 - 2 = 1\n\n(8) \u221a5 \u00f7 2 = 1.5",
        "gt_answers": "y = a ( x + m ) ^ { 2 } + k\n",
        "image_path": "./data/HME100K/test_images/test_5147.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is given by the formula:\n\n\\begin{align\\*}\na &= \\frac{1}{2}\\left(\\frac{1}{2} + \\frac{1}{2}\\right) + 1 = \\frac{1}{2}(1 + 1) + 1 = \\frac{1}{2} + 1 = \\frac{3}{2}\\\n\\end{align\\*}\n\nThis formula can be interpreted as follows: The value of the variable a is the sum of three-quarters of 1 and 1. Since the sum of any number",
        "gt_answers": "A E = A C , \\angle 1 = \\angle 2\n",
        "image_path": "./data/HME100K/test_images/test_5148.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is:\n\nA = l \\* w\n\nwhere l is the length and w is the width.\n\nFor a rectangle with a perimeter of 40 units and an area of 60 square units, the length and width would be:\n\nl = 60 / w\n\nSolving for w:\n\nw = 60 / l\n\nSubstituting the given values:\n\nl = 40\nw = 60 / 40 = 1.5\n\nSo, the width of the rectangle",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: \\frac{x^2 - y^2}{x - y} = \\frac{x^2 - y^2}{x - y}.\n\nTo derive the equation, we can use the formula for the distance between two points in the plane. The distance between two points (x1, y1) and (x2, y2) is given by:\nd = sqrt((x2 - x1)^2 + (y2 - y1)^2)\nWe can substitute x1 = 0 and y1 = 0 into this formula to get",
        "gt_answers": "\\vert - \\frac { 1 } { 7 } \\vert = \\frac { 1 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_5150.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the formula in the image is incomplete. It appears to be written in an unfamiliar language and is missing some important details. Without more context or information, it is not possible to write out the formula using LaTeX format.\n\nHowever, if you provide more details about the image and what you want to express with the formula, I can try to help you write it out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $ $\\text{sin( }$\\text{x)}$\\text{= }$\\text{0.5}$. This equation represents the sine of x equal to 0.5.",
        "gt_answers": "\\sin \\alpha = \\frac { B C } { A B }\n",
        "image_path": "./data/HME100K/test_images/test_5152.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image:\n\n\\begin{center}\n$x^2 + y^2 = r^2$\n\\end{center}\n\nHere, $x$ and $y$ are the coordinates of a point on the surface of a sphere with radius $r$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\nx &= 2y - 3z\\\ny &= 4z + 5x\\\nz &= 6x - 8y\n\\end{align\\*}\nThis system of linear equations can be solved by substitution, elimination, or matrices. Substitution involves solving for one variable in terms of the others, then substituting those values back into the other equations to solve for the remaining variables. Elimination involves adding or subtracting multi",
        "gt_answers": "x _ { 1 } = 3 x _ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_5157.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows an equation in LaTeX format. The equation is: \\frac{2x^2 + 5x - 3}{x + 2}. The equation is in the form of a fraction, with the numerator being 2x^2 + 5x - 3 and the denominator being x + 2.",
        "gt_answers": "1 \\geq \\sin A > \\sin B \\geq - 1\n",
        "image_path": "./data/HME100K/test_images/test_5158.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:$$\\text{x}^2 + 4\\text{x} - 4 = 0$$This is a quadratic equation with a constant term of 4 and a variable term of 4x. The solutions to this equation are x = 2 and x = -2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:A=lw,where l is the length of the rectangle and w is the width of the rectangle. The area of a rectangle is the amount of space inside the rectangle.",
        "gt_answers": "x < \\frac { 9 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5160.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{b}{a+b} $$\n\nwhere b is the blue number in the image and a is the sum of the two numbers in the image.",
        "gt_answers": "\\angle B = 1 0 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5161.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$ 1 + x = 5 $$\n\nwhere x is any variable.",
        "gt_answers": "k ^ { 2 } = \\frac { 5 } { 4 } b ^ { 2 } - 1\n",
        "image_path": "./data/HME100K/test_images/test_5164.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows:\n\n$$\\frac{3\\sin(2x)}{x^2+2x-3}$$\nThis is the equation of a parabola with a vertex at the origin and a minimum value of -1/4 at x=0.",
        "gt_answers": "\\frac { \\pi } { 2 } + 2 k \\pi\n",
        "image_path": "./data/HME100K/test_images/test_5165.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:3x + 2y = 6xy = 12xy = 42xy = 16xy = 32xy = 64xy = 128xy = 324xy = 1286xy = 3242xy = 1286xy = 3242xy = 1286xy = 3242xy = 1286xy = 3242xy = 1286xy = 3242",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$a = \\frac{m}{n}$$\n\nwhere a is the acceleration, m is the mass of the object being accelerated, and n is the number of particles making up the object. This formula describes the relationship between acceleration and mass for an object with a constant acceleration.",
        "gt_answers": "A D = \\frac { 2 } { 5 } \\sqrt { 5 } x\n",
        "image_path": "./data/HME100K/test_images/test_5167.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Slope} = \\frac{\\text{rise}}{\\text{run}}$$\n\nwhere $\\text{rise}$ is the vertical distance between the top and bottom of the image, and $\\text{run}$ is the horizontal distance between the left and right sides of the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "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: x = 3(2y - 4z).",
        "gt_answers": "x _ { 3 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5170.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula in the image using LaTeX format, we can write:\n\n$$\\text{width} = \\text{length} \\times \\text{height} \\times \\sqrt{\\text{perimeter}}$$\n\nwhere $\\text{width}$ and $\\text{height}$ are the width and height of the rectangle, respectively, and $\\text{perimeter}$ is the perimeter of the rectangle, which is given by the formula:\n\n$$\\text{perimeter} = 2 \\times \\text{length} + 2 \\times \\text{width}$$\n\nSubstitut",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image using LaTeX format:\n\n$$x = \\frac{3y - 4z}{7y + 5z}$$",
        "gt_answers": "( 2 b - 3 c ) - ( 2 a - 3 b ) = - d i\n",
        "image_path": "./data/HME100K/test_images/test_5172.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula:\n\n$$ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 45 $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{a^2 + b^2}{2ab}$.\n\nThis formula calculates the mean of the arithmetic and geometric means of two numbers a and b, denoted by $\\frac{a^2 + b^2}{2ab}$. The arithmetic mean of two numbers is their sum divided by 2, and the geometric mean is the nth root of the product of the two numbers. In this case, the arithmetic mean is $\\frac{a^2 + b^2}{2ab}$, and the geometric mean is $\\sqrt[\\frac{a",
        "gt_answers": "3 \\times 2 = 6 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5175.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 100% (1 + 0.9984x)where x is the number of hours that the phone was used.",
        "gt_answers": "7 5 : 6 = 0 . 5 : 0 . 8\n",
        "image_path": "./data/HME100K/test_images/test_5176.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{1}{1 + \\frac{3}{4}} = \\frac{4}{7} $$\n\nThis can be written in LaTeX format as:\n\n$$ \\frac{1}{1 + \\frac{3}{4}} = \\frac{4}{7} $$",
        "gt_answers": "2 k \\pi - \\frac { \\pi } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_5177.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\frac{d^2x}{dt^2} + \\frac{kx}{m} = \\frac{F}{m}\n```",
        "gt_answers": "1 \\div 1 1 = \\frac { 1 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5178.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b",
        "gt_answers": "a = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5179.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:$$\\frac{1}{2}(2x+3y)$$where $x$ and $y$ are the coordinates of the point on the line.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{1}{1+x^2}=\\frac{1}{1+x^2}$$This is a formula for a quadratic function in the form of y = ax^2 + bx + c, where a, b, and c are constants.",
        "gt_answers": "y _ { 1 } = 2 4\n",
        "image_path": "./data/HME100K/test_images/test_5181.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\begin{equation}\nx^2 + y^2 = r^2\n\\end{equation}\n```\nIn this equation, the variable 'x' is squared, as well as 'y'. The sum of 'x' and 'y' squared is equal to 'r' squared.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the given expression:\n\n$$\\frac{30}{x + 5} = \\frac{5000}{30} \\times \\frac{30}{x}$$\n\nIn words, the expression is 30 divided by x plus 5, which is equal to 5000 divided by 30 multiplied by 30 divided by x.",
        "gt_answers": "3 0 \\times \\frac { 3 2 } { 3 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5183.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image is given by:\n\n$$\\text{ImageContent} = \\frac{1}{2}\\left( \\frac{1}{2}\\left( \\frac{1}{4}\\left( \\frac{1}{3}\\left( \\frac{1}{2}\\left( \\frac{1}{1}\\left( \\frac{1}{0}\\left( \\frac{1}{0}\\left( \\frac{1}{0}\\left( \\frac{1}{0}\\left( \\frac{1}{0}\\left( \\frac{1}{0}\\",
        "gt_answers": "O B = \\frac { 2 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5184.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle is given by:\n\n$$ A = l \\times w $$\n\nwhere l and w are the length and width of the rectangle, respectively. The area of the rectangle is the product of its length and width.",
        "gt_answers": "\\angle A = \\frac { 1 } { 2 } \\times 8 0 ^ { \\circ } = 4 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5186.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is: $ \\frac{18}{2 + 4} = \\frac{9}{6} = \\frac{3}{3} = 1$\n\nIn LaTex format, the formula can be written as:\n\n$\\frac{18}{2 + 4} = \\frac{9}{6} = \\frac{3}{3} = 1$",
        "gt_answers": "1 8 \\div 2 4 2 = \\frac { 1 8 } { 2 4 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5187.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{x^2 + 3x - 5}{x - 2}$.\n\nTo write this in LaTeX format, we use the following code:\n\n$$\\frac{x^2 + 3x - 5}{x - 2}$$\n\nHere, the $\\frac$ symbol is used to denote the fraction. The $x^2$ and $3x$ terms are enclosed in parentheses, and the $-5$ term is enclosed in a set of parentheses with a negative sign. Finally, the $x -",
        "gt_answers": "2 t = 2 t\n",
        "image_path": "./data/HME100K/test_images/test_5188.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![](https://www.quicklatex.com/lc11/img/m/1/0/e/y/1/0/e/y/1/0/e/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/0/",
        "gt_answers": "k = \\frac { y _ { 1 } - y _ { 2 } } { x _ { 1 } - x _ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_5189.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression of the formula in the image using LaTeX format:$$\\frac{2x + 3y - 5z}{x - y + 2z}$$The expression can be read as: the ratio of 2x plus 3y, with a denominator of x minus y plus 2z. This can also be read as 2x plus 3y, divided by x minus y plus 2z. The image shows an equation with variables x, y, and z.",
        "gt_answers": "x = \\frac { 1 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5190.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a triangle with base angle of 75 degrees and height of 12 is given by:\n\nA = (1/2)bh = (1/2)base \\* height = (1/2) \\* 12 \\* 75 = 2343.75 cm\u00b22343.75 square cm\u00b2The area of a triangle with base angle of 75 degrees and height of 12 is given by the formula:A=12bh2=12base\u200b*height\u200b=122",
        "gt_answers": "x = - \\frac { 2 8 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5191.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, you would need to use the following LaTeX code:\n\n```latex\n\\frac{a+b}{c+d}\n```\n\nIn this formula, the variables a and b represent the numerator, while the variables c and d represent the denominator. The division symbol '/' is used to indicate the division operation, and the fraction bar '{' is used to denote the fraction.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{2x^3+3x^2+x}{x^2+x-2}$.",
        "gt_answers": "1 \u3001 \\sqrt { 2 5 - x ^ { 2 } } = x - 1\n",
        "image_path": "./data/HME100K/test_images/test_5193.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula in the image using LaTeX format, we can use the following steps:\n\n1. First, we need to define the variables and constants in the formula.\n2. We can use the variables and constants to represent the mathematical operations in the formula.\n3. Finally, we can write out the formula in LaTeX format using the variables and constants.\n\nUsing the given image, the formula is:\n\n$$\\frac{L}{T} = \\frac{V\\_{ss} - V\\_{dd}}{R\\_o}$$\n\nIn LaTeX format, this formula would be written as:",
        "gt_answers": "w = \\frac { V _ { 4 } } { r } = \\frac { 2 } { 0 . 2 } r a d / s = 1 0 r a d / s\n",
        "image_path": "./data/HME100K/test_images/test_5194.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:$$\\frac{\\text{A}}{\\text{B}+\\frac{\\text{C}}{\\text{D}}}$$where $\\text{A}$, $\\text{B}$, $\\text{C}$, and $\\text{D}$ are constants.",
        "gt_answers": "\\frac { 1 } { 5 } - \\frac { 1 } { 8 } = \\frac { 1 } { 8 } \\times A\n",
        "image_path": "./data/HME100K/test_images/test_5195.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula for calculating the probability of an event occurring, which is denoted as P(A). The formula uses the concept of conditional probability, which is the probability of an event occurring given that another event has occurred. The formula is written as P(A|B) = P(A and B) / P(B).",
        "gt_answers": "c \\% = \\frac { 5 . 3 g } { 2 0 g } \\times 1 0 0 \\% = 2 6 . 5 \\%\n",
        "image_path": "./data/HME100K/test_images/test_5196.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format of the expression in the image:\n\n$$\\frac{24 - 4i}{9 - 3i}$$\n\nwhich simplifies to:\n\n$$\\frac{20 - 7i}{5 - 3i}$$\n\nYou can use the above LaTeX code to display the expression in LaTeX format.",
        "gt_answers": "\\frac { 1 } { 6 } + \\frac { 1 } { 8 } = \\frac { 7 } { 2 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5198.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ E = \\frac{1}{2}mv^2 $$\n\nwhere E represents the energy of the object, m represents its mass, and v represents its velocity.",
        "gt_answers": "F _ { 1 } l _ { 1 } = F _ { 2 } l _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5199.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:\n\n$$\\frac{1}{2} x^2 + \\frac{1}{4} x - \\frac{1}{8}$$\n\nThis formula represents the parabolic equation with the vertex at the origin and the focus at the point $(h,k)$. The coefficients are chosen such that the curve passes through the given points $(1,3)$ and $(4,6)$.",
        "gt_answers": "= 3 5 1\n",
        "image_path": "./data/HME100K/test_images/test_5200.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX equation for the given image:\n\n\\begin{center}\n\\frac{1}{2}(x^2 + 4x + 3) + \\frac{1}{3}x^3 + \\frac{1}{4}x^4\n\\end{center}\n\nThe expression is the sum of the arithmetic series with first term 1/4, common difference 1/3, and n terms 3.",
        "gt_answers": "x = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5201.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written in LaTeX format as follows:\n\n\\frac{x^2 - y^2}{x^2 + y^2}\n\nwhere $x$ and $y$ are variables representing the distances from the origin to the two points in the image. The numerator of the fraction represents the difference in the squared distances between the two points, while the denominator represents the sum of the squared distances. The fraction can be interpreted as a ratio of the distances between the two points, with the value ranging from 0 to 1.",
        "gt_answers": "\\sqrt { x + y } = \\pm \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5202.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am unable to see the image you provided. Please provide the image again so I can help you with your question.",
        "gt_answers": "\\cos \\theta = \\frac { \\sqrt { 2 1 } } { 1 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5203.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{2}{5} + \\frac{3}{7} = \\frac{19}{35}$$",
        "gt_answers": "( 2 - x ) ^ { 2 } + ( 1 . 5 + 0 . 5 ) ^ { 2 } = ( 2 . 5 ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5204.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $\\frac{x}{2}+\\frac{y}{3}+\\frac{z}{4}$\n\nThis formula is obtained by summing the ratios of the values of x, y and z to their respective denominators.",
        "gt_answers": "x _ { 2 } =\n",
        "image_path": "./data/HME100K/test_images/test_5205.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows:\n\n\\begin{equation}\nf(x) = \\frac{x^2}{2} - \\frac{3x}{2} + 1\n\\end{equation}\n\nwhere x is any real number.",
        "gt_answers": "( G - F _ { 1 } ) L _ { 1 } = G _ { 2 } l _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5206.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{3\\sqrt{2}+2\\sqrt{5}}{6}$$",
        "gt_answers": "\\frac { 1 2 } { 5 } < R \\leq 3\n",
        "image_path": "./data/HME100K/test_images/test_5207.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the derivative of f(x) with respect to x, denoted as dfdx. In LaTeX format, it can be written as follows:",
        "gt_answers": "k = \\pm \\frac { 1 } { \\sqrt { 1 1 } } = \\pm \\frac { \\sqrt { 1 1 } } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5208.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n$$\\begin{aligned} 8 \\times \\frac{7\\sqrt{10}}{4} + 4 \\times \\frac{3\\sqrt{12}}{6} \\ &= \\ 56 + 24 \\\\ &= \\ 80 \\end{aligned}$$",
        "gt_answers": "\\therefore = 1 8\n",
        "image_path": "./data/HME100K/test_images/test_5209.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula is:$$\\frac{2x+4y}{x+3y}=4\\frac{x}{x+3y}=2$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by:\n\n$ 4l^2 + 6l + 8 = 0 $\n\nThe equation is in the form of a quadratic equation, which can be solved using the quadratic formula:\n\n$ x = \\frac {-b \u00b1 \u221a(b^2 - 4ac)}{2a} $\n\nwhere a = 1, b = 6, and c = 8. Substituting the values, we get:\n\n$ x = \\frac {-6 \u00b1 \u221a(6^2 - 4 \\*",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula is given below using LaTeX format.\n\n\\begin{align\\*}\nx & = \\frac{a^2 + 2ab + b^2}{a^2 + 2b^2} \\\n&= \\frac{(3 + 2\\*2 + 1^2)}{(3 + 2\\*1^2)} \\\n&= \\frac{7}{11}\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{1}{3}$.",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5213.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is $\\pi$r^2$, where r is the radius of the circle. Using LaTeX format, we can write this as $\\pi$r$^2$.",
        "gt_answers": "y = 4 \\therefore O O A = 1\n",
        "image_path": "./data/HME100K/test_images/test_5214.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n$$\\text{Average value of } f(x) = \\frac{1}{n}\\sum\\_{i=1}^{n}f\\_{i}(x)$$\n\nHere, $n$ is the number of terms in the sum. The average value of $f(x)$ is the sum of the values of $f(x)$ divided by the number of terms.",
        "gt_answers": "x _ { 2 } = \\frac { \\sqrt { 6 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5215.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\text{4cos^2\u03b8 + 3cos\u03b8 - 1}$$\n\nwhere $\\theta$ is the angle between the line joining the centres of the two circles and the x-axis.",
        "gt_answers": "3 1 4 \\times 6 ^ { 2 } = 1 1 3 . 0 4 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5216.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\frac{x}{y} = \\frac{a^2}{b^2} \\Rightarrow x = \\frac{a^2}{b^2} y$$\n\nThis formula is the proportion formula and it states that the ratio of x to y is equal to the ratio of a to b. In other words, if we divide x by y, we get the same result as dividing a by b.",
        "gt_answers": "y = \\ln ( 1 + \\frac { M } { m } )\n",
        "image_path": "./data/HME100K/test_images/test_5217.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with width w and height h is given by:\n\nA = wh\n\nThe area of a circle with radius r is given by:\n\nA = \u03c0r^2\n\nThe formula for the volume of a rectangular prism with length l, width w, and height h is given by:\n\nV = lwh\n\nThe formula for the surface area of a sphere with radius r is given by:\n\nA = 4\u03c0r^2\n\nThe formula for the volume of a sphere with radius r is given by:\n\nV =",
        "gt_answers": "\\therefore B C = \\sqrt { 3 ^ { 2 } + 4 ^ { 2 } } = 5\n",
        "image_path": "./data/HME100K/test_images/test_5218.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\text{golden ratio} = \\frac{a}{b}$$\n\nwhere a and b are the lengths of the line segments in the image that form the golden ratio.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with width w and height h is:\n\nA = w \u00d7 h\n\nwhere w and h are measured in the same units. In this case, the width is 2a and the height is 3a, so the area is:\n\nA = 2a \u00d7 3a\n\nwhich simplifies to:\n\nA = 6a\u00b2",
        "gt_answers": "\\angle A O C = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5220.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the image:\n\n\\begin{center}\n\\begin{equation}\nV = \\frac{P\\_{trap}}{n} \\cdot \\frac{t}{t + \\frac{1}{2}\\cdot\\sigma}\n\\end{equation}\n\\end{center}\n\nIn this equation, $V$ is the volume of the trap, $P\\_{trap}$ is the pressure of the gas in the trap, $n$ is the number of moles of gas in the trap, $t$ is the temperature in Kelvin",
        "gt_answers": "V < 2\n",
        "image_path": "./data/HME100K/test_images/test_5221.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by: $\\sum\\_{i=1}^{n} a\\_i + \\sum\\_{i=1}^{n} b\\_i + \\sum\\_{i=1}^{n} c\\_i = \\sum\\_{i=1}^{n} d\\_i$",
        "gt_answers": ": x _ { 1 } = - \\frac { \\sqrt { 1 7 } + 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5223.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula written in LaTeX format: $\\frac{3}{2}(2x + 5) - 8$\n\nThe formula calculates the difference between the average of two numbers and a constant value. The average is calculated by adding the two numbers and dividing by the number of terms, which in this case is two. The constant value is -8.\n\nSo the formula is: $\\frac{3}{2}(2x + 5) - 8$",
        "gt_answers": "\\frac { 3 - x } { 2 - x } = \\frac { 1 } { x - 2 } + 3\n",
        "image_path": "./data/HME100K/test_images/test_5224.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I cannot see the image as it appears to be broken. Can you please provide a different image?",
        "gt_answers": "B C = \\frac { 1 } { 2 } B D = 2\n",
        "image_path": "./data/HME100K/test_images/test_5225.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ \\frac{a+b+c}{d+e+f} $$ where a, b, c, d, e, and f are positive integers.",
        "gt_answers": "x = \\frac { 1 } { 3 } + \\frac { 1 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_5226.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$ \\text{sin}\\left(\\frac{\\text{t}}{2}\\right) = \\frac{2}{\\text{t}} $$\n\nwhere t is the time taken for the object to fall from rest to the ground.\n\nNote that this expression assumes that the acceleration of gravity is constant, which is a simplifying assumption that can be made for this problem.",
        "gt_answers": "G ( 2 , \\frac { 1 } { 2 } a ^ { 2 } - 2 a - 6 ) , G N = \\vert a - 2 \\vert\n",
        "image_path": "./data/HME100K/test_images/test_5227.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$I = \\frac{V\\_{OC}-V\\_{CC}}{R}$$\n\nwhere $V\\_{OC}$ is the open-circuit voltage, $V\\_{CC}$ is the short-circuit voltage, and $R$ is the resistance of the circuit.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\\begin{center}\n$\\text{H}^{2}\\text{O} \\rightarrow \\text{H}^{2}\\text{O} + \\text{2}\\text{H}^{+}$\n\\end{center}\n\nwhere H2O represents water and H+ represents protons.",
        "gt_answers": "\\therefore \\Delta = ( - 1 ) ^ { 2 } - 4 ( a - 1 ) \\leq 0\n",
        "image_path": "./data/HME100K/test_images/test_5229.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b \u222b ( \u222b f(x) dx) + \u222b \u222b ( \u222b g(x) dx) dx\n\n\nThe formula in the image is the sum of two integrals, each of which is the integral of a function over a certain interval. The first integral is the integral of f(x) over the interval [0, a], and the second integral is the integral of g(x) over the interval [b, \u03c0]. The outer integral is over the interval [0, \u03c0].",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the product of two binomials with coefficients $3$ and $5$, respectively. The coefficient of the second binomial is $2$.",
        "gt_answers": "x = \\frac { 4 0 } { 1 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5231.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n1. ) + ( ) ) ( ) ) ) ) ( ) ( ) ) ) ) ) ( ) ( ) ) ) ( ) ( ) ( ) ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )",
        "gt_answers": "\\therefore y = - \\frac { ( x _ { 1 } - x _ { 2 } ) ^ { 2 } } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5232.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression in LaTeX format is: $\\frac{1}{\\sqrt{5}}$.",
        "gt_answers": "x = 3 5 0\n",
        "image_path": "./data/HME100K/test_images/test_5233.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{1}{3} x^2 - \\frac{1}{2} xy + \\frac{1}{6} y^2$$\n\nNote that this is just the standard form of the equation of a parabola given its focus and directrix. The focus is at the origin, and the directrix is x = 0 or y = 0.",
        "gt_answers": "0 . 7 5 \\times 2 = 1 . 5 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5234.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\sqrt{x^2}$.",
        "gt_answers": "b _ { 2 } - b _ { 1 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5235.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given below:\n\n![](https://i.imgur.com/88yE1yE.png)\n\n![](https://i.imgur.com/88yE1yE.png)where x and y are the variables, and n is a constant. The expression represents a parabolic function, where x is the independent variable and y is the dependent variable. The constant n represents the coefficient of x2 in the parabolic equation. The solution of the equation is given by the point where the graph of the function intersects the x",
        "gt_answers": "2 5 4 . 3 4 - 1 5 3 . 8 6 = 1 0 0 . 4 8 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5236.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula:\n\n$$\\text{BaCO}\\_{3} + \\text{Cr}(NO)\\_{3} \\rightarrow \\text{BaCrO}_{3} + \\text{NO}\\_{2}$$",
        "gt_answers": "P Q = C Q = C Q \\sin C = ( 6 0 - 2 0 \\sqrt { 3 } ) \\sin 6 0 ^ { \\circ } = 3 0 ( \\sqrt { 3 } -\n",
        "image_path": "./data/HME100K/test_images/test_5237.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$$2x^2 + 2x - 8 = 0$$",
        "gt_answers": "2 \\cos \\alpha = \\frac { 5 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5238.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{1}{2}$$\n\nHere, the numerator is 1 and the denominator is 2, so the fraction is 1/2.",
        "gt_answers": "\\frac { 1 } { 2 } x + 1 - 1 = - 1\n",
        "image_path": "./data/HME100K/test_images/test_5239.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the equation can be written as follows:\n\nx^3 + 3x^2 - 4x + 2 = 0\n\nwhere x is the variable.",
        "gt_answers": "\\sqrt { 3 x - 2 } - \\sqrt { x + 3 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_5241.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\u200b\n\nThe expression for the given image using LaTeX format is:\n\n\\begin{center}\n\\begin{equation}\nx^2 + 3x + 2 = 0\n\\end{equation}\n\\end{center}\n\nThis is the equation of a quadratic equation with roots at $\\{-1, 2\\}$ and a constant term of $2$.",
        "gt_answers": "2 1 0 3 < 2 1 3 0 < 2 3 0 1 < 2 3 1 0 < 3 0 1 2 < 3 0 2 1 < 3 1 0 2 < 3 1 2\n",
        "image_path": "./data/HME100K/test_images/test_5242.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\nx = (100)(120/60) - 20 = 360 - 20 = 340",
        "gt_answers": "1 \\times 6 = 4 8 6 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5243.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\text{P} = \\frac{500}{x + 250}$$\n\nwhere $x$ is the number of people who are 5'10\" or taller.",
        "gt_answers": "5 5 - 5 ( > ) 5 5 - 5 0\n",
        "image_path": "./data/HME100K/test_images/test_5244.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of the triangle with sides measuring 6, 8, and 10 units can be written as:\n\nA = (1/2) \\* 8 \\* 6 = 144 square units.\n\nAlternatively, the formula can be written in terms of the side lengths:\n\nA = (base \\* height) / 2\nA = (6 \\* 10) / 2 = 30 square units.\n\nTherefore, the area of the triangle is 30 square units.",
        "gt_answers": "\\angle 2 + \\angle A D E = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5245.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a table with three columns: `Column 1`, `Column 2`, and `Column 3`. The first column has the numbers `1`, `2`, and `3`, the second column has the numbers `4`, `5`, and `6`, and the third column has the numbers `7`, `8`, and `9`. All the numbers are written in a simple mathematical notation.",
        "gt_answers": "2 - k = 3 + 2 k\n",
        "image_path": "./data/HME100K/test_images/test_5246.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not visible. Can you provide the formula?",
        "gt_answers": ": \\frac { 5 } { 2 } = 4 8\n",
        "image_path": "./data/HME100K/test_images/test_5247.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2x + 3y - 5xy + 4y.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the derivative of f(x) = x^2, we can use the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1). Applying this rule to f(x), we have:\n\nf'(x) = 2x\n\nSo the derivative of f(x) = x^2 is f'(x) = 2x.",
        "gt_answers": "x ^ { 9 m } = ( x ^ { 3 m } ) ^ { 3 } = 2 ^ { 3 } = 8\n",
        "image_path": "./data/HME100K/test_images/test_5249.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: x = - (a / b).\n\nThis formula is a simple algebraic expression that can be used to find the inverse of a linear function. The formula represents the slope of the inverse line, which is the reciprocal of the slope of the original line. In this case, the inverse slope is -1/3, which can be found by taking the reciprocal of the slope of the original line, which is 3.",
        "gt_answers": "x = \\frac { 1 2 0 } { 2 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5250.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the formula using LaTeX format. Here it is:\n\n$$\\text{Image content}$$\n\nIn this formula, the red ink is used to draw the image of a cat. The formula is written using the LaTeX command `\\text`, which allows for the insertion of text into mathematical expressions.",
        "gt_answers": "x = \\frac { 1 } { 2 } \\times ( \\frac { 6 } { 5 } x - \\frac { 3 6 } { 5 } )\n",
        "image_path": "./data/HME100K/test_images/test_5251.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the derivative of a quadratic function is given by:",
        "gt_answers": "a _ { 0 } + a _ { 1 } + a _ { 2 } + \\cdots + a _ { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_5253.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Average Value of Y} = \\frac{\\text{Sum of Y}}{\\text{Number of Observations}}$$\n\nWhere $\\text{Y}$ is the dependent variable, $\\text{Average Value of Y}$ is the average value of Y, $\\text{Sum of Y}$ is the sum of Y, and $\\text{Number of Observations}$ is the number of observations.",
        "gt_answers": "x < \\frac { 3 6 0 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_5255.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in LaTeX format is: $\\frac{3x^2+4x-5}{2x+3}$.",
        "gt_answers": "\\frac { 1 } { x + y } = 3\n",
        "image_path": "./data/HME100K/test_images/test_5256.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the number of moles of a substance can be expressed as:n=m/Mwhere n is the number of moles, m is the mass of the substance, and M is the molar mass of the substance. In this case, the molar mass of the substance is 32.0 g/mol.\n\nTo determine the number of moles of the substance, we need to know its mass. The mass of the substance is 225 g. Therefore, the number of moles of the substance is:n=(225 g",
        "gt_answers": "h = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5257.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression using LaTeX format.\n\nThe expression in the image is: $\\frac{x+4}{x-2}$.\n\nIn LaTeX format, this expression can be written as: $\\frac{x+4}{x-2}$.",
        "gt_answers": "\\{ x \\vert 3 \\leq x \\leq - b \\}\n",
        "image_path": "./data/HME100K/test_images/test_5258.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a diagram with various mathematical expressions, including a variable x, a variable y, and a variable z. There are two equations given: the first is a quadratic equation of the form ax^2 + bx + c = 0, with a = 1, b = 4, and c = -3. The second equation is a line equation of the form y = mx + b, with m = 2 and b = 5.\n\nThe image is asking to solve the system of equations given in the diagram using the substitution method.\n\nThe solution is:\n\nx = (-",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression for the formula in the image using LaTeX format:\n\n$$\\frac{p \\cdot (a + b)}{q}$$\n\nwhere $p$ and $q$ are positive integers and $a$ and $b$ are positive real numbers.",
        "gt_answers": "\\varphi = c m \\Delta t = 4 2 0 0 \\times 2 \\times 1 0 = 8 4 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_5260.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of x can be written as:",
        "gt_answers": "( a - 1 ) x = b + 2 a\n",
        "image_path": "./data/HME100K/test_images/test_5261.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n$ \\frac{x}{2} - \\frac{x^3}{6} = \\frac{1}{4}$\n\\end{center}\n\nIn this formula, $\\frac{x}{2}$ represents the median of the data set, $\\frac{x^3}{6}$ represents the sum of the data set, and $\\frac{1}{4}$ represents the sample variance. By dividing the median by the sum and then dividing by the sample size, we obtain the sample mean.",
        "gt_answers": "\\sin B = \\frac { 2 R } { 2 R } = \\frac { b } { 2 R }\n",
        "image_path": "./data/HME100K/test_images/test_5262.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n$$\\text{Image Content}$$",
        "gt_answers": "\\angle A O C = 3 6 0 ^ { \\circ } - 1 5 8 ^ { \\circ } - 1 2 2 ^ { \\circ } = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5263.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\documentclass{article}\n\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{equation}\nx^2 + 2x - 3 = 0\n\\end{equation}\n\n\\end{document}\n```",
        "gt_answers": "3 y - 2 - 9 - y - 3 = - . \\sqrt { y + 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5264.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is A = \u03c0r^2, where r is the radius of the circle. The formula for the volume of a sphere is V = (4/3)\u03c0r^3, where r is the radius of the sphere.\n\nTo find the area of the circle in the image, we can substitute the radius, r, into the formula for the area of a circle: A = \u03c0r^2. The radius of the circle is approximately 1.7 cm, so the area of the circle is approximately 12.68 cm^2.",
        "gt_answers": "x = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5265.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\text{Area} = \\frac{1}{2}ab$$\n\nwhere 'a' and 'b' are the lengths of the two parallel sides of the rectangle.",
        "gt_answers": "= 9 \\times ( - \\frac { 3 } { 5 } ) - 1 2 = - 1 7 \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5266.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as follows:\n\n$$x^2 + 2x + 1 = 0$$\n\nThis is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = 2, and c = 1. The solutions to this equation are the values of x that make the equation true, which are x = - b/2a and x = - b/2a.\n\nThe discriminant, b^2 - 4ac, of this equation is (-2)^2",
        "gt_answers": "1 2 . 5 x - 8 . 3 x = 1 8 . 9\n",
        "image_path": "./data/HME100K/test_images/test_5268.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression of the formula in the image:\n\n$$\\begin{aligned} 2x^2 - 3x + 1 &= 0 \\qquad \\text{by substitution}\\\\\\\nx &= \\frac{1}{2} \\qquad \\text{by solving for} x\\end{aligned}$$\n\nThis expression represents the equation of a parabola with an axis of symmetry at x = 1/2 and a vertex at the origin. The solutions to the equation are x = 1/2 and x = -1/2.",
        "gt_answers": "x = \\frac { - b \\pm \\sqrt { \\Delta } } { 2 a } = \\frac { 4 \\sqrt { 3 } \\pm 2 \\sqrt { 2 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5269.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:xmyn=(a1(1x+b1y)+c1)&#x2212;(a2(2x+b2y)+c2)&#x2212;&#x03B1;(x&#x2212;a1)(y&#x2212;b1)+&#x03B1;(x&#x2212;a2)(y&#x2212;b2)+c2)xmyn=(a1(",
        "gt_answers": "x ^ { 2 } ( m - 1 ) = 1\n",
        "image_path": "./data/HME100K/test_images/test_5270.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:$$\\frac{d}{dt} \\left(\\frac{dx}{dt}\\right)= \\frac{1}{2}\\left(\\frac{d^2x}{dt^2}\\right) - \\frac{3}{2}x^2$$This can be derived from the given formula for the derivative of x with respect to time, $dx/dt=3x^2$, by applying the chain rule of differentiation. The expression gives the rate of change of the derivative of x with respect to time, which is equal to the derivative of the",
        "gt_answers": "2 9 \\approx 3 0\n",
        "image_path": "./data/HME100K/test_images/test_5271.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I cannot see the image as it is not provided. Please provide the image so that I can write out the expression of the formula using LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{5+7+9+11+13}{2+3+5+7+9}$ which simplifies to $\\frac{59}{20}$ in LaTex format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as follows in LaTeX format:\n\n\\begin{align\\*}\nx^2 + 3x + 1 = 0 \\\n\\end{align\\*}\n\nThe image shows the quadratic equation x^2 + 3x + 1 = 0, with the solution x = -3. This equation can be solved using the quadratic formula:\n\n\\begin{align\\*}\nx = -\\frac{b \\pm \\sqrt{b^2 - 4ac}}{2a} \\\n\\end{align\\*}\n\nPlugging",
        "gt_answers": "( x _ { 1 } - x _ { 2 } ) ^ { 2 } >\n",
        "image_path": "./data/HME100K/test_images/test_5274.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{A - B}{C - D}$. Here, $A$ and $B$ represent the two quantities to be added or subtracted, and $C$ and $D$ represent the two quantities to be subtracted or added. The formula is read as \"the ratio of A minus B to C minus D.\"",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: y = x4 - 6x3 + 10x2 + 12x + 5.",
        "gt_answers": "4 x ^ { 2 } y \\cdot 3 x y ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5276.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the derivative of a given function f(x), we can use the chain rule. The chain rule states that the derivative of a composite function f(g(x)) is given by:\n\n(f(g(x))') = f'(g(x)) \\* g'(x)\n\nwhere f'(g(x)) is the derivative of f evaluated at g(x), g'(x) is the derivative of g evaluated at x, and f'(x) is the derivative of f evaluated at x.\n\nApplying the chain rule to the given function, we have:\n\n(",
        "gt_answers": "\\frac { C E } { Q A } = \\frac { A E } { P A }\n",
        "image_path": "./data/HME100K/test_images/test_5278.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be written as follows using LaTeX format:\n\n$$\\begin{aligned} x^2 + 2x + 1 &= x^2 + 2x + 1 \\Rightarrow 2x + 1 = 0 \\\\ 2x + 1 &= 0 \\Rightarrow x = -\\frac{1}{2} \\end{aligned}$$",
        "gt_answers": "\\frac { 2 } { 3 } x + 1 = \\frac { 3 } { 4 } x\n",
        "image_path": "./data/HME100K/test_images/test_5279.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the expression: $\\frac{100}{200 - 100}$",
        "gt_answers": "y = x ^ { 2 } - 2 x + 3 = x ^ { 2 } - 2 x + 1 - 1 + 3\n",
        "image_path": "./data/HME100K/test_images/test_5280.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 6 inches can be written as follows:\n\nA = \u03c0r^2\n\nwhere r is the radius of the circle, which is 6 inches. Therefore, the area of the circle is:\n\nA = \u03c0(6)^2\n= 31.41592653589793238462640622089883374475941753584400869565",
        "gt_answers": "A F ^ { 2 } + F C ^ { 2 } = A C ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5282.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is: m = (n / (a + b)) where m is the midpoint, n is the number of terms in the arithmetic sequence, a is the first term, and b is the common difference.",
        "gt_answers": "a _ { n } = \\frac { [ 1 + ( 2 n - 1 ) ] \\cdot ( n + 5 ) } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5283.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{3\\times 4+2\\times 5}{2\\times 3}$$This can be written as follows:$$\\frac{3x4+2x5}{2x3}$$In LaTeX format, the expression would be written as:$$\\frac{3x4+2x5}{2x3}$$",
        "gt_answers": "x + \\frac { \\pi } { 4 } = \\frac { \\pi } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5284.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:\n\n$$\\frac{x^2 + y^2}{2xy}$$",
        "gt_answers": "A D = A B\n",
        "image_path": "./data/HME100K/test_images/test_5285.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n$$\\begin{aligned}\\text{Gravitational}\\_\\_ \\_\\_ &= \\text{acceleration} \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\_ \\_\\",
        "gt_answers": "\\frac { 1 } { y } = 0 ,\n",
        "image_path": "./data/HME100K/test_images/test_5286.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image in LaTeX format is:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick] (0,0) -- (1,0) node[midway,right] {$ \\frac{a}{b} $};\n\\draw[thick] (0,1) -- (1,1) node[midway,right] {$ \\frac{c}{d} $};\n\\draw[thick] (0,2) -- (1,2) node[midway,right] {$ \\frac{e}{f} $};\n\\draw",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows:\n\n\\begin{align}\n4x^2 + 4y^2 &= 16 \\\n\\end{align}\n\nThis is a quadratic equation in two variables, x and y, with a constant term of 16. The image shows a parabola with its vertex at the origin and its axis of symmetry passing through the points (1,0) and (0,1). The equation represents a sphere centered at the origin with a radius of 4.",
        "gt_answers": "y = \\frac { 1 6 } { 4 } y = 4\n",
        "image_path": "./data/HME100K/test_images/test_5290.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the number of triangles in the image is:\n\nTriangles = 1 + 5 + 4 + 9 = 19 triangles\n\nTherefore, there are 19 triangles in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\frac{1}{x^2 + 4x - 8}\n```",
        "gt_answers": "x = \\pm \\sqrt { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_5292.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a line with slope 1/4 that passes through the point (2, -1/4).\n\nThe equation can be written as:\ny = 1/4x + 3/4",
        "gt_answers": "y - \\frac { 2 } { y } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_5294.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{center}\n  \\frac{1}{2}\\left(\\frac{3\\left(\\frac{5}{6}\\right)^2 - 4\\left(\\frac{1}{3}\\right)^2}{5 - 4}\\right)\n\\end{center}\n```",
        "gt_answers": "3 a - 1 2 + 5 8 = 8 0\n",
        "image_path": "./data/HME100K/test_images/test_5295.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r can be expressed as:\n\nA = \u03c0r^2\n\nwhere A is the area and r is the radius of the circle.",
        "gt_answers": "x = \\frac { \\sqrt { 5 m - 1 } } { 1 m - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5297.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: \\frac{l}{b+c}\\frac{a}{b+c}\\frac{a}{b+c}\\frac{c}{b+c}\\frac{c}{b+c}\n\nwhere l is the length of the rectangle, a is the width of the rectangle, b is the width of the image, and c is the height of the image.",
        "gt_answers": "- \\angle B O A = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5298.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $\\frac{23}{4} + 5 = \\frac{30}{4}$.",
        "gt_answers": "\\frac { 3 6 } { 1 8 } = \\frac { 2 } { 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5299.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is not clear and cannot be written out using LaTeX format. It appears to be a scribble with no discernible meaning.",
        "gt_answers": "4 \\in \\{ x \\vert x = k \\pi , k \\in z \\}\n",
        "image_path": "./data/HME100K/test_images/test_5300.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 2x + 5y = 30. This can be rewritten as: 2x + 5y = 30.",
        "gt_answers": "x _ { 2 } = - \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5301.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is given by:$\\text{Average gradient of an image} = \\frac{1}{N}\\sum\\_{i=1}^{N} \\frac{\\text{pixel value at location } i}{\\text{pixel value at location } i - \\frac{1}{2}\\text{width of the image}}$where N is the total number of pixels in the image and $\\frac{1}{2}\\text{width of the image}$ is the width of the image divided by 2.\n\nNote: The above formula assumes that the image is a grayscale image,",
        "gt_answers": "y _ { 1 } = \\frac { 8 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5302.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a question asking for the expression of the formula in the image using LaTeX format. The formula is 2x + 3y = 12.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n\\begin{align}\nx &= \\frac{2}{3}\\left(\\frac{100}{99}+\\frac{100}{98}+\\frac{100}{97}\\right)\\left(\\frac{100}{96}+\\frac{100}{95}+\\frac{100}{94}\\right)\\left(\\frac{100}{93}+\\frac{100}{92}+\\frac{100}{91}\\right)\\left(\\frac",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n\u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b \u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is: ( 5 \\* 20) - 20 = 100.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned}x^2 + 4x - 12 &= 0\\end{aligned}$$",
        "gt_answers": "x _ { 2 } = - \\frac { \\sqrt { 1 0 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5307.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a linear equation in two variables. To write it in LaTeX format, we can use the following code:\n\n$$\\begin{aligned}x + 2y &= 4\\ \\\\ 3x - y &= 1\\end{aligned}$$\n\nThe first equation represents the line in the image with slope 2 and y-intercept 2. The second equation represents the line with slope 3 and y-intercept 1. The intersection of these two lines is the point where they intersect, which is represented by the equation:\n\n$$\\begin{aligned}x",
        "gt_answers": "\\frac { x + 2 } { 5 } = 2 - \\frac { 1 0 x - 1 0 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5308.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:\n\n$$\\frac{4(x^2+y^2)}{x^2-y^2}=4\\sqrt{x^2+y^2}$$\n\nwhere x and y are real numbers.",
        "gt_answers": "4 \\sqrt { 3 } \\times 4 \\sqrt { 3 } = 4 8 ( m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5309.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression in the image:\n\n\\begin{aligned} x^2 + 3x + 2 &= 0 \\ \\Rightarrow x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} \\\n\\end{aligned}\n\nwhere a, b, and c are the coefficients of the quadratic equation:\n\n\\begin{aligned} ax^2 + bx + c &= 0 \\ \\Rightarrow x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} \\",
        "gt_answers": "\\frac { 5 x } { y } \\cdot \\frac { y } { 1 5 x ^ { 2 } } = \\frac { 5 x - y } { y . 1 5 x ^ { 2 } } = \\frac { 1 } { 3 x }\n",
        "image_path": "./data/HME100K/test_images/test_5310.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear to me as it is written in a language I do not understand.\n\nHowever, the image shows a series of mathematical expressions that appear to be the equations of a mathematical function. The function appears to be nonlinear, with a graph that is concave upward. The variable x appears in the denominator, indicating that it is a factor in the function's output.\n\nIf you provide the image, I can attempt to solve the function.",
        "gt_answers": "x _ { 1 } = - \\sqrt { 2 1 } x _ { 2 } = \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5311.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula is:\n\n$$\\text{H}\\_{40}^{4 + } = \\frac{1}{2} \\cdot \\frac{1}{3} \\cdot \\frac{4 + 1}{3} \\cdot \\frac{4 + 1}{2}$$\n\nExpanding the product inside the parentheses, we get:\n\n$$\\frac{1}{2} \\cdot \\frac{1}{3} \\cdot \\frac{4 + 1}{3} \\cdot \\frac{4 + 1}{2} = \\frac{1}{6}",
        "gt_answers": "4 0 8 \\div 4 \u3001 8 1 2 \\div 4\n",
        "image_path": "./data/HME100K/test_images/test_5313.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the number of moles of a substance is given by:n = m/M, where m is the mass of the substance and M is the molar mass of the substance. The formula for the number of moles of a substance can be derived from the formula for the number of particles in a substance. The formula for the number of particles in a substance is given by:n = N/V, where N is the number of particles and V is the volume of the substance. The formula for the number of particles in a substance can be derived from the formula for the",
        "gt_answers": "F = P S = 3 . 3 \\times 1 0 ^ { 3 } P a\n",
        "image_path": "./data/HME100K/test_images/test_5315.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image can be written as follows:\n\nFor the image, we have:\n\nr= (456-234)2-(123+56)2r = (456 - 234)^2 - (123 + 56)^2r = (456 - 234)^2 - (123 + 56)^2r = (x - 234)^2 - (y + 56)^2r = (x - 234)^2 - (y + 5",
        "gt_answers": "\\frac { 1 } { 2 . 2 } = \\frac { 2 } { 4 . 4 } = \\frac { 3 } { 6 . 6 } = \\frac { 4 } { 8 . 8 } = \\frac { 5 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5316.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the formula in the image:\n\n$$ H\\_2O = \\ce{H2O} $$\n\nThis formula is written in LaTeX format, which is a mathematical typesetting language used to write mathematical equations and formulas. The formula is simply the chemical formula for water, written in LaTeX format.",
        "gt_answers": "C H _ { 2 } = C H - C O O C _ { 2 } H _ { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5317.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{2x+3y}{x-y}=\\frac{2(2x+3y)}{x-y}=4x+6y$$",
        "gt_answers": "\\frac { x + y + 2 \\sqrt { x y } } { x + y } = 1 + \\frac { 2 \\sqrt { x y } } { x + y } \\leq 1 + 1\n",
        "image_path": "./data/HME100K/test_images/test_5318.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x + 3x = 10x + 3x.",
        "gt_answers": "x _ { 2 } = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5319.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle can be represented as:\n\nA = lw + bhA = lw + bhA = lw + bhwhere l is the length of the rectangle and w is the width of the rectangle. The height of the rectangle is represented by h.\n\nTo find the area of the rectangle in the image, we can substitute the given values into the equation:\n\nA = 3.5 + 2(1)A = 3.5 + 2(1)A = 3.5 + 2(1)3.5 +",
        "gt_answers": "x _ { 3 } = \\frac { 1 } { 2 } + \\frac { \\sqrt { 2 1 } } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_5320.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$$\\text{FOCUS} = \\frac{12}{6}\\times\\frac{10}{6}\\times\\frac{8}{5}\\times\\frac{6}{5} + \\frac{30}{6}\\times\\frac{4}{6}\\times\\frac{7}{5}\\times\\frac{6}{5} + \\frac{15}{6}\\times\\frac{5}{6}\\times\\frac{9}{5}\\times\\frac{6}{5} + \\frac",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n\u222b(1/(x^2 + 1)) dx = - (1/2)log|x| + C.",
        "gt_answers": "\\frac { 1 } { x } = \\frac { 1 } { 0 . 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5325.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is as follows:\n\n\u222b\u222b \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\begin{align*}\n    x &= 2 \\\\\n    y &= -3 \\\\\n    z &= 4\n\\end{align*}\n```",
        "gt_answers": "A E = \\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_5328.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$P = \\frac{E \\cdot V}{T}$$\n\nwhere P is the pressure of the gas in the container, E is the energy required to lift the gas from its container, V is the volume of the container and T is the temperature of the gas in Kelvin.",
        "gt_answers": "\\angle D F B = \\angle D E B = \\angle H B C = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5329.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{3}{4} + \\frac{1}{2} = \\frac{5}{4} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given by the equation:</img>f(x) = 3x^2 - 5x + 2</img>This formula represents the area under the curve of the parabolic function y = x^2.</img>Note: The LaTeX format is not supported in this chat.</img>",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=0.5]\n\\draw[black,thick] (0,0) -- (10,0) node[midway,right] {$x$};\n\\draw[black,thick] (0,0) -- (0,10) node[midway,above] {$y$};\n\\draw[black,thick] (0,0) -- (2,5) node[midway,above right] {$z$};\n\\draw[black,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n\\begin{center} $ \\frac{m}{m+n} $ \\end{center}\n\nwhere $m$ and $n$ are the number of white and black balls in the image, respectively.",
        "gt_answers": "( a + 2 ) x + 4 b = a - 2\n",
        "image_path": "./data/HME100K/test_images/test_5334.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the area of the circle, we can use the formula for the area of a circle, A = \u03c0r^2, where r is the radius of the circle.\n\nThe radius of the circle is given as 5 cm in the image. Therefore, the area of the circle is:\n\nA = \u03c0r^2\nA = \u03c0(0.05)^2\nA = 0.0592\u03c0\n\nThe perimeter of the circle is given as 24 cm in the image. Therefore, the perimeter of the circle is:\n\nP =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a graph with the equation y = x^2. The x-axis represents the x-values and the y-axis represents the y-values. The graph is a parabolic shape with a vertex at the origin.",
        "gt_answers": "x = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5336.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$ P = \\frac{F \\* E}{L \\* C} $$\n\nWhere:\n\n* P is the pressure of the fluid in the system\n* F is the force applied to the piston\n* E is the energy stored in the compressed fluid\n* L is the length of the piston stroke\n* C is the specific heat capacity of the fluid.",
        "gt_answers": "0 < a < 1\n",
        "image_path": "./data/HME100K/test_images/test_5337.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 4 + 2x^2 - 4x + 5x^2 - 4x^2 + 6x + 4x^2 + 2x^2 - 3x - 5x + 4x^2 - 6x + 5x^2 - 5x + 6x - 3x^2 + 2x - 5x^2 + 2x^2 - 5x + 6x - 3x^2 + 2x - 5",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows in LaTeX format:\n\n\\begin{center}\n\\begin{aligned}\n& & \\text{ImageContent} & & \\text{ImageContent} & & \\text{ImageContent} & & \\text{ImageContent} & & \\text{ImageContent} & & \\text{ImageContent} & & \\text{ImageContent} & & \\text{ImageContent} & & \\text{ImageContent} & & \\text{ImageContent} & & \\text{ImageContent} & & \\text{ImageContent} & & \\text",
        "gt_answers": "x \\leq - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5339.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can follow the steps below:\n\n1. Convert the image into a LaTeX document by copying and pasting the image into a text editor and then saving it as a LaTeX file.\n2. Identify the variables and constants in the formula and represent them with the corresponding LaTeX commands. For example, the variable x can be represented with the command x, and the constant 2 can be represented with the command 2.\n3. Write the formula in LaTeX format using the identified variables and constants. The formula in the image is given by the equation",
        "gt_answers": "\\sqrt { \\frac { 9 } { y } } + \\sqrt { y } = 4\n",
        "image_path": "./data/HME100K/test_images/test_5340.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n$$\\text{Image Content}$$\n\nIn this formula, the letters \"t\" and \"a\" represent the subscript indices of the variables \"c\" and \"e\", respectively, in the formula. The subscript index \"a\" represents the coefficient of \"c\" in the formula, and the subscript index \"t\" represents the exponent of \"e\" in the formula.",
        "gt_answers": "\\overrightarrow { A E } / / \\overrightarrow { A T }\n",
        "image_path": "./data/HME100K/test_images/test_5342.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{10 - 5}{2 + 4}$",
        "gt_answers": "\\frac { 2 } { 3 } - \\frac { 1 } { 8 } = \\frac { 1 3 } { 2 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5344.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can follow these steps:\n\n1. Identify the variables in the formula. In this case, there are two variables: x and y.\n2. Write out the formula using LaTeX notation. We can use the following LaTeX commands to write out the formula:\n3. Substitute the values of x and y into the formula. In this case, we have x = 3 and y = 4. So the formula becomes:\n4. Simplify the formula if possible. In this case, the formula is already simplified,",
        "gt_answers": "\\frac { D E } { E G } = \\frac { C E } { E F }\n",
        "image_path": "./data/HME100K/test_images/test_5345.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:$$\\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}{3}+1+\\frac{1}{4}+1+\\frac{1}{5}+1+\\frac{1}{6}+1+\\frac{1}{7}+1+\\frac{1}{8}+1+\\frac{1}{9}+1+\\frac{1}{10",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by the equation x = 2y + 3z, where x, y, and z are variables. This equation is a linear equation with a slope of 2 and an intercept of 3.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is the derivative of the logarithmic function y = x\\*\\*log(x).",
        "gt_answers": "\\frac { x ^ { 2 } } { 9 } - \\frac { y ^ { 2 } } { 1 6 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_5348.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$3^2 - 4 \\times 3 + 1$$",
        "gt_answers": "\\vert 3 b - 1 \\vert = 0\n",
        "image_path": "./data/HME100K/test_images/test_5349.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX code for the formula in the image:\n\n$$\\frac{m}{m+n}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle can be represented using the formula A = \u03c0r^2, where r is the radius of the circle. Using LaTeX format, this can be written as:\n\n$$A = \\pi r^2$$\n\nwhere A is the area of the circle, r is the radius of the circle, and \u03c0 is the mathematical constant that is approximately equal to 3.14159.",
        "gt_answers": "\\vert - \\frac { 7 } { 1 6 } \\vert = \\frac { 7 } { 1 6 }\n",
        "image_path": "./data/HME100K/test_images/test_5351.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 3x + 2y = 11, where x and y are the variables.",
        "gt_answers": "\\frac { x } { 2 } = \\frac { y } { 3 } = \\frac { z } { 4 } = m\n",
        "image_path": "./data/HME100K/test_images/test_5352.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n\\begin{center}\n\\begin{aligned}\nP(X = x) &= P(X = x \\cap A) + P(X = x \\cap B) \\\\\n&= P(A \\cap X = x) + P(B \\cap X = x)\n\\end{aligned}\n\\end{center}\n\nHere, P(X = x) is the probability that the random variable X takes the value x. P(A \\cap X = x) and P(B \\cap X",
        "gt_answers": "b = - 2 c _ { 2 } - 4\n",
        "image_path": "./data/HME100K/test_images/test_5354.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: 2 + 2 = 4.",
        "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": "MiniGPT4"
    },
    {
        "question": "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\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "\\frac { 8 } { 1 2 } = \\frac { 4 } { 4 } = \\frac { 1 } { 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5356.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of the circle with radius 3 is given by the formula:\n\nA = \u03c0r^2\n\nwhere r is the radius of the circle. In this case, the radius is 3, so the formula becomes:\n\nA = \u03c0 \\* 3^2\nA = 3.14 \\* 9\nA = 28.26\n\nTherefore, the area of the circle with radius 3 is approximately 28.26 square centimetres.",
        "gt_answers": "A E = A B + B E = 3 0 m\n",
        "image_path": "./data/HME100K/test_images/test_5358.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the image is not provided, so I cannot write out the expression of the formula in the image using LaTeX format. Please provide the image so I can assist you.",
        "gt_answers": "x + y = 3\n",
        "image_path": "./data/HME100K/test_images/test_5359.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$\\frac{x\\_2-x\\_1}{x\\_3-x\\_2}$$",
        "gt_answers": "b ^ { 2 } > a ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5360.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we need to add the parentheses and multiplication symbol after the variable.\n\nThe expression is:\n\n$$x^4 - 3x^2 + 2x + 1$$\n\nNote that we need to add a negative sign before the second term, as it is a negative binomial coefficient.",
        "gt_answers": "8 ) - ( 2 ) = ( 6 )\n",
        "image_path": "./data/HME100K/test_images/test_5361.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n\\begin{center}\n\\frac{3x+4}{2x+8}=\\frac{3(x+2)+4(2x+4)}{2(x+2)+8(2x+4)}=\\frac{3x+6}{x+4}=\\frac{9}{x+4}\\end{center}\n\nThis expression represents the equation shown in the image, with the variable x on the left side and the variable x on the right side.",
        "gt_answers": "\\frac { 1 } { 0 . 5 } = \\frac { 2 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_5364.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX formula for the expression in the image:\n\n\\begin{center}\n$ f(x) = \\frac{1}{2}x^2 + 4x - 6 $\n\\end{center}\n\nThe function is a quadratic function with a constant term of 6 and leading coefficient of 4. The x-intercepts are x = -2 and x = 2, and the vertex is at x = -1. The maximum value of the function is 12 and the minimum value is -6.",
        "gt_answers": "x _ { 2 } = - \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5365.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format. The formula is a simple arithmetic expression that can be expressed as follows:",
        "gt_answers": "q = I \\cdot 1 .\n",
        "image_path": "./data/HME100K/test_images/test_5366.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$ ( x - y) \\times ( b - a) = (x - a) \\times (b - y) $$\n\nwhere $a$ and $b$ are the coordinates of the points $A$ and $B$, respectively, and $x$ and $y$ are the coordinates of the point $C$.",
        "gt_answers": "y _ { 2 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5370.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle can be written as:\n\nA = l x w,\n\nwhere A is the area of the rectangle, l is the length and w is the width.",
        "gt_answers": "f ( a _ { n } ) = ( - 2 ) \\times 2 ^ { n - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5371.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a perfect square is given by:\n\n$$ x = \\sqrt{a^2 + b^2} $$\n\nwhere $a$ and $b$ are the lengths of the two sides of the square. In this case, the length of one side of the square is 200 mm and the length of the other side is 300 mm. So, we can write:\n\n$$ x = \\sqrt{(200)^2 + (300)^2} $$\n\nSimplifying the expression, we get:\n\n$$ x = \\sqrt{2",
        "gt_answers": "- 8 0 x + 2 0 0 0 = - 2 5 0 x + 5 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_5372.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the sum of consecutive integers is given by:$$\\sum\\_{i=1}^{n} i$$This formula adds up all the numbers from 1 to n, and the result is the sum of the consecutive integers from 1 to n.",
        "gt_answers": "= \\frac { 1 } { 1 0 0 } - 1 = - \\frac { 9 9 } { 1 0 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5373.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\text{sin}(x) - \\text{cos}(x) = \\sin(x)$. This can be written in LaTeX format as $\\sin(x) - \\cos(x) = \\sin(x)$.",
        "gt_answers": "y = \\frac { 8 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_5375.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$ \\text{hilal = \\frac{1}{2}} $$\n\nwhere hilal is the image of the expression.",
        "gt_answers": "H C l + A g N O _ { 3 } = H N O _ { 3 } + A g C I \\downarrow\n",
        "image_path": "./data/HME100K/test_images/test_5376.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\na + bx + cx^2 = (a + b)(1 + cx)\n\\end{align\\*}",
        "gt_answers": "a \\geq \\frac { 1 } { 2 } ( 2 0 0 - 2 a )\n",
        "image_path": "./data/HME100K/test_images/test_5377.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n\u222bab[f(x)]dx=\u222bbaf(x)dx.\u222bab[f(x)]dx=\u222bbaf(x)dx.\n\nThis is the Fundamental Theorem of Calculus, which states that the definite integral of a function from a to b is equal to the antiderivative of the function evaluated at the upper limit minus the antiderivative evaluated at the lower limit.\u222bab[f(x)]dx=\u222bbaf(x)dx.\u222bab[f(x)]dx=\u222bbaf(",
        "gt_answers": "B D = O D = \\frac { 1 } { 2 } B D , A C \\bot B D \\angle 4 = \\angle 5\n",
        "image_path": "./data/HME100K/test_images/test_5378.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write the formula in LaTeX format. Here's the formula for the given image:\n\n\\begin{center}\n$$ V = \\frac{1}{2}m\\_o g t^2 + \\frac{1}{2}mv^2 $$\n\\end{center}\n\nwhere\n\n* $V$ is the volume of the sphere\n* $m\\_o$ is the mass of the sphere\n* $g$ is the acceleration due to gravity\n* $t$ is the time taken for the ball to fall from rest to the ground\n* $v",
        "gt_answers": "V = \\frac { m } { \\rho } = \\frac { 0 . 5 k g } { 1 . 0 \\times 1 0 ^ { 3 } k g / m ^ { 3 } } = 0 . 5 \\times 1 0 ^ { - 3 } k g / m ^ { 3 } .\n",
        "image_path": "./data/HME100K/test_images/test_5379.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I cannot see the image you have provided. Can you please provide a link or a way to access the image?\n\nOnce I have access to the image, I can write out the expression of the formula using LaTeX format.",
        "gt_answers": "\\vert - 3 \\vert - ( 3 - \\pi ) ^ { \\circ } - 2 \\sin 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5380.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: ( 2 - 1) \\* 3 + 2 = 10.",
        "gt_answers": "D E ^ { 2 } = D O \\cdot D B\n",
        "image_path": "./data/HME100K/test_images/test_5382.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:$$x^2+5x-3$$This is the formula for the parabolic function.",
        "gt_answers": "x = \\frac { \\sqrt { 3 } } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5383.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is:\n\n4(sqrt((52 - 25)^2 + (38 - 25)^2) - 3(25 - 20)^2 + (50 - 25)^2)/((sqrt((52 - 25)^2 + (38 - 25)^2) - 3(25 - 20)^2 + (50 - 25)^2))^2\n\nwhere:\nsqrt((52 - 25)^2 + (38 - 25",
        "gt_answers": "1 1 4 ^ { \\circ } \\times \\frac { 1 } { 2 } = 5 7 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5385.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression in the image:\n\n\\begin{center}\n$ x^2 + 2x + 1 = 0 $\n\\end{center}\n\nNote: This is a quadratic equation with roots at $ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} $.",
        "gt_answers": "y _ { 4 } = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5386.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$y = \\frac{500}{x + 500}$$\n\nwhere $x$ is the number of hours it takes for the temperature to drop from 90 degrees Fahrenheit to 60 degrees Fahrenheit, and $y$ is the number of hours it takes for the temperature to drop from 70 degrees Fahrenheit to 60 degrees Fahrenheit.",
        "gt_answers": "S = \\frac { 1 0 } { 9 } x - \\frac { 5 0 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_5387.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{\\text{mass}}{\\text{volume}}$$\n\nwhere mass is the variable representing the weight of the object in the image, and volume is the variable representing the volume of the object in the image.",
        "gt_answers": "\\downarrow F = \\downarrow P \\overline { S }\n",
        "image_path": "./data/HME100K/test_images/test_5388.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\nThe expression is a rational expression, which means that it is in the form of p/q, where p and q are polynomials. To write it in LaTeX format, we need to use the \\frac command, which creates a fraction.\n\nThe numerator is p(x) = 2x - 3 and the denominator is q(x) = x + 1. Therefore, the expression can be written as:\n\n$$\\frac{2x - 3}{x + 1}$$\n\nIn LaTeX format, this is",
        "gt_answers": "\\frac { 1 } { R } = \\frac { 1 } { R _ { 1 } } + \\frac { 1 } { R _ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_5389.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$x + 2 = 4$$\n\nThis formula represents a line that passes through the point (1, 3) and has a slope of 2. To graph this equation, we can plot the point (1, 3) on the x-axis and use the slope 2 to find the y-intercept.\n\n$$y = 2x + 4$$\n\nWe can substitute the x-value of 1 into this equation to find the y-value:\n\n$$y = 2(1) +",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is 4 - 2 x + 3.",
        "gt_answers": "y = \\frac { 1 } { 2 } ( x ^ { 2 } - 2 x - 3 )\n",
        "image_path": "./data/HME100K/test_images/test_5391.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\nThe formula is an algebraic expression that represents a function of x.\n\nThe variable x appears in the denominator, so this is a fractional expression.\nThe variable x is raised to the power of 2, which means that the expression will have the form of a parabola with an axis of symmetry at x = 0.\nThe coefficient of x in the numerator is 2, which means that the function is quadratic, with the constant term equal to 2.\nThe constant term in the denominator is 2, which means that the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n$$ f(x) = \\frac{2x^2 + 6x - 3}{x^2 - 4x + 1} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is \\frac{1}{2}\\sum\\_{i=1}^{n}\\sum\\_{j=1}^{i}a\\_jx\\_i=\\frac{1}{2}\\sum\\_{i=1}^{n}x\\_i\\sum\\_{j=1}^{i}a\\_j.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for a right triangle with a hypotenuse of 6 cm and a height of 5 cm. The formula is given by: $\\text{x}^2 + \\text{y}^2 = \\text{h}^2$ and $\\text{x} = \\sqrt{\\text{h}^2 - \\text{y}^2}$ where $\\text{x}$ and $\\text{y}$ are the lengths of the legs of the triangle and $\\text{h}$ is the height.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is: `2x^2 + 8x - 12`.",
        "gt_answers": "A C = 1 2\n",
        "image_path": "./data/HME100K/test_images/test_5396.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n$\\text{T}\\_n=\\frac{\\text{C}\\_n + \\text{O}\\_n}{2}$\n```",
        "gt_answers": "C O = \\sqrt { A O ^ { 2 } - A C ^ { 2 } } = 3\n",
        "image_path": "./data/HME100K/test_images/test_5397.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is written as follows in LaTeX format:\n\n\\begin{center}\n\\frac{d^2x}{dt^2} + 2g\\omega\\_n\\sin(\\omega\\_nt - \\theta\\_n) = 0\n\\end{center}\n\nwhere $x$ is the position of the pendulum as a function of time $t$, $g$ is the acceleration due to gravity, $\\omega\\_n$ is the angular frequency of the pendulum, and $\\theta\\_n$ is the phase angle of the driving force.",
        "gt_answers": "( x - y ) ( x ^ { 2 } + x y + y ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5398.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$3x^2 + 2x - 1$",
        "gt_answers": "\\vert y = 3 \\vert y = - 2\n",
        "image_path": "./data/HME100K/test_images/test_5399.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} 3x + 5 &= 13 \\ \\text{or} \\ 3x + 5 = 13 \\end{aligned}$$\n\nExplanation:\nThe formula in the image is written as $\\text{3x + 5 = 13}$. In LaTeX format, we can write this as:\n\n$$\\begin{aligned} 3x + 5 &= 13 \\ \\text{or} \\ 3x + 5 = 13 \\end",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n\\begin{equation}\nf(x) = \\frac{1}{\\sqrt{x^2 + 4}}\n\\end{equation}\nNote that the expression is written in a different format than the one given in the image, since LaTeX is not capable of drawing images.",
        "gt_answers": "7 3 x < 2 x + 4\n",
        "image_path": "./data/HME100K/test_images/test_5401.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{1}{x}$.\n\nThis formula is derived from the fundamental theorem of algebra, which states that any non-constant polynomial with real coefficients has at least one real root. In this case, the polynomial is $x^2 + 1 = 0$, which has a root of $x = -1$. Therefore, the formula is $\\frac{1}{-1} = -1$.",
        "gt_answers": "a + b = 4 , a b = 1\n",
        "image_path": "./data/HME100K/test_images/test_5402.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x^2+y^2}{x^2+y^2}=\\frac{x^2}{x^2}+\\frac{y^2}{y^2}=\\frac{1}{2}+\\frac{1}{2}=\\frac{1}{2}$.",
        "gt_answers": "x > - \\frac { 1 9 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5403.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```scss\n\n\\begin{aligned}\nx & = & 4 \\\\\ny & = & \\frac{x}{2} \\\\\nz & = & \\frac{y}{3}\n\\end{aligned}\n```",
        "gt_answers": "0 . 4 : \\frac { 3 } { 5 } = x : 1 \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5404.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{1}{2}(b + \\frac{1}{2}a) + \\frac{1}{4}a^2$$This can be derived by applying the formula for the moment of inertia of a rectangle about an axis passing through its center of mass. The moment of inertia of a rectangle about an axis passing through its center of mass is given by the formula:$$I = \\frac{1}{2}bh^2 + \\frac{1}{4}ah^2$$where b is the length of the rectangle parallel",
        "gt_answers": "\\cdot D E \\bot B E , D F \\bot A B\n",
        "image_path": "./data/HME100K/test_images/test_5405.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n$$ v = \\frac{3v}{4v+2v} $$\n\nwhere v is the velocity of the object and the expression represents its kinetic energy in terms of its velocity.",
        "gt_answers": "V = \\frac { 1 } { 3 } s h\n",
        "image_path": "./data/HME100K/test_images/test_5406.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the number of sides of a regular polygon with n sides is:\n\nn sides = n\n\nThe number of diagonals of a regular polygon with n sides is:\n\nn - 4\n\nThe sum of the degrees of all the vertices of a regular polygon with n sides is:\n\n(n - 2) + (n - 3) +... + 3 + 2 + 1 = (n - 2)(n - 3)/2 = (n^2 - 6n + 8)/2 = (n^2 - 4n +",
        "gt_answers": "1 6 8 \\div 3 2 0 = \\frac { 1 6 8 } { 3 2 0 } = \\frac { 2 1 } { 4 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5407.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation of a linear line in 2D space.\n\nThe equation of a linear line in 2D space is given by:\n\ny = mx + b\n\nwhere m is the slope of the line and b is the y-intercept.\n\nThe image shows the equation of a line with slope 3 and y-intercept 5.\n\nThe equation can be written as:\n\ny = 3x + 5\n\nThis equation represents a line that passes through the point (0, 5) and has a slope of 3.",
        "gt_answers": "S _ { \\Delta A O B } = \\vert S _ { \\Delta } O A D - S _ { \\Delta } O B D \\vert = \\frac { 1 } { 2 } ( x _ { 1 } - x _ { 2 } ) =\n",
        "image_path": "./data/HME100K/test_images/test_5408.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$d = \\frac{1}{2}\\left( \\sqrt{x^2 + y^2} - \\sqrt{x^2 + y^2 - 2xy} \\right)$$This is a formula for the distance between two points in a two-dimensional space. The formula is based on the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this formula, the variable x represents the horizontal distance from the origin to one",
        "gt_answers": "\\frac { D E } { B C } = 2\n",
        "image_path": "./data/HME100K/test_images/test_5409.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned}\nf(x) &= \\frac{1}{x^2+3x-5} \\\n&= \\frac{x-2}{x^2+3x-5} \\\n&= \\frac{x-2}{x+1}\n\\end{aligned}$$",
        "gt_answers": "x = \\frac { 6 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_5410.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n$$ \\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 \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression:\n\n\\begin{align\\*}\n 16x^2 + 14x - 6 &= 0 \\\n \\therefore x = \\frac{14 \\pm \\sqrt{16^2 - 4(14)(-6)}}{2(14)} = \\frac{7 \\pm \\sqrt{11}}{4} = \\frac{7 \\pm 3.71}{2} = \\frac{7 + 3.71}{2} = 5.355 \\\n \\end{",
        "gt_answers": "( a + b ) \\times c = a \\times c + b \\times c\n",
        "image_path": "./data/HME100K/test_images/test_5413.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the expression in the image:\n\n\\begin{equation}\n\\frac{2x^2+5x-3}{x+2}=\\frac{2(x+1)(x+2)}{(x+2)^2+5x+3}\n\\end{equation}",
        "gt_answers": "x + 2 = \\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_5414.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$y = \\frac{100000}{x^2 + 1}$$",
        "gt_answers": "G E / / A B , P F / / A B\n",
        "image_path": "./data/HME100K/test_images/test_5415.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n$$\\frac{1}{\\sqrt{2}}$$\n\nThis formula is a fraction with the numerator equal to 1 and the denominator equal to the square root of 2. This is a common formula used in calculus to find the square root of a number.",
        "gt_answers": "y _ { 2 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5416.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ 2x^2 + 2x - 6 = 0$$This is a quadratic equation in standard form, with the coefficient of $x^2$ being 2 and the constant term being -6. To solve this equation, we can use the quadratic formula:$$x = {-b \u00b1 \u221a(b^2 - 4ac) } / 2a$$Substituting the values for $a = 1$, $b = 2$, and $c = -6$, we get:$$x = {-",
        "gt_answers": "2 a - 2 b = 2 ( a - b )\n",
        "image_path": "./data/HME100K/test_images/test_5417.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not provided. However, assuming that it is the sum of two numbers, we can write it as:\n\n10 + 20 = 30",
        "gt_answers": "\\frac { 4 0 0 0 } { x } - \\frac { 4 0 0 0 } { 1 . 2 5 x } = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_5419.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format. Here's the LaTeX code for the formula:\n\n\\begin{center}\n$\\frac{a}{b} = \\frac{m}{n}$\n\\end{center}\n\nIn this formula, $a$, $b$, $m$, and $n$ are variables. The expression $\\frac{a}{b}$ is equivalent to $\\frac{m}{n}$ because they represent the same value. This formula can be used to solve various types of equations involving fractions.",
        "gt_answers": "\\frac { A ^ { \\prime } B } { A ^ { \\prime } N } \\cdot \\frac { D M } { M A ^ { \\prime } } = \\frac { D M } { M A } = 2\n",
        "image_path": "./data/HME100K/test_images/test_5421.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n$$p + a + b + p$$",
        "gt_answers": "P A = B A - P B = 5 - \\frac { 2 5 } { 9 } = \\frac { 2 0 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_5422.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{5\\times10^3 + 7\\times10^2 + 6\\times10^1 + 2\\times10^0}{20}$$",
        "gt_answers": "P _ { 1 } = \\frac { 3 + \\sqrt { 1 3 } } { 2 } \\cdot P _ { 2 } = \\frac { 3 - \\sqrt { 1 3 } } { 2 } \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_5423.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image appears to show a mathematical expression involving the binomial theorem and an exponent of 4. The expression is: (a+b)^4= a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4.\\nThe binomial theorem states that for any nonnegative integer n, (a+b)^n= a^n + na^(n-1)b + (n-1)a^(n-2)b^2 +... + b^n.\\nThe exponent 4 in the image is raised to the power",
        "gt_answers": "a ^ { 2 } + b ^ { 2 } < c ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5424.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression that describes the relationship between two variables. The expression is written as:y = x\u00b2 + 2x + 1where y is the dependent variable and x is the independent variable. This means that the value of y is directly proportional to the value of x, with an increase of 2x and a constant value of 1.\n\nThis expression can be used to find the equation of a line of best fit for a set of data points, as it represents the linear relationship between the two variables. The coefficient of determination (r\u00b2) can be calculated to measure the goodness of",
        "gt_answers": "\\frac { x ^ { 2 } } { 2 } + y ^ { 2 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_5425.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{\\text{Image Content}}{\\text{Original Image Content}}$$\n\nwhere $\\text{Image Content}$ is the value obtained by the image processing algorithm and $\\text{Original Image Content}$ is the original value of the image before processing.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The formula in the image is:c3 + b2 - 4a2 = 0. This is a quadratic equation in the form ofax2+bx+c=0. To solve for x, we can use the quadratic formula:x=\u2212b\u00b1b2\u22124ac2ax=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}x=2a\u2212b\u00b1b2\u22124ac\u200b2a\u200bTo find the value of x that satisfies the equation, we substitute the values of a, b,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given below in LaTeX format.\n\n\\begin{center}\n\\begin{tikzpicture}\n\\begin{axis}[\nwidth=10cm,\nheight=10cm,\nxlabel=$x$,\nylabel=$y$,\nxmin=-5, xmax=5,\nymin=-5, ymax=5,\ngrid=both,\n]\n\\addplot[blue,thick,label={$y=ax$}] {x};\n\\addplot[red,thick,label={$y=bx+c$}] {",
        "gt_answers": "\\angle A K H = \\angle E K G = 6 0\n",
        "image_path": "./data/HME100K/test_images/test_5428.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by: \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that! Here's the LaTeX code for the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[line width=0.5pt, fill=black] (0,0) circle (1cm);\n\\node[anchor=center] at (0.5,0.5) {$ \\frac{1}{2} $};\n\\end{tikzpicture}\n\\end{center}\nThis code draws a circle with radius 1cm, centred at the origin, and labels it with $\\frac{1}{2}$.",
        "gt_answers": "y ^ { 2 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5430.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{aligned}\n\\frac{1}{2} + \\frac{3}{4} &= \\frac{5}{8} \\\n\\end{aligned}\n\\end{center}\n\nThe expression represents a simple arithmetic expression where we add the fractions $\\frac{1}{2}$ and $\\frac{3}{4}$ and simplify the result to $\\frac{5}{8}$. The expression can be read as \"one half plus three fourths is equal to five eighths\".\n##",
        "gt_answers": "1 2 \\times \\frac { 3 } { 8 } = \\frac { 9 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5431.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nx^2 + 4x + 4 = 0\n```",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$x = \\frac{a\\*b}{c}$$where a, b, and c are constants.\n\nThe expression for the formula in LaTeX format is:$$x = \\frac{a b}{c}$$where a, b, and c are constants.",
        "gt_answers": "- \\frac { 1 } { 2 } x - a = - 1\n",
        "image_path": "./data/HME100K/test_images/test_5433.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression of the formula in the image:\n\n$$ \\text{lead} = \\frac{60}{50} $$\n\nThe expression is simply the ratio of the lead content (in parts per million, or ppm) to the overall concentration of the sample (in grams per liter, or g/l).\n\nI hope this helps! Let me know if you have any other questions.",
        "gt_answers": "\\angle E A D = \\angle A D F = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5434.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\n3x + 5y = 10\n\\end{align\\*}\n\nNote: The image is not displaying, so I am unable to determine the exact values for x and y in the formula.",
        "gt_answers": "y _ { 3 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5435.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the derivative of y with respect to x. It is given by: dy/dx= 3x - 5y.",
        "gt_answers": "l y _ { 1 } = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5436.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is written as:\n\n$$x^2 + 3x + 4 = 0$$\n\nThis is a quadratic equation with two variables, x and y. The solutions to the equation are the values of x and y that make the equation true. The solutions to this equation are x = -3 and x = 1. The discriminant of the equation is b^2 - 4ac, which is equal to 9 - 4(1)(-3) = 18. Since the discriminant is positive, the equation has two real solutions.",
        "gt_answers": "\\frac { V } { V _ { m } } = \\frac { 1 0 . 0 8 L } { 2 2 . 4 2 / m o l } \\approx 0 . 4 5 m o l\n",
        "image_path": "./data/HME100K/test_images/test_5438.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the equation in the image is y = x^2.\n\nIn LaTeX format, the equation is written as:\n\n$$y = x^2$$\n\nwhere $x$ is the independent variable and $y$ is the dependent variable.",
        "gt_answers": "y = \\frac { 9 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5441.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$E=mc^2$$where E is the energy of the system, m is the mass of the system, and c is the speed of light in a vacuum.",
        "gt_answers": "R _ { 2 } = \\frac { 1 2 V } { 1 A } = 1 2 \\Omega\n",
        "image_path": "./data/HME100K/test_images/test_5442.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$ 3x + 2y = 7 $$",
        "gt_answers": "y = \\frac { 1 7 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5443.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\begin{aligned} \\frac{1}{2}(x^2 + 4x) - 3x + 1\\end{aligned}$$",
        "gt_answers": "2 0 x = 1\n",
        "image_path": "./data/HME100K/test_images/test_5445.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}\ny &= \\frac{a + b}{c + d} \\\n&= \\frac{4x + 3y - 2z}{2x + 4y - 5z} \\\n&= \\frac{x + \\frac{3y}{2} - \\frac{z}{2}}{x + \\frac{4y}{2} - \\frac{5z}{2}} \\\n&= \\frac{x + \\frac{y}{2} - \\frac{z",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:$\\sum\\_{i=1}^{n}x\\_i$where $x\\_1, x\\_2, \\ldots, x\\_n$ are the data points in the scatter plot. The sum is taken over all $i=1$ to $n$.",
        "gt_answers": "\\frac { x } { x ^ { 2 } - 1 } = \\frac { 7 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5447.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by: $\\frac{a}{b} = \\frac{c}{d}$\n\nwhere $a, b, c, and d$ are positive integers with $a < b$ and $c < d$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ E = mc^2 $$\n\nwhere E is the energy of the object, m is its mass, and c is the speed of light in a vacuum. This equation states that the energy of an object is equal to its mass multiplied by the square of the speed of light.",
        "gt_answers": "3 0 m = 3 0 0 0 c m\n",
        "image_path": "./data/HME100K/test_images/test_5449.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $latex x = \\frac{3xy + 4y}{5x + 4y}$$latex x = \\frac{3xy + 4y}{5x + 4y}$$latex x = \\frac{3xy + 4y}{5x + 4y}$$latex x = \\frac{3xy + 4y}{5x + 4y}$$latex x = \\frac{3xy + 4y}{5x + 4y}$$latex x = \\frac{3xy + 4y",
        "gt_answers": "I = I _ { 1 } + I _ { x } = 0 . 3 A + 0 . 6 A = 0 9\n",
        "image_path": "./data/HME100K/test_images/test_5450.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$i = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$$",
        "gt_answers": "y _ { 1 } = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5451.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\n\\begin{equation}\nP = \\frac{1}{2}mv^2 + \\frac{1}{2}kx^2\n\\end{equation}\n```\nIn this equation, P represents the potential energy of the system, m represents the mass of the object, v represents its velocity, k represents the spring constant, and x represents the displacement of the object from its equilibrium position.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{x^3 + 3x^2 - 5x - 4}{x + 2}$.",
        "gt_answers": "\\frac { 2 k - 1 } { 5 } \\leq \\frac { k + 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5453.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as follows:\n\na + b = c\n\nwhere a, b, and c are variables.",
        "gt_answers": "a = \\frac { c \\sin A } { \\sin C }\n",
        "image_path": "./data/HME100K/test_images/test_5454.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\sqrt{\\frac{1}{4}}\\cdot\\frac{1}{2}+\\frac{1}{8}\\cdot\\frac{1}{4}=\\frac{1}{4}+\\frac{1}{8}=\\frac{9}{16}$\n\nThis formula represents the sum of the two expressions: $\\sqrt{\\frac{1}{4}}\\cdot\\frac{1}{2}$ and $\\frac{1}{8}\\cdot\\frac{1}{4}$ and can be written as $\\frac{1}{4}+\\frac{1}{8}=\\frac{",
        "gt_answers": "\\frac { 1 } { 2 } x = - 2\n",
        "image_path": "./data/HME100K/test_images/test_5456.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we need to first identify the variables and mathematical operations in the formula. Then we can use LaTeX commands to typeset the formula.\n\nThe formula in the image is:\n\n<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><msub><mi>r</mi><mi>2</mi></msub><msub><mi>h</mi><mi>2</mi></msub><mo>=</mo><msub",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression. Here is the LaTeX format of the expression:\n\n$$\\frac{100 + 96 - 12}{24} = 5$$\n\nIn words, this expression is adding 100, 96, and 12, then dividing the sum by 24. The result is 5.",
        "gt_answers": "m ^ { 2 } y ^ { 2 } + 1 + 2 m y + 4 y ^ { 2 } - 4 = 0 .\n",
        "image_path": "./data/HME100K/test_images/test_5462.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a formula in LaTeX format: \\frac{x^2+7x+15}{x^2+2x+6}.",
        "gt_answers": "x = \\frac { 5 } { 1 7 }\n",
        "image_path": "./data/HME100K/test_images/test_5463.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a quadratic equation, represented by the following LaTeX expression:ax^2+bx+c=0where a, b, and c are constants. The formula is used to find the roots (solutions) of the equation. The image is showing the formula being written on a piece of paper with a pen. The formula is written in a mathematical notation, with the variables and constants written in bold font and the equal sign written in normal font. The formula is written in a standard format, with the constants and variables written on separate lines. The constants are written in a bold font, and the variables",
        "gt_answers": "A C = \\sqrt { O A ^ { 2 } + D C ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_5465.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is given by:\n\n$$x^2 + y^2 = 1$$\n\nThis equation represents a circle with a radius of 1 centered at the origin. The center of the circle is at the point (0,0).",
        "gt_answers": "y _ { 3 } = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5466.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is x / ( 2 - x ), which is the derivative of the expression x / 2 with respect to x.",
        "gt_answers": "\\frac { 3 } { 1 0 } + \\frac { 1 } { 1 0 } = \\frac { 4 } { 1 0 } .\n",
        "image_path": "./data/HME100K/test_images/test_5467.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image provided is a mathematical expression that represents the formula for the area of a rectangle with length `l` and width `w`.\n\nThe formula for the area of a rectangle with length `l` and width `w` is `A = lw`.\n\nTherefore, the image provided represents the formula for the area of a rectangle with length `l` and width `w`.",
        "gt_answers": "( y - 1 5 ) ( y + 1 ) \\geq 0\n",
        "image_path": "./data/HME100K/test_images/test_5468.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$$p = \\frac{1}{2} \\times 10 + \\frac{1}{4} \\times 20 + \\frac{1}{8} \\times 30 + \\frac{1}{16} \\times 40 + \\frac{1}{32} \\times 50$$\n\nThis formula calculates the sum of the products of the fractions of the given numbers, where each fraction is the numerator divided by the denominator.",
        "gt_answers": "P _ { 4 } ( . - 1 , 0 )\n",
        "image_path": "./data/HME100K/test_images/test_5469.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is $\\frac{b}{a^2}$.",
        "gt_answers": "\\div \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5470.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX equation for the expression in the image:$$x^2 + y^2 = r^2$$where x and y are the coordinates of the point and r is the radius of the circle.\n\nTo write out the equation using LaTeX format, you can use the following syntax:\n$$\\text{expression}$$where $\\text{expression}$ is the mathematical expression you want to write out in LaTeX format.\n\nSo in this case, the LaTeX equation for the expression in the image would be:$$x^2 + y^2 = r^2$$",
        "gt_answers": "y = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5471.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is A = \u03c0r^2, where A is the area, r is the radius, and \u03c0 is a mathematical constant approximately equal to 3.14. To find the area of the circle shown in the image, we can substitute the given values into the formula:\n\nA = \u03c0(5cm/2)^2 = \u03c0(2.5cm)^2 = 7.85cm^2\n\nTherefore, the area of the circle is approximately 7.85 cm^2.",
        "gt_answers": "1 . 5 \\times 3 0 0 = 4 5 0 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_5472.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} & x^2 - 6x + 8 = 0 \\Rightarrow x = \\frac{2\\pm\\sqrt{6}}{2} \\Rightarrow x = 1 \\pm 3i \\end{aligned}$$\n\nAlternatively, we can use the quadratic formula to find the solutions:\n\n$$\\begin{aligned} ax^2 + bx + c = 0 \\Rightarrow x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}",
        "gt_answers": "( 7 0 - y ) \\div 2 = 5 y\n",
        "image_path": "./data/HME100K/test_images/test_5473.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{\\text{a}}{\\text{b}}$.",
        "gt_answers": "A O = \\frac { \\sqrt { 3 } } { 2 } a\n",
        "image_path": "./data/HME100K/test_images/test_5474.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is:\n\n$$e = 2 \\times 10^6 V \\cdot t + 10^4 J$$\nThis formula describes the energy stored in a capacitor with a capacitance of $10\\:\\text{mF}$ and a voltage of $2\\times 10^6$ volts, after a time $t$ has elapsed. The energy stored in the capacitor is equal to the product of the capacitance and voltage, and the time elapsed.\n\nThe formula is derived using the equation for energy stored in a capacitor, which",
        "gt_answers": "\\angle F E C = 2 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5476.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:y = - x + 3x\u00b2 - 2x\u00b3+x\u2074.",
        "gt_answers": "\\frac { 1 } { x - y } = v\n",
        "image_path": "./data/HME100K/test_images/test_5477.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I don't see any image attached to your message. Can you please provide the image so that I can assist you?",
        "gt_answers": "\\angle C A D + \\angle 3 = 1 8 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5478.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} 2x + 3 &= 6 \\ \\rightarrow x = \\frac{6 - 3}{2} = 2 \\ \\rightarrow x^2 + 2x + 3 = 6 \\ \\rightarrow x = \\frac{6 - 2x - 3}{2} = 2 \\end{aligned}$$\n\nAlternatively, you can use the following LaTeX code to write out the expression:\n\n$$\\begin{aligned} 2x + 3 &= 6 \\",
        "gt_answers": "\\frac { - 2 - a } { 3 } - \\frac { ( - 1 ) - a } { 2 } = - 2\n",
        "image_path": "./data/HME100K/test_images/test_5479.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is the derivative of the function y = x^2 with respect to x, denoted as d/dx y = x. This can be written in LaTeX as:$\\frac{d}{dx} y=x^2$",
        "gt_answers": "\\overrightarrow { B N } = \\frac { 1 } { 2 } \\overrightarrow { A D } = \\frac { 1 } { 2 } \\overrightarrow { b } + D \\overrightarrow { a }\n",
        "image_path": "./data/HME100K/test_images/test_5480.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 4x + 3y = 9.",
        "gt_answers": "- \\frac { 8 } { 3 } = \\frac { 4 } { 3 } + m\n",
        "image_path": "./data/HME100K/test_images/test_5481.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n$$\\text{mass}=\\frac{1}{2}\\text{magnitude}^2$$\nThis formula represents the mass of an object as the product of its magnitude and magnitude squared. The constant of 1/2 is used to convert the magnitude to mass.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![](https://i.imgur.com/1NxJ3aS.png)\n\nwhere:\n\na = 10\nb = 20\nc = 30\nd = 40\ne = 50\nf = 60\ng = 70\nh = 80\ni = 90\nj = 100\nk = 110\nl = 120\nm = 130\nn = 140\no",
        "gt_answers": "a ^ { 2 } + b ^ { 2 } \\geq 2 a b = 2\n",
        "image_path": "./data/HME100K/test_images/test_5485.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the LaTeX expression for the formula in the image: $\\frac{3x+2y}{x+y}=\\frac{5}{2}$",
        "gt_answers": "\\frac { 6 } { 3 - 2 } + \\frac { m } { 3 - 2 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_5486.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\text{Sin}\\left( \\frac{4}{x}+\\frac{3}{x^2}\\right)=\\frac{4}{x}+\\frac{3}{x^2}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we need to identify the variables and coefficients in the formula and write them in the appropriate format.\n\nFrom the image, we can see that the formula is in the form of x + y = 10.\n\nWe can write this formula as follows:\n\n$$x + y = 10$$\n\nThis formula can be read as \"x plus y equals 10.\" The variables in this formula are x and y, and the coefficient for x is 1 and the coefficient for y is 1.\n\nIn LaTeX",
        "gt_answers": "x - \\frac { 3 } { 4 } = \\pm \\frac { \\sqrt { 3 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5489.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: x2 - y2 = ( x1 - y1 )2.",
        "gt_answers": "x = \\sqrt { 5 0 4 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5490.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula:\n\n\\begin{center}\n\\begin{aligned}\n\\text{ImageContent} & = & \\text{0.56}\\times\\text{1.56}\\times\\text{1.56}\\times\\text{2.89}\\times\\text{0.75}\\times\\text{0.75}\\times\\text{0.56}\\times\\text{0.32} \\\\\n& = & \\frac{1}{8}\\times\\frac{1}{2}\\times\\frac",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not provided.\n\nThe expression in LaTeX format for the given formula is: $\\frac{3x^2+4x-5}{x^2-3x+1}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is 4x\u00b2 - (x + 3)\u00b2 - 2x.\n\nThe formula represents the area of a rectangle with base 4x and height x + 3. To find the area of the rectangle, we use the formula:\n\nArea = base x height\n\nSubstituting the values for base and height in the formula, we get:\n\nArea = 4x x (x + 3)\n\nExpanding the parentheses inside the formula, we get:\n\nArea = 4x x (x + 3)",
        "gt_answers": "x ^ { - } = \\pm \\sqrt { \\frac { 2 } { a - 1 } }\n",
        "image_path": "./data/HME100K/test_images/test_5494.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, the expression for the formula in the image is:\n\n$$ ( x + 4) \\times (y - 2) = (a + 2) \\times (b - 1)$$\n\nIn this formula, x and y represent the number of males and females in the population, respectively. The variables a and b represent the number of males and females in the sample, respectively.",
        "gt_answers": "C _ { \\Delta E D F } = 3 D E = 6 \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5495.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as follows:\n\n$$\\frac{x+y+z}{4}$$",
        "gt_answers": "\\sqrt { 2 x - 1 } \\geq 0\n",
        "image_path": "./data/HME100K/test_images/test_5496.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 10 - 3x + 2x^2 $$\n\nwhere x is the variable representing the time in minutes.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=0.5]\n\\draw[black] (0,0) rectangle (2,2);\n\\draw[white] (0.5,0.5) circle (0.5);\n\\node[above right, black] at (1,1) {$f(x) = \\frac{x^2}{2}$};\n\\draw[black] (2.5,0) -- (2.5,2);\n\\node[right, black] at (",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\n\\frac{x^{2}}{x^{2}+4} &= \\frac{x^{2}}{x^{2}+4} \\\\\n&= \\frac{1}{1+4} \\\\\n&= 0.25\n\\end{align\\*}",
        "gt_answers": "x _ { 1 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5499.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is 2\\*((15\\*0.9)\\*0.5) + 6 = 20.75.",
        "gt_answers": "b = \\frac { a \\sin B } { \\sin A } = \\sqrt { 3 } + 1\n",
        "image_path": "./data/HME100K/test_images/test_5500.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{50 + 30\\frac{x + 3}{x - 1}}{100 - \\frac{30}{x - 1}}$$",
        "gt_answers": "x _ { 1 } = \\frac { 2 } { 5 } x _ { 2 } = \\frac { 3 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_5501.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $\\frac{1}{\\sqrt{2}}$x^2 + $\\frac{1}{2}$x + $\\frac{1}{4}$",
        "gt_answers": "c = - 2\n",
        "image_path": "./data/HME100K/test_images/test_5502.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. Here's the LaTeX format for the given expression:\n\n\\begin{align\\*}\na = \\frac{1}{2}b + \\frac{1}{3}c + \\frac{1}{4}d\n\\end{align\\*}\n\nThis is a simple arithmetic expression that adds up the fractions of $a$, $b$, $c$, and $d$. To display it in LaTeX, we use the align environment to line up the equations, and the fraction function to typeset the fractions.\n\nI hope that helps! Let",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that.\n\nThe expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\nf(x) & = \\frac{1}{2}(x - 2)^2 + 1 & \\text{for } -2 \\leq x \\leq 2 \\\\\n    & = \\frac{1}{2}(x - 3)(x + 1) + 1 & \\text{for } -3 \\leq x \\leq 3\n\\end{align\\*}\n\nThe first equation is the quadratic formula for the",
        "gt_answers": "a + b = \\pm\n",
        "image_path": "./data/HME100K/test_images/test_5505.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```scss\n\nThe formula for the sum of the first n positive integers is:\n\nn^2 + (n - 1)^2\n```",
        "gt_answers": "x = \\frac { b } { a }\n",
        "image_path": "./data/HME100K/test_images/test_5507.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be written as follows:\n\n\\begin{align\\*}\nx^2 + 3x + 1 &= 0 \\\n&\\iff x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} \\\n&= \\frac{-3 \\pm \\sqrt{9 - 4 \\* 1 \\* 2}}{2 \\* 1} \\\n&= \\frac{-3 \\pm \\sqrt{7}}{2} \\\n&= \\frac{1 \\pm \\sqrt{7}}{2}\n\\end{align",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression that represents the formula for the area of a circle. The formula is A = pi \\* r^2, where pi is the mathematical constant 3.14 and r is the radius of the circle. To calculate the area, we substitute the values for pi and r into the formula, resulting in A = 3.14 \\* r^2. The image displays the formula as a series of equations and variables, with the radius variable represented by the number 5.2 and the pi variable represented by the constant value of 3.14.\n\nThe formula for the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: \u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": ": a = 4 b : 6\n",
        "image_path": "./data/HME100K/test_images/test_5511.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "1. The sum of 3 and 5 is 8.\n\n2. The difference of 7 and 9 is 2.\n\n3. The product of 2 and 6 is 12.\n\n4. The quotient of 10 and 4 is 2.5.\n\n5. The square root of 16 is 4.\n\n6. The cube root of 8 is 2.\n\n7. The reciprocal of 0.5 is undefined.\n\n8. The integral of 3x^2 from x=",
        "gt_answers": "x 1 = \\frac { 1 } { 2 } \\sqrt { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5512.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of the triangle shown in the image is:\n\nA = (1/2) \\* base \\* height\n\nwhere the base is 4 cm and the height is 6 cm.\n\nA = (1/2) \\* 4 cm \\* 6 cm\nA = (1/2) \\* 4 cm \\* 6 cm = 12 cm^2",
        "gt_answers": "g ^ { \\prime } = \\frac { 4 } { 9 } g\n",
        "image_path": "./data/HME100K/test_images/test_5513.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $ x = 2\\sin(y) - 2\\cos(y) $\n\nwhere $ x $ and $ y $ are variables.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $ $\\frac {a^2+b^2}{2ab}=\\frac{a^2+b^2}{2}$$. This equation represents the geometric mean of two numbers, a and b.",
        "gt_answers": "x = \\frac { 8 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5515.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\text{ImageContent} = \\frac{3\\times2 + 5\\times3 + 7\\times4}{9\\times1 + 8\\times2 + 11\\times3} $$\n\nThe formula for this expression is:\n\n$$ \\text{ImageContent} = \\frac{\\text{Sum of terms in the numerator}}{\\text{Sum of terms in the denominator}} $$\n\nThe numerator of the formula is $3\\times2 + 5\\times3 + 7\\times4",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression for the formula in the image:\n\n\\begin{align} \\\nx &= \\frac{5}{2}\\left( \\frac{2t}{15}+\\frac{3t}{10} \\right) \\\ny &= \\frac{t}{2}\n\\end{align}\nIn this formula, t is a variable representing time, and x and y are functions of t representing the position of an object at time t. The formula shows how the position of the object changes with time.",
        "gt_answers": "\\cot A = \\frac { 7 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5517.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a diameter of 6 cm is:\n\nA = \u03c0r^2, where r is the radius of the circle.\n\nUsing the given diameter of 6 cm, we can find the radius:\n\nr = diameter/2 = 6 cm/2 = 3 cm.\n\nSubstituting this value into the formula, we get:\n\nA = \u03c0(3 cm)^2 = 3.14159 \u00d7 9 cm^2 = 28.2148 cm^2.\n\nThere",
        "gt_answers": "2 x = 4 8\n",
        "image_path": "./data/HME100K/test_images/test_5518.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, you can use the following LaTeX code:\n\n$$\\frac{a + b}{c + d} = \\frac{a + b}{c + d}$$\nThis is because the numerator and denominator have the same terms.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$ f = \\frac{a \\cdot b}{c} $\n\nWhere a, b, and c are the variables given in the formula.",
        "gt_answers": "5 0 N l _ { 1 } = 3 0 N l _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5520.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$x=\\frac{2(1)(2(3)(4))-(1)(2(3))}{(3)(4)}$$",
        "gt_answers": "x _ { 1 } = \\frac { \\sqrt { a } } { a }\n",
        "image_path": "./data/HME100K/test_images/test_5522.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula for the sum of the squares of two numbers. The formula is written in LaTeX format as follows:\n\n$$\\sum\\_{i=1}^{n} x\\_i^2 = \\frac{n\\left(n+1\\right)}{2}$$\n\nThis formula is derived from the formula for the sum of an arithmetic series, which is given by:\n\n$$\\sum\\_{i=1}^{n} a\\_i = \\frac{n\\left(a\\_1 + an\\right)}{2}$$\n\nTo get the sum of the squares of two numbers,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is y = 2x + 2.\n\nThis can be verified by substituting x = 0, x = 1, and x = 2 into the equation and verifying that the resulting values are 2, 4, and 6, respectively.",
        "gt_answers": "y _ { 3 } = 2 , y _ { 4 } = - 2\n",
        "image_path": "./data/HME100K/test_images/test_5524.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression for the formula in the image:$$m = \\frac{3x^2+5x-2}{x^2+7x+2}$$This formula represents the equation of a parabolic function with vertex at the origin and a y-intercept of -2. The coefficient of x^2 is 3, the coefficient of x is 5, and the constant term is -2.",
        "gt_answers": "m ^ { 2 } + 1 = 2 m = 1\n",
        "image_path": "./data/HME100K/test_images/test_5525.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image can be written as follows:\n\n$$2x^2+2y^2=16$$\n\nThis is the equation of a circle in the Cartesian plane with center at the origin and radius 4.",
        "gt_answers": "x ^ { 2 } + 2 + \\frac { 1 } { x ^ { 2 } } = 9\n",
        "image_path": "./data/HME100K/test_images/test_5527.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the expression:\n\nA = l \\* w\n\nwhere l is the length and w is the width of the rectangle. In this case, the length is 4 cm and the width is 5 cm, so the area of the rectangle is:\n\nA = 4 \\* 5 = 20 cm2\n\nTherefore, the area of the rectangle is 20 cm2.",
        "gt_answers": "x = 1\n",
        "image_path": "./data/HME100K/test_images/test_5528.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is a representation of the electric field at a distance from the charged object. The electric field lines are shown as dashed lines, and the electric flux density is shown as a solid line. The equation is as follows:\n\nElectric flux density = Electric field x Area of surface\n\nIn this equation, E is the electric field strength, A is the area of the surface over which the electric flux is being measured, and E.sub. is the electric flux density.\n\nThe electric field strength can be calculated using the equation:\n\nE = (1/4\u03c0\u03b5) x (",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is 3x + 4y = 15.\n\nThe x-coordinate of the image is 3x = 9, since 3x + 4y = 15 and y = 15 - 4x.\nThe y-coordinate of the image is 4y = 12, since 3x + 4y = 15 and x = 3(12).\nTherefore, the equation of the line passing through the image is y = 12 - 3x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{1000 \\* \\frac{1}{2}}{(240 - 49.9) + 19.9\\*\\frac{1}{2}}$$This formula is used to calculate the average return on investment for a stock over a certain period of time. It takes into account the current stock price, the expected return, and the time period over which the stock will be held. The expected return is the average return that the stock is expected to earn over the period of time.\n\nThe formula",
        "gt_answers": "x _ { 3 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5531.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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$$ \\text{A} = \\frac{2 \\times 4 - 10}{5 + 3} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\begin{aligned} 3x^2 - 5x + 2 &= 3(x^2 - 5x) + 2 \\  \\\\ &= 3(x - 5/3)(x + 2/3) \\  \\\\ &= (3x - 5/3)(3x + 2/3) \\  \\\\ &= 9x^2 - 15x + 6/3 \\  \\\\ &= 9x^2 - 15x + 2 \\  \\\\ &=",
        "gt_answers": "y _ { 4 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5533.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the formula in the image:\n\n\u222bdF/dt=\u2202F/\u2202t+v\u00d7F\\int \\frac{dF}{dt} = \\frac{\\partial F}{\\partial t} + v \\times F\u222bdF\u200b/dt\u200b=\u2202F\u200b/\u2202t\u200b+v\u00d7F\u200bwhere F is the force acting on an object, v is the velocity of the object, and t is time.\n\nThe formula represents the change in force over time, taking into account both the velocity of the object and any external forces acting on it.\n##",
        "gt_answers": "\\angle A O C = 3 6 0 ^ { \\circ } - 1 5 0 ^ { \\circ } - 1 2 0 ^ { \\circ } = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5536.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression of the formula in the image:\n\n$$\\text{F} = m \\frac{dv}{dt} + \\frac{1}{2}mv^2$$\n\nwhere $F$ is the force acting on the object, $m$ is the mass of the object, $v$ is the velocity of the object, and $dv/dt$ is the time derivative of the velocity.",
        "gt_answers": "D E \\bot A C\n",
        "image_path": "./data/HME100K/test_images/test_5537.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: y = 6x^2 - 10x + 8.\n\nHere's the LaTeX code for the expression:\n\n$$ y = 6x^2 - 10x + 8 $$\n\nIn the image, the function is a parabolic function with an equation of y = 6x^2 - 10x + 8, which passes through the points (0, 1) and (2, 4). The graph of the function has a minimum value of 1 at x = 0 and a maximum value",
        "gt_answers": "y = 6 \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5538.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image: $\\frac{b}{a} - \\frac{c}{d}$\n\nNote that the variables a, b, c, and d are used to represent the values in the formula. The symbols '+' and '-' are used to denote addition and subtraction, respectively. The fraction bar '|' is used to denote the fraction. The variable 'x' is used to represent the variable in the formula.",
        "gt_answers": "\\frac { B E } { A D } = \\frac { E M } { A M } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5540.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:\n\nA = l \\* w\n\nwhere l is the length of the rectangle and w is the width of the rectangle.",
        "gt_answers": "\\angle D = \\angle B = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5541.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is a^(4/3)\\*c^(2/3)\\*d^2. This can be written as a^(4/3)\\*c^(2/3)\\*d^2.\n\nHere is the LaTeX format for the expression:\n\n$$ \\left(\\frac{a}{b}\\right)^{\\frac{4}{3}} \\left(\\frac{c}{d}\\right)^{\\frac{2}{3}} d^2 $$\nThis formula represents the area of a triangle with sides of length a, b, and c and height d. The value of",
        "gt_answers": "\\frac { A B } { A O } = \\frac { A D } { A C }\n",
        "image_path": "./data/HME100K/test_images/test_5542.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: $\\frac{1}{2}mv^2$\n\nwhere $m$ is the mass of the object, $v$ is its velocity, and $2$ is a constant.",
        "gt_answers": "m g R = \\frac { 1 } { 2 } m V _ { 3 } ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5543.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the formula in the image using LaTeX format, we need to add the numbers 2, 1, and 3 as the coefficients of the variables x, y, and z, respectively. Then we can write the equation as follows:$$5x^2 + 3xy - 2y^2 = 4xy - x^3$$This equation represents the formula shown in the image.",
        "gt_answers": "\\frac { 1 } { 1 0 } + \\frac { 2 } { 5 } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5544.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image can be written as follows:\n\n$$ \\text{y} = \\text{a}x + \\text{b}x^2 + \\text{c}x^3 + \\text{d}x^4 $$\nwhere a, b, c, and d are constants and x is the independent variable.",
        "gt_answers": "( 4 0 + x - 3 0 ) ( 6 0 0 - 1 0 x ) = 1 0 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_5545.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{align}\n 5x^2 + 20x - 3y^2 - 13y + 5 &= 0 \\\n     \\frac{5x^2 + 20x - 3y^2 - 13y + 5}{x^2 + 5xy + 20y^2 - 3y^2 - 13y + 5} &= 0 \\\n        \\frac{5x + 20x(y + 1) -",
        "gt_answers": "x + y ^ { 1 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_5546.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n\\begin{align\\*}\n4x^2 - 9x + 3 &= 0 \\\n\\end{align\\*}\n\nThis equation is a quadratic equation in the form of a polynomial equation, which can be solved by completing the square method or using the quadratic formula.",
        "gt_answers": "4 a ^ { 2 } - 4 \\times 2 ( a ^ { 2 } - 1 ) \\geq o\n",
        "image_path": "./data/HME100K/test_images/test_5549.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{2x+3y=5}$$\n\nWhere x is the independent variable and y is the dependent variable.",
        "gt_answers": "y = - \\frac { 1 } { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_5550.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$ a = \\frac{b}{c}$$where$a, b,$ and$c$are integers.",
        "gt_answers": "a = - \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5551.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following steps:\n\n1. Identify the variables:\n\nx = distance from the camera to the object\ny = distance from the camera to the floor\n2. Write out the formula:\nf = (x^2 + (y+20)^2)^(1/2)\n3. Use LaTeX to format the formula:\n\\begin{align} f = \\left(\\left(x^2 + \\left(y+\\frac{20}{2}\\right)^2\\right)\\right)^{",
        "gt_answers": "2 0 0 + 3 0 + 6 0 + 9 = 2 9 9\n",
        "image_path": "./data/HME100K/test_images/test_5552.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $ f(x) = 3x^2 + 2x - 5 $\n\nTo write this formula in LaTeX format, you would use the following code:\n\n$$ f(x) = 3x^2 + 2x - 5 $$",
        "gt_answers": "\\vert A B \\vert = \\sqrt { 1 + t ^ { 2 } } \\vert x _ { 1 } - x _ { 2 } \\vert = \\sqrt { 1 + t ^ { 2 } } \\cdot \\sqrt { ( x _ { 1 } + x _ { 2 } ) ^ { 2 } - 4 x _ { 1 } x _ { 2 } } = 2 ( t ^ { 2 } + 1 )\n",
        "image_path": "./data/HME100K/test_images/test_5554.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is \\frac{1}{x+2} - \\frac{1}{x-1}.",
        "gt_answers": "x = \\frac { 3 9 } { 2 8 } \\times \\frac { 4 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_5556.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\n$$ y = \\frac{2x^2 + 4x - 3}{x - 1} $$",
        "gt_answers": "x ( x - a ) - 3 ( x - 1 ) = x ( x - 1 )\n",
        "image_path": "./data/HME100K/test_images/test_5557.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression in the image:\n\n\\begin{align\\*}\n\\frac{\\frac{1}{3} - \\frac{5}{6}}{\\frac{2}{5} - \\frac{3}{4}} = \\frac{1}{14}\n\\end{align\\*}",
        "gt_answers": "D _ { 1 } F = \\frac { 1 } { 2 } D _ { 1 } C\n",
        "image_path": "./data/HME100K/test_images/test_5558.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is not provided. However, we can represent the formula as follows:",
        "gt_answers": "\\tan C = \\frac { A F } { C F } = \\frac { B F } { C F } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5559.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ 6x^2 + 4x - 50 = 0 $$This is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 6$, $b = 4$, $c = -50$, and $x$ is the variable. The solution to this equation is obtained by factoring the quadratic expression and solving for the variable $x$.",
        "gt_answers": "\\frac { 6 } { 2 0 } = \\frac { 6 \\div 2 } { 2 0 \\div 2 } = \\frac { 3 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5560.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\frac{\\text{sin}(x)}{x}$",
        "gt_answers": "1 6 X ^ { 2 } - \\pi x = 0\n",
        "image_path": "./data/HME100K/test_images/test_5561.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by:A=lxwxwhere l is the length, w is the width, and x is the height. In the image, the length of the rectangle is 5, the width is 3, and the height is 1. Therefore, the area of the rectangle is 5 \u00d7 3 \u00d7 1 = 5 units.",
        "gt_answers": "1 6 0 ^ { \\circ } - a = 2 \\cdot ( 9 0 ^ { \\circ } \\cdot 3 0 ^ { \\circ } ) + 1 6 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5562.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{1}{3} \\times 2 + 1 = \\frac{1}{3} \\times 3 + 1 = 3$$This equation shows that the sum of 1 and 2 is equal to the sum of 1 and 3, which is 3. The fraction 1/3 represents the ratio of the two numbers being added.",
        "gt_answers": "2 0 x = 2 . 5 - 1 . 5\n",
        "image_path": "./data/HME100K/test_images/test_5563.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ \\frac{1}{12} \\cdot \\frac{2}{5} + \\frac{5}{12} \\cdot \\frac{2}{3} $$\n\nwhich simplifies to:\n\n$$ \\frac{1}{6} + \\frac{1}{6} = \\frac{1}{3} $$",
        "gt_answers": "1 3 \u3001 - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5564.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression for the formula in LaTeX format:\n\n\\begin{align}\n\\frac{a}{b} = \\frac{c}{d} + \\frac{e}{f}\n\\end{align}\n\nwhere $a, b, c, d, e, and f$ are constants.",
        "gt_answers": "\\frac { 1 } { 4 } > \\frac { m } { 3 2 } \\textcircled { 1 } < 8\n",
        "image_path": "./data/HME100K/test_images/test_5566.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$x^2 + 3x + 2 = 0$$\n\nwhere x is the variable.",
        "gt_answers": "l _ { A B } : y = k x + b 3\n",
        "image_path": "./data/HME100K/test_images/test_5569.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is not provided, so it cannot be written in LaTeX format. However, the image shows two overlapping circles, one with a radius of 5cm and the other with a radius of 3cm, with the smaller circle completely inside the larger one.",
        "gt_answers": "\\frac { O A } { O C } = \\frac { O C } { O B }\n",
        "image_path": "./data/HME100K/test_images/test_5570.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is $\\frac{4x+3y}{2}$.\n\nThe image shows a rectangle with its width and height marked. The width is marked as 4x, and the height is marked as 3y. The fraction $\\frac{4x+3y}{2}$ is used to represent the area of the rectangle. The denominator $2$ is used to cancel out the fraction's numerator $4x$ and denominator $3y$, resulting in the area of the rectangle, which is the value of the fraction.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the number of integers in the set {3, 4, 5, 6, 7} is 3 + 4 + 5 + 6 + 7 = 25.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{5x+4y-2z}{7x+3y-z}$$",
        "gt_answers": "x = \\frac { 4 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5573.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression for the given image in LaTeX format, we can use the following code:\n\n$$\\begin{aligned} 3x + 4y &= 15 \\ \\ \\ 2x - 3y &= 5 \\end{aligned}$$\n\nThis will give us the following system of equations:\n\n$$\\begin{aligned} 3x + 4y &= 15 \\ \\ \\ 2x - 3y &= 5 \\end{aligned}$$\n\nSolving this system of equations using the substitution method, we get:\n\n$$\\begin{aligned",
        "gt_answers": "\\frac { 3 } { 8 } \\times \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5574.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b \u222bf(x)dx+C\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "1 ) \\Delta G = \\Delta H - T \\Delta S < 0\n",
        "image_path": "./data/HME100K/test_images/test_5576.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is tan(3\u03c0/2).\n\nHere is the LaTeX format for the formula:\n\ntan\u2061(3\u03c0/2)=1",
        "gt_answers": "\\tan \\angle C B A = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5577.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n$$ E = mc^2 $$\n\nwhere E is the energy of the object, m is its mass, and c is the speed of light in a vacuum.",
        "gt_answers": "\\angle C = 9 0 ^ { \\circ } A D = A D\n",
        "image_path": "./data/HME100K/test_images/test_5578.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{align\\*}\nf(x) = \\frac{1}{2}\\left(\\frac{1}{x}+\\frac{1}{x^2}\\right)\n\\end{align\\*}",
        "gt_answers": "= x ^ { 3 } - 2 c x ^ { 2 } + c ^ { 2 } x\n",
        "image_path": "./data/HME100K/test_images/test_5579.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is:\n\n$$\\text{SOAP} = \\text{Sodium Alkyl Sulfonate}$$\n\nNote: The formula is written in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the equation: a = l \\* w, where a is the area, l is the length, and w is the width. In this case, the length is 4 and the width is 6, so the area is 4 \\* 6 = 24 cm^2.",
        "gt_answers": "1 + 8 = 9\n",
        "image_path": "./data/HME100K/test_images/test_5582.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a mathematical expression for a fraction, which is the ratio of two numbers. The numerator is 4, and the denominator is 5. So the fraction is 4/5, which can also be written as 0.8.",
        "gt_answers": "x _ { 2 } = \\frac { 1 0 } { 5 } = 2 0 \\%\n",
        "image_path": "./data/HME100K/test_images/test_5583.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{SIN}(\\theta) = \\frac{\\text{sin}(\\theta)}{\\theta}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not shown as it is in LaTeX format. To write it out in LaTeX format, you would need to use the equation editor to enter the expression, which is given by the equation.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following code:\n\n\\begin{align\\*}\nf(x) = \\frac{1}{x^2 + 1}\n\\end{align\\*}\n\nThis formula is a piecewise function that is defined for $x \\in (-1,1)$. The function is equal to $\\frac{1}{x^2 + 1}$ for $x \\in (-1,0)$, and is equal to $\\frac{0}{x^2 + 1}$ for $x \\in (0,",
        "gt_answers": "\\frac { 1 } { 2 } x = \\frac { 1 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5587.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image you provided. Can you please provide the image again so that I can help you with your questions?",
        "gt_answers": "O C = 6 \\sqrt { 1 3 } + y\n",
        "image_path": "./data/HME100K/test_images/test_5589.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 5 + 2x^3 + 8x^2 - 15x + 12.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given formula in LaTeX format is:\n\n$$\\mathrm{CH\\_3COOH + CH\\_3CHO \\rightarrow CH\\_3COOC\\_{2}H}\\;$$\n\nwhere $\\mathrm{CH\\_3COOH}$ represents acetic acid and $\\mathrm{CH\\_3CHO}$ represents methyl alcohol. The product is ethyl acetate, represented by $\\mathrm{CH\\_3COOC\\_{2}H}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the expression for the formula in the image:$$5x^2 + 3y^2 = 30$$This is a quadratic equation with a constant term of 30. The coefficients of x^2 and y^2 are 5 and 3, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\frac{3\\times 4 + 6}{8\\times 7 - 10}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n&#x2211;x&#x2212;&#x2211;y&#x2212;1&#x2212;2&#x2211;z&#x2212;&#x2211;t&#x2212;2\" role=\"presentation\" style=\"position: relative;\">f(x,y,z,t)=0f(x,y,z,t)=0f(x,y,z,t)=",
        "gt_answers": "1 - p = \\pm \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5594.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the equation for the area of a triangle. It is written in LaTex as: $\\text{area of triangle}=\\frac{1}{2}bh$. This formula states that the area of a triangle is equal to half the base times the height.",
        "gt_answers": "y = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5595.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This formula is used to find the slope of a line using the negative reciprocal method. The slope of the line is given by the negative reciprocal of the y-intercept. The formula for the negative reciprocal is given by:\n\nm = - (y - y1) / (x - x1)\n\nwhere m is the slope of the line, y and y1 are the coordinates of the two points on the line, and x and x1 are the coordinates of the two points on the x-axis.",
        "gt_answers": "\\frac { a } { 3 } - \\frac { a } { 3 } + 1 = 1\n",
        "image_path": "./data/HME100K/test_images/test_5596.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The formula in the image is the formula for calculating the area of a triangle with two sides and an included angle of 60 degrees:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is x + 5y - 15z.\n\nThe equation is a linear equation, which means that the sum of the variables is zero. In this case, the x variable is added to the sum, and the y and z variables are subtracted from the sum. The coefficient of x is 1, the coefficient of y is 5, and the coefficient of z is - 15.\n\nTo represent this equation in LaTeX format, you can use the following code:\n\nx + 5y - 15z\n\nThis will display the",
        "gt_answers": "x = \\frac { 1 5 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5598.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the volume of a cube with side length 2, which is given by V = 2. This is a common formula for the volume of a cube, where the length of each side is the length of the cube.",
        "gt_answers": "3 . 2 \\div 1 0 0 = 0 . 0 3 2\n",
        "image_path": "./data/HME100K/test_images/test_5599.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\begin{equation}\n  a = \\frac{b \\cdot c}{d}\n```\n\nwhere\n\n`a` is the result of the formula\n`b` is the first term\n`c` is the second term\n`d` is the denominator\n\nThis formula states that the value of `a` is equal to the product of `b` and `c` divided by `d`",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a right triangle with sides of 4 cm and 6 cm and an included angle of 60 degrees. The formula for the length of the hypotenuse is given by:\n\nh = sqrt(s\u00b2 + 3\u00b2)\n\nwhere s is the length of the side opposite the included angle.\n\nTherefore, the length of the hypotenuse is:\n\nh = sqrt(4\u00b2 + 3\u00b2)\nh = sqrt(20 + 9)\nh = sqrt(29)\nh = 5.384 cm",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize, but I cannot see the image as it is not provided. Please provide the image for me to solve the problem.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\text{m} = \\frac{1}{2}(5x + 3y)$",
        "gt_answers": "x ^ { 2 } = \\frac { 5 } { m - 1 . }\n",
        "image_path": "./data/HME100K/test_images/test_5603.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a width of 3 inches and a height of 5 inches is: A = (length \\* width) / 2 = (3 \\* 5) / 2 = 15 inches^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{align}\na^2 + b^2 = c^2 \\\n\\end{align}\nwhere a, b, and c are the sides of the triangle.",
        "gt_answers": "D H = D G = \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5605.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by the following LaTeX expression:\n\n\\begin{align\\*}\nx + 2 = 3x\n\\end{align\\*}\nThe formula is in the slope intercept form of a line, where x is the input variable and 3 is the slope and x is the y-intercept.",
        "gt_answers": "\\frac { 1 } { 2 0 } \\times 9 = \\frac { 9 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5606.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the LaTeX expression for the given formula:\n\n\\begin{aligned}\n\\frac{1}{2}x^2 + \\frac{3}{2}x - \\frac{41}{6} &= \\frac{1}{2}(4x^2 + 3x - 41) \\\n&= \\frac{1}{2}x^2 + \\frac{3}{2}x - \\frac{41}{6} \\\n&= \\frac{1}{2}x^2 + \\frac{3}{2}x - \\frac{41",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the image you provided:\n\n$$\\text{Image: } \\frac{x+2}{x-1} = 4$$\n\nThis expression represents the slope of the line passing through the points $(1,2)$ and $(2,4)$. The slope of the line is given by the formula $\\frac{x+2}{x-1}$, which simplifies to $2$. The y-coordinate of the second point is $4$, so the equation represents a line with a slope of $2$ that passes through the point $(2,4)$.\n##",
        "gt_answers": "x ^ { 2 } = \\frac { 2 2 5 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5608.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is $\\pi r^2$. To express this formula in LaTeX, we can write it as $\\frac{\\pi}{r^2}$. The image shows the formula written out in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The expression for the formula in the image is:\n\n$$\\frac{40}{x^2 + 16x - 136}$$\n\nwhere $x$ is an integer variable. The variable $x$ can be replaced by any integer value, and the expression will give the corresponding value of the function. For example, if $x = 5$, then the expression evaluates to:\n\n$$\\frac{40}{5^2 + 16\\*5 - 136} = \\frac{40}{2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression given in the image is: 3x + 5y - 2z = 11.\n\nHere is the LaTeX format for the formula:\n\n\\begin{align\\*}\n3x + 5y - 2z &= 11\n\\end{align\\*}",
        "gt_answers": "x = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5612.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\nThe expression in the image is:\n\n$ E = mc^2 $\n\nwhich is the equation of energy and mass.\n```",
        "gt_answers": "\\angle B A C = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5614.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is: $\\frac{8 - 3 + 5}{9 - 4 + 3} = \\frac{5}{5} = 1$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is given by: $\\frac{y^2 - xy}{x^2 + y^2}$.",
        "gt_answers": "\\vert n \\vert - 2 = 1\n",
        "image_path": "./data/HME100K/test_images/test_5616.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:$$k\\_n = \\frac{k\\_{n-1}}{n-1}$$This is a recursive equation that describes the relationship between the current term and the previous term in a sequence, where $k\\_0$ is the first term and $k\\_n$ is the $n$th term. The recurrence relation can be derived using mathematical induction.",
        "gt_answers": "k ^ { \\prime } = k ^ { n }\n",
        "image_path": "./data/HME100K/test_images/test_5617.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the number of squares in an image with n rows and m columns is given by: p = n \u00d7 m.",
        "gt_answers": "P = \\frac { 5 } { 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5618.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x2 + 3x - 4 = 0.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the line shown in the image can be written as follows: y = 3x + 4. This is a linear equation with a slope of 3 and an intercept of 4.\n\nNote that the equation is written in slope-intercept form, where the slope is represented by the coefficient of x and the intercept is represented by the constant term. In this case, the slope is 3 and the intercept is 4.",
        "gt_answers": "a ^ { 2 } - \\frac { a } { b } + 2 + a\n",
        "image_path": "./data/HME100K/test_images/test_5620.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\frac{a + b - c}{d + e - f}$$\n\nWhere,\n\na = 3\nb = 1\nc = 5\nd = 2\ne = 1\nf = 4",
        "gt_answers": "x = \\frac { 1 3 } { 7 - a }\n",
        "image_path": "./data/HME100K/test_images/test_5621.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format of the expression for the formula in the image:\n\n$$\\frac{a+b+c}{2}$$\n\nwhere a, b, and c are the numbers shown in the image.",
        "gt_answers": "\\frac { 1 } { 5 } = \\frac { 2 } { 1 0 } = \\frac { \\cdot 3 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5622.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation can be written as:\n\n$$\\text{2x + 4y} = 10$$\n\nThis equation is in slope intercept form and represents a line that passes through the point (2, 4) with a slope of 2 and intercepts the y-axis at the point (0, 0).\n\nTo solve for the x-coordinate of the point where the line intersects the x-axis, we set y = 0 in the equation and solve for x:\n\n$$\\text{2x} = 10$$\n\nDividing both sides",
        "gt_answers": "2 V - 3 + V = 2 4 .\n",
        "image_path": "./data/HME100K/test_images/test_5625.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is written as follows:$$ \\frac{d^2x}{dt^2} + \\frac{d^2y}{dt^2} = \\frac{k}{m} \\frac{dx}{dt} \\frac{dy}{dt}$$This equation represents the dynamics of a simple harmonic oscillator with damping. It can be used to determine the response of the system to an external forcing function.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: $\\frac{x}{x^2}$. This is a simple quadratic equation that can be factored as $(x - 0)(x + 0)$.\n\nIn LaTeX format, this can be written as:\n\n\\begin{align\\*}\n\\frac{x}{x^2}\n&= (x - 0)(x + 0)\\\n\\end{align\\*}",
        "gt_answers": "\\frac { 1 } { 2 } x = 1\n",
        "image_path": "./data/HME100K/test_images/test_5627.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by:\n\nA = \u03c0r^2\n\nwhere r is the radius of the circle. To express this formula in LaTeX format, we can use the following code:\n\n$ A = \\pi r^2 $\n\nwhere $A$ is the area of the circle, $r$ is the radius of the circle, and $\\pi$ is the mathematical constant pi, which is approximately equal to 3.14.",
        "gt_answers": "0 . 3 \\times 1 0 0 = 3 0\n",
        "image_path": "./data/HME100K/test_images/test_5628.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given by: x^2 + y^2 = r^2, where x and y are the coordinates of the point (x, y) on the x-y plane and r is the radius of the circle centered at that point.",
        "gt_answers": "y = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5629.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $ 2x^2 + 4x + 3 = 0 $\n\nThis is a quadratic equation with two variables, x and y, and four terms, including the constant term of 3. The coefficient of x is 2, the coefficient of x squared is 4, and the constant term is 3.\n\nTo solve this equation, we can use the quadratic formula:\n\nx = (-b +/- sqrt(b^2 - 4ac)) / 2a\ny = (-b -/- sqrt(b",
        "gt_answers": "\\frac { 3 } { 4 } x - \\frac { 1 } { 2 } x = 1\n",
        "image_path": "./data/HME100K/test_images/test_5630.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed as:\n\narea = pi \\* r^2\n\nwhere pi is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.",
        "gt_answers": "a < 1 \\frac { 1 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5631.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is given by the expression:\n\n$A = \\frac{1}{2}bh$\n\nwhere $A$ is the area of the triangle, $b$ is the base, and $h$ is the height.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle can be expressed using LaTeX as follows:\n\n\\begin{center}\nA = $\\pi$r^2\n\\end{center}\n\nwhere A is the area of the circle and r is its radius.",
        "gt_answers": "2 ( x ^ { 2 } - 4 ) = 2 ( x + 2 ) ( x - 2 )\n",
        "image_path": "./data/HME100K/test_images/test_5633.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\frac{a}{b} = \\frac{(a - b)(b - a)}{2b}$$where a and b are the two numbers in the image. The fraction $\\frac{a}{b}$ represents the ratio of a to b. The fraction $\\frac{(a - b)(b - a)}{2b}$ is the difference between the two fractions, $\\frac{a}{b}$ and $\\frac{b}{a}$. The fraction $\\frac{2b}{a - b}$ is the common denominator of the two fractions.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression of the formula in the image using LaTeX format:\n\n\\begin{center}\n$\\frac{3x+4y}{5xy}=\\frac{9x+12y}{5x+6y}$\n\\end{center}\n\nThis equation is the result of simplifying the image expression, which is $\\frac{3x+4y}{5xy}+\\frac{9x+12y}{5x+6y}$. The denominator $5xy$ cancels out with the denominator $5x+6y$ to give the simplified expression.",
        "gt_answers": "\\cdot : 8 x = 3 \\times \\frac { 9 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5635.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is given by:$\\frac{1}{x^{2}+5x+6}$.",
        "gt_answers": "B D = \\frac { 6 } { \\sqrt { 3 } }\n",
        "image_path": "./data/HME100K/test_images/test_5636.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with width w and height h is A = w \\* h. The formula for the area of a rectangle with width w and height h is A = (w + 2h) \\* (h - 3).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{1}{1+x^2}$$\n\nwhere x is the variable.",
        "gt_answers": "d d \\times d d\n",
        "image_path": "./data/HME100K/test_images/test_5639.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the equation: y = (x + 1)(x - 1)2.\n\nTo write this out in LaTeX format, we can use the following code:\n\n$$y = (x + 1)^2 - x^2$$\n\nThis gives us the formula in the image as:\n\ny = (x + 1)\u00b2 - x\u00b2\n\nThis formula represents the equation of a parabolic function with a vertex at the point (1, -1) and a minimum value of -1 at the point (0, 0).##",
        "gt_answers": "P ( C ) = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5640.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression in the image:$$\\frac{1}{2}\\times\\frac{2}{3}\\times\\frac{3}{4}$$The expression is a product of three fractions, each with a denominator of 4, 3, and 2, respectively.",
        "gt_answers": "\\frac { x - 3 } { 2 } = 2 - \\frac { 3 - x } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5642.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:$\\frac{5x+6y+8z}{x+2y+3z}$",
        "gt_answers": "y _ { 1 } y _ { 2 } = x _ { 1 } + x _ { 2 } + 4 = \\frac { 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5644.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$\\frac{1}{2} x^2 + \\frac{1}{4} x - \\frac{1}{8} = \\frac{1}{2} x^2 + \\frac{1}{4} x + \\frac{1}{8} - 1$$\n\nThis formula is a quadratic equation with a constant term of -1 on the left side. The variable x is on the right side of the equation, and the coefficients of the quadratic term are $\\frac{1}{2}$, $\\frac{1",
        "gt_answers": "1 . 5 \\times 1 . 2 \\times 0 . 4 = 0 . 1 2 ( m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_5645.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$a + b + c = d + e + f$",
        "gt_answers": "\\frac { a _ { 1 } } { a _ { 2 } } = \\frac { b _ { 1 } } { b _ { 2 } } = \\frac { c _ { 1 } } { c _ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_5646.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$\\frac{x^2+y^2}{2x+3y}$$The variable x represents the length of the hypotenuse of a right triangle, and the variable y represents the length of the other leg. The denominator is the sum of the two legs, and the numerator is the square of the length of the hypotenuse.",
        "gt_answers": "2 4 0 + ( 2 4 0 \\times 0 . 5 ) x = ( 2 4 0 0 \\times 0 . 6 ) x + 1 4 4\n",
        "image_path": "./data/HME100K/test_images/test_5647.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n$$ \\text{Number of moles of $H\\_2$O = moles of $H\\_2$O} $$\n\nThis formula shows that the number of moles of water is equal to the number of moles of water.",
        "gt_answers": "t x _ { 2 } = - 2 a . x _ { 1 } x _ { 2 } = a ^ { 2 } + 4 a - 2\n",
        "image_path": "./data/HME100K/test_images/test_5648.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a circle is given by the formula A = \u03c0r^2, where r is the radius of the circle. To find the radius of the circle in the image, we can use the formula r = diameter/2. Using this formula, we can find that the radius of the circle is approximately 0.36 meters. To find the area of the circle, we can use the formula A = \u03c0r^2, which gives us an area of approximately 1.01 square meters.\n\nThe volume of the cylinder can be found using the formula V = \u03c0",
        "gt_answers": "\\frac { O E } { O O ^ { \\prime } } = \\frac { A E } { O ^ { \\prime } A ^ { \\prime } }\n",
        "image_path": "./data/HME100K/test_images/test_5650.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in LaTeX format for the expression shown in the image is:\n\n$$ \\frac{100 - 50}{25 + 5} = \\frac{50}{75} $$\n\nwhich simplifies to:\n\n$$ \\frac{50}{75} = \\frac{50}{75} $$\n\nwhich is equal to 1.",
        "gt_answers": "\\frac { 2 } { 3 } x = 1 0\n",
        "image_path": "./data/HME100K/test_images/test_5651.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression of the image can be written as follows:\n\n![](https://i.imgur.com/g20y2fO.png)\n\nwhere the variable x represents the position of the point and the variable y represents the position of the line. The distance formula used in this image is:\n\nd = \u221a((x2 - x1)2 + (y2 - y1)2)\n\nSubstituting the values given in the image, we have:\n\nd = \u221a((3 - 0)2 + (4 - 0)",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "x _ { 1 } = 3 x _ { 2 } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_5653.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:\n\n$$y = 2x + 3$$\n\nwhere x is the input variable and y is the output variable.",
        "gt_answers": "\\frac { x - 2 } { x } = - 1\n",
        "image_path": "./data/HME100K/test_images/test_5654.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the number 36 in the given image is:\n\n36 = (9 + 3) \\* (6 - 2) / 2 = 9 \\* 6 / 2 = 18\n\nSo, the sum of 9 and 3 is 9 and 3, and the difference of 6 and 2 is 4. The expression evaluates to 18.",
        "gt_answers": "\\frac { 6 9 } { 2 0 } = 3 \\frac { 9 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5655.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{Sin}(\\theta) = \\frac{y}{x} \\cdot \\text{tan}(\\theta)$$This formula is used to find the sine of an angle in terms of the tangent of the angle.",
        "gt_answers": "\\Rightarrow \\frac { 1 } { y } - \\frac { 1 } { x } = \\frac { 1 } { 3 0 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5656.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ 3x + 4y = 14 $$\n\nwhere x and y are variables representing the number of apples and oranges, respectively.",
        "gt_answers": "3 = c\n",
        "image_path": "./data/HME100K/test_images/test_5657.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the given expression:\n\n$$\\text{2 + 3} \\times 4 = \\frac{11}{3}$$",
        "gt_answers": "( 2 , 3 ) = 1 ( 3 , 4 ) = 1\n",
        "image_path": "./data/HME100K/test_images/test_5658.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the slope of the tangent line at a point on the curve y = x^2 at x = 4.\n\nThe slope of the tangent line at a point on a curve can be calculated as follows:\n\nd/dx [y = f(x)] = f'(x)\n\nwhere f'(x) is the derivative of the function f(x) evaluated at x.\n\nThe slope of the tangent line at x = 4 on the curve y = x^2 is f'(4), which is equal to 8.\n\nTherefore,",
        "gt_answers": "B F = B P - F P = \\sqrt { x ^ { 2 } - 8 x + 8 0 } - y\n",
        "image_path": "./data/HME100K/test_images/test_5659.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n$$\\frac{1000}{2000 - 500} = \\frac{1000 \\times 500}{1500} = 0.5$$\n```",
        "gt_answers": "9 \\div \\frac { 1 } { 1 0 0 } = 9 0 0 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_5660.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle can be written as:\n\nA = l x w\n\nwhere l is the length of the rectangle and w is the width of the rectangle. In the image, the length of the rectangle is 12 and the width is 9, so the area of the rectangle is:\n\nA = 12 x 9 = 108",
        "gt_answers": ": ( N H _ { 4 } ) = S O _ { 4 } + C a ( O H ) _ { 2 } = C a S O _ { 4 } + 2 H _ { 2 } O + 2 N H _ { 3 } \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_5661.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given formula:\n\n$$\\frac{m\\_2^2 - (m\\_1 + m\\_2)^2}{2m\\_1m\\_2} = \\frac{m\\_2^2 - m\\_1^2 - 2m\\_1m\\_2 + m\\_2^2}{2m\\_1m\\_2} = \\frac{m\\_2^2 - m\\_1^2}{2m\\_1}$$",
        "gt_answers": "m = - 2 \\sqrt { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5662.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as:\n\n$$\\frac{1}{4}\\left(2+\\frac{1}{2}\\right)^2 = \\frac{1}{16}\\left(4+\\frac{1}{2}\\right)^2 = \\frac{1}{64}\\left(8+\\frac{1}{2}\\right)^2 = \\frac{1}{256}\\left(16+\\frac{1}{2}\\right)^2 = \\frac{1}{512}\\left(32+\\frac{1}{2}\\right)^2 = \\frac",
        "gt_answers": "1 . 2 \\times 2 = 2 . 4 m ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5663.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{1}{x + 4}$\n\nNote: The expression assumes that x is the variable being solved for.",
        "gt_answers": "y = 4\n",
        "image_path": "./data/HME100K/test_images/test_5665.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n    $\\frac{a}{b}$\n```",
        "gt_answers": "\\frac { O A } { A E } = \\frac { A C } { A B }\n",
        "image_path": "./data/HME100K/test_images/test_5666.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX representation of the expression for the formula in the image:\n\n\\begin{align\\*}\nf(x) &= \\frac{1}{x^{2}+4x+4} \\quad \\text{for }x\\in\\left[-2,2\\right]\n\\end{align\\*}\n\nThis formula is a piecewise function that is defined for $x\\in\\left[-2,2\\right]$. The function is defined as the reciprocal of the square of $x$ plus four times $x$ plus four. This is a piecewise function because it",
        "gt_answers": "\\frac { 3 } { 2 } x - 4 ( h - 1 ) = - 4 - 2\n",
        "image_path": "./data/HME100K/test_images/test_5667.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as follows:\n\n$$\\frac{\\frac{\\frac{2}{3}}{\\frac{1}{2}} + \\frac{4}{5}}{\\frac{2}{3}} = \\frac{2}{5} + \\frac{4}{7} = \\frac{6}{14}$$\n\nThe expression simplifies to $\\frac{6}{14}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression:\n\n\\begin{center}\n$ 2x^2 + 2x - 6 = 0$\n\\end{center}\n\nTo display the equation in LaTeX format, you can use the following code:\n\n\\begin{center}\n$ 2x^2 + 2x - 6 = 0$\n\\end{center}\n\nThe \"$\" symbols denote the beginning and end of the equation, and the \"=\" symbol denotes the equals sign. The \"center\" environment is used to center the equation.",
        "gt_answers": "m a = 2 - x + \\frac { 4 x } { 8 - 2 x }\n",
        "image_path": "./data/HME100K/test_images/test_5670.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\sum \\_{i=1}^n (3x\\_i^2+5x\\_i+6)(2x\\_i^2+7x\\_i+8)$\n\nThis is a polynomial equation with four terms, each of which consists of a power of x multiplied by a coefficient and another term. The first term is 3x\\_i^2+5x\\_i+6, the second term is 2x\\_i^2+7x\\_i+8, the third term is 3x\\_i^",
        "gt_answers": "x _ { 2 } = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5672.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2 + 3x = 10.",
        "gt_answers": "C ^ { \\prime } M + M D \\geq D C ^ { \\prime }\n",
        "image_path": "./data/HME100K/test_images/test_5673.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: $\\text{dd}t = \\frac{\\text{d}\\mathbf{x}}{\\text{dt}} = \\frac{\\text{d}\\mathbf{v}}{\\text{dt}} + \\frac{\\text{d}\\mathbf{a}}{\\text{dt}} = \\mathbf{F}$ where $\\mathbf{F}$ is the force acting on the body.",
        "gt_answers": "A D / / B E\n",
        "image_path": "./data/HME100K/test_images/test_5674.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The chemical formula in the image is not shown, as it is written in a different format. The expression cannot be written in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a mathematical expression that represents the ratio of two variables. The numerator, x, is the independent variable, and the denominator, y, is the dependent variable.\n\nThe equation can be rewritten in LaTeX format as follows:\n\n$$\\frac{x}{y} = \\frac{a}{b}$$\n\nwhere x and y are the variables in the equation, and a and b are the values of x and y, respectively.\n\nThe equation represents a mathematical relationship between two variables, where x is the independent variable and y is the dependent variable. The value of the dependent variable is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the expression in the image using LaTeX format is:$$\\text{x}\\_1 = \\frac{3}{4}\\left(\\frac{x\\_2}{x\\_3}+\\frac{x\\_4}{x\\_3}\\right)$$\n\nThe variable x1 is equal to 3/4 of the sum of x2/x3 and x4/x3.",
        "gt_answers": "C _ { 1 } : y = - x ^ { 2 } - 2 x + 3\n",
        "image_path": "./data/HME100K/test_images/test_5677.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is 5 + 4.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image using LaTeX format is:\n\n$$ a = \\frac{1}{2} \\cdot \\frac{1}{4} \\cdot \\frac{1}{8} \\cdot \\frac{1}{16} = \\frac{1}{16}$$\n\nThis is obtained by dividing the area of the rectangle with the area of the square.",
        "gt_answers": "( a - b ) ( a + b + c ) = 0 .\n",
        "image_path": "./data/HME100K/test_images/test_5679.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows:\n\n![image of a number line](https://www.quickmath.com/websolve/wp-content/uploads/2018/05/Number-Line-Worksheet.png)\n\nWhere x is the number being plotted on the number line, and a and b are the two given numbers. The solution will be the point at which the line intersects the x-axis.",
        "gt_answers": "\\frac { x - 4 } { 2 5 } = \\frac { 1 . 2 } { 7 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5682.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$a = 60 \\times 60$$\n\nwhere a is the area of the rectangle with length 60 and width 60.",
        "gt_answers": "\\angle A O B = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5683.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$\\frac{1}{2} \\times \\frac{1}{2} \\times 4 + 2 = \\frac{5}{4}$$",
        "gt_answers": "\\therefore M E / / A C\n",
        "image_path": "./data/HME100K/test_images/test_5684.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$ \\frac{1}{x^2 - 4x + 4} $$This is a quadratic equation with a leading coefficient of 1 and a constant term of 4. The coefficients are 4 and -4.",
        "gt_answers": "= ( \\sqrt { 3 } ) ^ { 2 } + 1 = 4\n",
        "image_path": "./data/HME100K/test_images/test_5685.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick] (0,0) -- (2,0) node[midway, below] {$x$};\n\\draw[thick] (0,0) -- (0,2) node[midway, left] {$y$};\n\\draw[thick] (2,0) -- (0,2);\n\\draw[thick, dashed] (1,1) -- (1,0) node[midway, right] {$y=2x",
        "gt_answers": "\\frac { 4 0 - x ^ { 4 } } { 4 } = 1 2\n",
        "image_path": "./data/HME100K/test_images/test_5686.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is x^2 - 3x + 2.",
        "gt_answers": "7 x = 2 3 6 . 8\n",
        "image_path": "./data/HME100K/test_images/test_5687.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that.\n\nHere's the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\nx^2 + 3x + 2 = 0\n\\end{align\\*}\n\nThe formula is a quadratic equation in standard form, with the variable x raised to the second power and an additional term of 3x. The coefficient of x squared is 1, the constant term is 2, and the coefficient of x is 3.\n\nThe solution to this equation is given by the quadratic formula:\n\nx = (-",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{Im}\\_{456} = \\frac{1}{2} \\times \\frac{1}{3} + \\frac{1}{2} \\times \\frac{1}{4} + \\frac{1}{2} \\times \\frac{1}{5} + \\frac{1}{2} \\times \\frac{1}{6} + \\frac{1}{2} \\times \\frac{1}{7} + \\frac{1}{2} \\times \\frac{1}{8} +",
        "gt_answers": "\\frac { 2 3 } { 2 1 } x = x + 4 0\n",
        "image_path": "./data/HME100K/test_images/test_5689.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is x + y = 2.",
        "gt_answers": "\\frac { y } { 3 } = 1 2\n",
        "image_path": "./data/HME100K/test_images/test_5691.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not a LaTeX expression, but rather an expression written out in regular text. It reads:$$k = \\frac{f(x)}{g(x)}$$where $$k$$ is the constant of integration, $$f(x)$$ is the integrand, and $$g(x)$$ is the integrating factor. The equation is used to evaluate the definite integral of a function.\n\nIn LaTeX format, the equation would be written as:$$\\int\\_a^b f(x)g(x)dx=k$$where $$a$$ and $$b$$ are the upper and",
        "gt_answers": "k = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5692.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression shown in the image is:$$3x^2 + 2x - 1$$This can be written in LaTeX format as:$$\\frac{3x^2 + 2x - 1}{x^2 + 2x - 1}$$The fraction is a quotient of two polynomial expressions, with the numerator being $3x^2$ and the denominator being $x^2 + 2x - 1$. The coefficients of the polynomials are $3$ and $2$, respectively.",
        "gt_answers": "x _ { 4 } = 5 . 9 7 c m\n",
        "image_path": "./data/HME100K/test_images/test_5694.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by $\\pi$r^2$, where r is the radius of the circle. Using the formula, we can find the area of the circle in the image. The radius of the circle is approximately 0.5cm, which means that the area of the circle is approximately 0.25cm^2.\n\nHowever, the formula provided is not in LaTeX format. Here is the formula for the area of a circle in LaTeX format: $\\pi$r$^2$\n\nThe radius of the circle in the image is approximately 0.5cm,",
        "gt_answers": "\\frac { 1 } { x } = \\frac { 1 } { 0 . 0 8 } \\therefore x = 0 . 0 8\n",
        "image_path": "./data/HME100K/test_images/test_5695.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following code:\n\n$$\\begin{aligned}x^2+y^2&=r^2\\end{aligned}$$\nIn this formula, x and y represent the coordinates of a point on a circle with radius r. We can use the LaTeX commands to write out the formula, as follows:\n\n$$\\begin{aligned}x^2+y^2&=r^2\\end{aligned}$$\nThis formula can be used to calculate the distance between two points on a circle.",
        "gt_answers": "x _ { 1 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5696.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:",
        "gt_answers": "\\therefore c = 2\n",
        "image_path": "./data/HME100K/test_images/test_5697.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is: \\frac{3x}{2}+\\frac{4y}{3} = 8.",
        "gt_answers": "b = \\frac { 5 8 } { 2 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5698.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is A = \u03c0r^2. Using LaTeX format, this can be written as:\n\nA = \\pi r^2\n\nwhere \u03c0 is the mathematical constant that represents the ratio of a circle's circumference to its diameter, and r is the radius of the circle.",
        "gt_answers": "x - 6 x \\leq 6 - 1\n",
        "image_path": "./data/HME100K/test_images/test_5699.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is given below:\n\n\\begin{center}\n\\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} + \\frac{1}{32} + \\frac{1}{64} = \\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} + \\frac{1}{32} + \\frac{1}{64} = \\frac{7}{128",
        "gt_answers": "\\frac { 2 a + 1 } { 3 } - \\frac { 1 - b } { 6 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_5700.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for a circle with radius r and center at the point (x0, y0) is given by:\n\n(x - x0)^2 + (y - y0)^2 = r^2\n\nSubstituting x = 3 and y = 4 into this equation, we get:\n\n(x - 3)^2 + (y - 4)^2 = 9\nSimplifying this equation, we get:\nx^2 + y^2 = 9\nThis is the equation of a circle with center at (3,4) and radius 3",
        "gt_answers": "B G = F G = x\n",
        "image_path": "./data/HME100K/test_images/test_5701.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is:\n\nA = \u03c0r^2\n\nwhere A is the area of the circle, r is the radius of the circle, and \u03c0 is a mathematical constant approximately equal to 3.14159.\n\nSo, to find the area of the circle in the image, we can substitute the given values into the formula:\n\nA = \u03c0(40^2) = \u03c0(1600) \u2248 502.930\n\nTherefore, the area of the circle in the image is approximately",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\begin{aligned} x &= 2 - 3i \\ \\ \\text{or} \\ x &= 2 + 3i \\end{aligned}$$This is a system of linear equations that can be represented by a matrix. The matrix is given by:$$\\begin{bmatrix} 1 & 2 & 3i \\ 1 & 2 & -3i \\end{bmatrix}$$The solution to the system is given by:$$\\begin{aligned} x &= 2 - 3i \\ \\ \\text{or",
        "gt_answers": "( x _ { 1 } - 2 ) ( x _ { 2 } - 6 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_5703.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the binomial distribution, which is a mathematical model for the probability of getting a certain number of successes in a fixed number of trials, where each trial has only two possible outcomes (success or failure). The binomial distribution is defined by the following equation:\n\nP(X=x) = (n choose x) \\* p^x \\* (1-p)^(n-x)\n\nWhere n is the number of trials, p is the probability of success in each trial, and x is the number of successes in the n trials.\n##",
        "gt_answers": "\\sin ( B + C ) = 2 \\sin A \\cos B\n",
        "image_path": "./data/HME100K/test_images/test_5704.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Please provide the image so I can help you with the LaTeX formula.",
        "gt_answers": "x ^ { 2 } + 9 + x ^ { 2 } - 6 x - 8 = 0\n",
        "image_path": "./data/HME100K/test_images/test_5705.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\nx + 3 = 4x2\n\nTo solve for x, divide both sides of the equation by 2:\n\nx + 3 = 2(4x2)\nx = 2x2 - 3\n\nTherefore, the solution to the equation is x = 2x2 - 3.",
        "gt_answers": "\\frac { 6 x - 3 } { 6 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_5706.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be:\n\n$$z = \\frac{1}{2}\\left(a + b + c\\right)$$\n\nwhere $a, b, c$ are the numbers given in the image: 5, 7, and 9.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 36.\n\nTo write this in LaTeX format, you would use the following code:\n\n$\\sum\\_{i=0}^{10} i = 36$\n\nThis code tells the LaTeX system to sum the numbers from 0 to 10, and the result is 36. The dollar sign before the sum symbol indicates that it is a mathematical expression.",
        "gt_answers": "\\angle A O C = 5 4 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5708.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{1}{2} - \\frac{1}{4} = \\frac{3}{8}$$",
        "gt_answers": "\\frac { 1 } { 3 - x } + \\frac { 4 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5709.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{3x^2 - 5x - 4}{2x + 1}$$\n\nThis is the simplified form of the rational function given in the image.",
        "gt_answers": "( 1 ) - 3 x \\cdot ( 2 x ^ { 2 } + x - 1 )\n",
        "image_path": "./data/HME100K/test_images/test_5710.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a representation of the number of integers from 1 to 10, with each integer represented by a different digit.",
        "gt_answers": "\\frac { 1 2 5 } { 2 7 } = ( \\frac { 5 } { 3 } ) ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5711.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\text{0.5}\\times \\text{0.6}\\times \\text{0.8}\\times \\text{1.0} \\times \\text{0.5}\\times \\text{0.2}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\begin{aligned} x^2+2x-5&=0 \\qquad \\text{or} \\qquad x^2+2x-5&=4 \\end{aligned}$$\n\nThis is a quadratic equation in one variable, which can be solved using the quadratic formula:\n\n$$\\begin{aligned} x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a} \\end{aligned}$$\n\nwhere a, b, and c are the coefficients of the quadratic equation. Plugging in",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: 16x^5 + 8x^4 + 4x^3 + 2x^2 + x + 1.\n\nHere's how to write it in LaTeX format:\n\n16x\\^{5} + 8x\\^{4} + 4x\\^{3} + 2x\\^{2} + x + 1\n\nThe expression is a polynomial equation of degree 5 with terms 16x^5, 8x^4, 4x^3, 2x^",
        "gt_answers": "x = 5\n",
        "image_path": "./data/HME100K/test_images/test_5714.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression of the formula in the image:\n\n$$\\begin{aligned} \\frac{dV}{dt} &= r \\cdot I\\_{c} \\cdot \\left(\\frac{dI}{dt}\\right) + \\frac{V}{C} \\cdot \\left(\\frac{dC}{dt}\\right) \\cdot I\\_{c}\\\n\\end{aligned}$$\n\nwhere $V$ is the voltage, $I\\_{c}$ is the current in the capacitor, $C$ is the capacitance of the capacitor",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is:\n\n\\begin{align\\*}\n\\frac{4 \\* 6 + 5 \\* 2 + 3 \\* 9}{10}\n&= \\frac{26 + 10}{10} \\\\\n&= 2.6 \\\\\n&= 26 / 10\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression given in the image is:\n\n$\\frac{5}{2} + \\frac{4}{6} + \\frac{8}{10}$\n\nwhich simplifies to:\n\n$\\frac{17}{12}$\n\nThe image shows a calculator display with the numerical expression entered into it. The calculator has a display of 8.0, indicating that the expression evaluates to 8.0. The expression is written in latex format with the numbers entered as mathematical expressions.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a diagram of a right triangle with hypotenuse length of 6 units and legs of length 5 and 8 units. The area of the triangle is 30 square units.\n\nUsing the Pythagorean theorem, we can find the length of the missing leg of the triangle:\n\nc^2 = a^2 + b^2\nc = sqrt(a^2 + b^2)\n\nWe know a = 8 and b = 5, so we can substitute these values into the equation:\n\nc = sqrt(8^2 +",
        "gt_answers": "x _ { 1 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5719.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is:\n\n$$d = \\frac{2b + 3a}{b + 4a}$$\n\nIn the image, the line segment OM represents the midpoint of the line segment OA, which is the endpoint of the line segment OB. The coordinates of the points O, M, A, and B are:\n\nO(0, 0)\nM(2, 1)\nA(3, 4)\nB(5, 7)\n\nTherefore, the coordinates of the midpoint OM are:\n\nOM",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{equation} x^{2}+3x+1 = 0 \\end{equation}",
        "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": "MiniGPT4"
    },
    {
        "question": "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$$ \\text{Area} = \\frac{1}{2}bh $$\n\nwhere $b$ is the base and $h$ is the height of the trapezoid.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the image you provided:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw[thick, ->] (0,0) -- (2,0) node[below] {$x$};\n\\draw[thick, ->] (0,0) -- (0,2) node[left] {$y$};\n\\filldraw (1,1) circle (2pt) node[above right] {$($};\n\\filldraw (1,0) circle (2pt) node[above] {$($};\n\\filldraw (0",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:\n\nsin(x) + 2cos(x) - 4sin(x) + 3cos(x) + 5cos(x) - 6sin(x) + 4cos(x) + 2sin(x) - 3cos(x) - 5sin(x) + 6cos(x) + 4sin(x) + 5cos(x) - 7sin(x) - 3cos(x) - 5sin(x) - 4cos(x)",
        "gt_answers": "\\frac { 1 } { 2 } - \\frac { 1 } { 8 } = \\frac { 3 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_5724.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format.\n\nThe formula in the image is:\n\n![](https://latex.codecogs.com/svg.image?%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5",
        "gt_answers": "6 x + 9 = 8 4 x - 2 1 - 3 5\n",
        "image_path": "./data/HME100K/test_images/test_5725.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $ y= 2x^2 + 3x - 1 $. This can be written as$ $\\frac{y}{x^2+3x-1}$$.",
        "gt_answers": "A B / / C D , \\angle A = 1 0 0 ^ { \\circ } , \\angle C = 1 1 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5726.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write the expression of the formula in the image using LaTeX format.\n\nThe given image represents the formula for finding the area of a circle. The formula for the area of a circle is:\n\nA = \u03c0r^2\n\nwhere A is the area of the circle, r is the radius of the circle, and \u03c0 is the mathematical constant pi (approximately equal to 3.14159).\n\nTherefore, the formula for finding the area of the circle in the given image is:\n\nA = \u03c0r^2\n\nHere",
        "gt_answers": "\\frac { 5 x } { 3 } = 3 x - 4 - 1 6\n",
        "image_path": "./data/HME100K/test_images/test_5728.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I don't see any image. Please provide the image so that I can write the expression of the formula in LaTeX format.",
        "gt_answers": "\\frac { x y + 3 x z - y z } { x y - 3 x ( z - y ) z } = \\frac { x _ { z } + y _ { z } + 3 x z - y _ { z } } { x _ { 8 } + y _ { z } - 3 x 8 - y _ { z } } = \\frac { 4 x z } { - 2 x z } = - 2\n",
        "image_path": "./data/HME100K/test_images/test_5729.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression:\n\n$$\\text{Image Content}\\_{1} + \\text{Image Content}\\_{2} = \\text{Image Content}\\_{3}$$\n\nwhere $\\text{Image Content}\\_{1}$, $\\text{Image Content}\\_{2}$, and $\\text{Image Content}\\_{3}$ are the expressions for the respective images.",
        "gt_answers": "\\frac { 6 6 } { x } = \\frac { 1 2 0 } { x } - 6\n",
        "image_path": "./data/HME100K/test_images/test_5731.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2}\\left(\\frac{1}{3}+\\frac{1}{4}\\right)=0.5$",
        "gt_answers": "u _ { 3 } = u v\n",
        "image_path": "./data/HME100K/test_images/test_5732.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{2}x^2 + 10x - 5$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "x = 1 0 - y\n",
        "image_path": "./data/HME100K/test_images/test_5734.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ f(x) = \\frac{x^2}{12} + \\frac{3x}{2} $$",
        "gt_answers": "\\frac { 1 } { 2 } \\pi < B < \\pi\n",
        "image_path": "./data/HME100K/test_images/test_5735.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\n\u222bab \u222bcdf(x,y)dxdy=\u222bab\u222bcdf(y,x)dxdy\\int\\_{a}^{b} \\int\\_{c}^{d} f(x,y) dxdy=\\int\\_{a}^{b} \\int\\_{c}^{d} f(y,x) dxdy\u222bac\u200b\u222bdy\u200b\u222bbx\u200b\u222bcdf\u200b(x,y)dx\u200bdy\u200b=\u222bab\u200b\u222bcdf\u200b(y,x)dx\u200bdy\u200bTherefore,",
        "gt_answers": "\\therefore x = 2\n",
        "image_path": "./data/HME100K/test_images/test_5738.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is:\n\n$$scda\\_d = \\frac{1}{2}scda\\_d + \\frac{1}{2}scda\\_b$$\n\nwhere $scda\\_d$ and $scda\\_b$ are the sum of the squares of the deviations of the independent variables from their respective means.",
        "gt_answers": "\\frac { S _ { \\Delta A B D } } { S _ { \\Delta A D E } } = \\frac { B D } { D E } = \\alpha\n",
        "image_path": "./data/HME100K/test_images/test_5739.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$$\\begin{aligned} \\frac{3x^2 - 5x - 2}{x - 2} &= \\frac{3x^2 - 5x - 2}{x - 2} \\end{aligned}$$Note that the equation is not written in LaTeX format as it is not a mathematical expression.\n\nHere's the same expression in LaTeX format:$$\\begin{aligned} \\frac{3x^2 - 5x - 2}{x - 2} \\end{aligned}$$",
        "gt_answers": "\\frac { 8 } { 3 } > \\frac { 7 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5740.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\begin{center}\n$\\frac{3(x - 1)}{x - 5}$\n\\end{center}\n\nNote: This expression is for the derivative of the function f(x) = 3x - 5.",
        "gt_answers": "\\frac { 2 } { 3 } = \\frac { 1 0 } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5742.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{sin}^2(x) + \\cos^2(x) = 1$$\n\nThe image shows a square with sides of length $2$ units, and a point $P$ on the side of the square, such that the length of the hypotenuse of the right triangle OPP is equal to $1$. The expression expresses the sum of the squares of the sine and cosine of the angle $x$ in the triangle OPP, which is equal to $1$ by the given condition.",
        "gt_answers": "\\square \\div 7 = 7 \\cdots 6\n",
        "image_path": "./data/HME100K/test_images/test_5743.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for a quadratic function is given by the equation $y = ax^2 + bx + c$, where a, b, and c are constants.",
        "gt_answers": "\\sin \\theta \\cos \\theta = 3 \\cos ^ { 2 } \\theta = \\frac { 3 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5744.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the sum of 10 terms is given by:\n\n$$\\text{sum of 10 terms} = \\frac{n}{2}\\cdot\\frac{n+1}{2}\\cdot\\frac{n+2}{2}\\cdot\\frac{n+3}{2}\\cdot\\frac{n+4}{2}\\cdot\\frac{n+5}{2}\\cdot\\frac{n+6}{2}\\cdot\\frac{n+7}{2}\\cdot\\frac{n+8}{2}\\cdot\\frac{n+9}{2}$$\n\nwhere",
        "gt_answers": "\\frac { 5 7 } { 2 4 } > \\frac { 5 4 } { 2 4 } > \\frac { 5 2 } { 2 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5745.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by the following LaTeX code:\n\n$$x + 2 = \\frac{9}{x-2}$$\n\nwhere x is an integer variable.",
        "gt_answers": "6 \\times 6 \\times 2 = 7 2 ( c m ^ { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5746.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle with a width of 10 and a height of 5 is:\n\nA = lw = 10 \\* 5 = 50 ft\u00b2",
        "gt_answers": "3 x - 5 y = 1 6\n",
        "image_path": "./data/HME100K/test_images/test_5747.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is 2x + 3 = 7.",
        "gt_answers": "\\tan \\alpha = \\frac { 5 } { - 1 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5748.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:$$\\frac{A+B}{2}$$where A and B are the areas of the rectangles shown in the image.",
        "gt_answers": "9 \\times 9 \\times 9 = 7 2 9 ( c m ^ { 3 } )\n",
        "image_path": "./data/HME100K/test_images/test_5749.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is: $\\frac{m}{n}$\n\nWhere m and n are integers.",
        "gt_answers": "S n = n ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5750.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```latex\n\nThe image shows the formula for the area of a rectangle with length 2a and width 3b. The formula is given by the expression 2a x 3b.\n\nThe formula for the area of a rectangle can be derived using the following steps:\n\n1. The width of the rectangle is w.\n2. The height of the rectangle is h.\n3. The formula for the area of the rectangle is given by A = l x w, where l is the length of the rectangle.\n4. Substituting h for l, we get A = w x",
        "gt_answers": "B P \\bot B O\n",
        "image_path": "./data/HME100K/test_images/test_5751.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the given formula using LaTeX format, we can use the following code:\n\n$$\\begin{aligned} x &= \\frac{a}{b} \\text{ or } x = \\frac{b}{a} \\end{aligned}$$\n\nThe formula states that the value of x is equal to the ratio of a and b, or the ratio of b and a. In LaTeX format, we can use the fraction symbol to represent the ratio, and the equals sign to indicate that the two expressions are equivalent.",
        "gt_answers": "\\cos \\frac { 2 } { 3 } \\pi = - \\frac { \\sqrt { 3 } } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5752.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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![Image Content](https://www.example.com/image.png)\n\nwhere 'l' is the length of the rectangle, 'w' is the width of the rectangle, 'h' is the height of the rectangle, and 'c' is the center point of the rectangle. The image itself shows a rectangle with length 5 units, width 3 units, and height 2 units, with its center point at the coordinates (2, 1).",
        "gt_answers": "\\angle B O C = 1 2 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5753.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with a length of 8 cm and a width of 6 cm is: 8 \u00d7 6 = 48 square centimeters.\n\nTo find the perimeter of the rectangle, you can use the formula: perimeter = 2 (length + width). In this case, the length is 8 cm and the width is 6 cm, so the perimeter is: 2 (8 + 6) = 2 \u00d7 14 = 28 centimeters.\n\nTo find the volume of the rectangle, you can use the formula:",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$ 2^{2019} \\times 3^{4019} \\times 5^{2019} = 5 \\times 10^{4019} $$\n\nwhere $2$, $3$, and $5$ are exponents, and $2019$ is the base.",
        "gt_answers": "\\frac { 1 9 3 7 } { 2 0 0 5 } < \\frac { 1 9 4 0 } { 2 0 0 8 }\n",
        "image_path": "./data/HME100K/test_images/test_5755.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{32\\times78+100}{60}=4.67+100=150$$This formula calculates the average of 32 and 78 and adds it to 100, then divides by 60 to get the average of 100.",
        "gt_answers": "f ^ { \\prime } ( 1 ) = 1 - a\n",
        "image_path": "./data/HME100K/test_images/test_5756.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression is: $\\textstyle \\frac{a^2}{b^3}=\\frac{a^2}{b^3}=\\frac{a^2b^3}{a^2b^3}=\\frac{a}{b}=\\frac{1}{b}$.",
        "gt_answers": "A . a b > 0\n",
        "image_path": "./data/HME100K/test_images/test_5757.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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(x+4)\\(x-3)+5x(x+4)\\(x-3)+11.",
        "gt_answers": "1 2 \\times \\frac { 2 } { 8 } = \\frac { 2 4 } { 8 }\n",
        "image_path": "./data/HME100K/test_images/test_5759.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not written in LaTeX format, so it is difficult to determine what it represents. However, the equation appears to be an expression for a function of a variable x. The expression can be written in LaTeX as: $\\frac{x^4 - 6x^2 + 11}{x - 3}$. This equation represents a polynomial function of degree 3 with a leading coefficient of 1 and a constant term of 11. The roots of this equation are the values of x that make the denominator equal to zero, which are x = 3 and x = -3.##",
        "gt_answers": "x _ { 2 } = \\frac { 4 \\sqrt { 1 7 } } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_5760.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the formula for the sum of three numbers. The formula is written in LaTeX format as follows:\n\n$$\\text{3+5+7}=\\text{30}$$",
        "gt_answers": "x = \\frac { 3 } { 1 0 }\n",
        "image_path": "./data/HME100K/test_images/test_5761.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression of the formula in the image using LaTeX format. The formula is:$$\\frac{x^2+y^2}{x+y}=\\frac{x^2+y^2}{2xy}\\frac{x^2+y^2}{2xy}=\\frac{1}{2}$$This formula is derived by the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, x",
        "gt_answers": ". x _ { 2 } = \\frac { 3 } { \\sqrt { 5 - \\sqrt { 2 } } }\n",
        "image_path": "./data/HME100K/test_images/test_5762.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Q} = \\frac{E}{t} + \\frac{V}{2}$$\n\nwhere $\\text{Q}$ is the work done by the capacitor, $E$ is the energy stored in the capacitor, $t$ is the time for which the capacitor is charged, and $V$ is the voltage applied to the capacitor.",
        "gt_answers": "S _ { \\Delta D C O } = \\frac { 1 } { 2 } \\times C O \\times Q\n",
        "image_path": "./data/HME100K/test_images/test_5763.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is not showing, so I cannot determine the expression of the formula. Please provide the image so that I can assist you with the LaTeX format.",
        "gt_answers": "x < \\frac { k - 3 } { k - 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5766.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the image is:\n\n$$ \\text{ImageContent} = \\frac{1}{2}(x^2 + 3x + 2) $$\n\nwhere x is the number of pixels in the image.",
        "gt_answers": "1 0 ( \\frac { 1 } { 5 x } - 2 ) = 2 5 ( \\frac { 8 } { 5 } x + \\frac { 3 } { 2 5 } )\n",
        "image_path": "./data/HME100K/test_images/test_5767.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is $\\text{A} = l \\times w$. In the given image, the length of the rectangle is $l = 4$ and the width is $w = 6$. Therefore, the area of the rectangle is $\\text{A} = 4 \\times 6 = 24$.",
        "gt_answers": "A F = \\frac { \\sqrt { 7 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5768.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{Imaginary part of } z = \\sqrt{2} + i\\sqrt{3}$$\nThe real part of $z$ is $-1$.",
        "gt_answers": "\\angle E A C = 1 5 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5769.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$ 2x - 3y + 4z = 7$$where x, y, and z are variables representing the distances from the origin to the points on the graph. The value of z is fixed at 4, while the values of x and y are to be determined by solving the equation.",
        "gt_answers": "O B = 0 . 7\n",
        "image_path": "./data/HME100K/test_images/test_5770.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222ba(b) \u222b\u222bc(d)f(x,y)dxdy=\u222ba(b)\u222b\u222bc(d)f(x,y)dxdy\\int\\_a^b \\int\\_c^d f(x,y) dxdy=\\int\\_a^b \\int\\_c^d f(x,y) dxdy\u200b\u200bHere, a and b are the limits of integration, c and d are the variables with respect to which the integral is taken, and f(x,",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{minipage}{0.4\\textwidth}\n\\begin{align*}\n2x^2 + 2y^2 &= 2(x^2 + y^2) - 2xy \\\n\\end{align*}\n\\end{minipage}\n\\end{center}\n\nThis equation represents the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot generate an image as I am a text-based language model. I can only provide mathematical expressions in LaTeX format. Please provide the expression you would like to see in LaTeX format.",
        "gt_answers": "b x - a y = 4\n",
        "image_path": "./data/HME100K/test_images/test_5773.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, the expression for the formula in the image is:\n\n$$ \\text{c} = \\frac{2}{x} $$\n\nThis is the equation of a line with a slope of 2 and an x-intercept of x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the equation $a + b = c$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression on the image is: y = a\\*(1-x/100)\\*b\\*(c/100)\\*d.",
        "gt_answers": "A B / / D C >\n",
        "image_path": "./data/HME100K/test_images/test_5780.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with width w and height h can be expressed as:\n\nA = wh\n\nwhere A represents the area, w represents the width, and h represents the height.",
        "gt_answers": "y = x ^ { 2 } - 4 x + c ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5781.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the derivative of the function f(x) = x^3 - 4, we can use the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1).\n\nSo, applying the power rule to f(x) = x^3 - 4, we have:\n\nf'(x) = 3x^2 - 4\n\nSimplifying this expression, we get:\n\nf'(x) = 3x^2\n\nTherefore, the derivative of f(x",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle is given by the formula:\n\narea = length \\* width\n\nIn the given image, the length of the rectangle is given by the equation:\n\n2x = 4\n\nThe width of the rectangle is given by the equation:\n\nx = 2\n\nTherefore, the area of the rectangle is given by the formula:\n\narea = 2x \\* x = 2 \\* 2 = 4",
        "gt_answers": "( x - 2 0 ) ( x - 1 0 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_5784.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, we can use the following syntax:\n\n\\begin{align\\*}\nx & = \\frac{a + b}{c + d} \\\n&= \\frac{(b - a)(c + d)}{(b - a)(c + d)} \\\n&= \\frac{c + d - b + a}{c + d} \\\n&= 1 - \\frac{b - a}{c + d}\n\\end{align\\*}\n\nHere, $x$ is the solution to the equation, $a$ and $",
        "gt_answers": "t = \\frac { 6 } { V . }\n",
        "image_path": "./data/HME100K/test_images/test_5785.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is $\\frac{1}{4}$.\n\nHere is the LaTeX code for the expression:\n\n\\frac{1}{4}",
        "gt_answers": "N _ { 2 } ( 8 - 4 \\sqrt { 5 } , 0 )\n",
        "image_path": "./data/HME100K/test_images/test_5786.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: \\frac{3x}{2y + 5z}.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX code for the expression of the formula in the image:\n\n$$I = \\frac{V^2}{R}$$\n\nwhere $I$ is the current flowing through the resistor, $V$ is the voltage applied to the resistor, and $R$ is the resistance of the resistor.",
        "gt_answers": "i A C = \\frac { C F } { A F } = \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5789.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but the provided image is not clear enough to read the expression written on it. Could you please provide a clearer image or a clearer description of the expression?",
        "gt_answers": "\\angle D A C = 2 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5790.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n\\begin{align\\*}\nP &= \\frac{1}{2} \\left(\\frac{1}{4} - \\frac{1}{8}\\right) + \\frac{1}{2}\\left(\\frac{9}{4} - \\frac{1}{8}\\right) \\\n\\end{align\\*}\n\nIn this formula, we're finding the average of the difference between the two numbers 1/4 and 9/4, which are 0.25 and 2.25",
        "gt_answers": "1 9 9 4 \\div 4 = 4 9 8 \\cdots 2\n",
        "image_path": "./data/HME100K/test_images/test_5791.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX expression for the formula in the image:\n\n$$\\begin{aligned}x^2+y^2=2xy\\end{aligned}$$",
        "gt_answers": "= 2 3 2 + 8\n",
        "image_path": "./data/HME100K/test_images/test_5792.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format.",
        "gt_answers": "D ( 4 . 1 ) E ( 3 . 0 )\n",
        "image_path": "./data/HME100K/test_images/test_5793.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image provided. Please provide a clear image that I can use to answer your question.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a mathematical expression written in LaTeX format:\n\n\\begin{align\\*}\n5x^2 + 6x - 1 = 0\n\\end{align\\*}\n\nIn this equation, x is the variable. The coefficient 5 in front of x^2 represents the power to which x is raised, and 6 in front of x represents the number of times x is multiplied by itself. The -1 in the equation represents the constant term.\n\nTo solve this equation, we can use the quadratic formula:\n\nx = (-b +/- sqrt(b^2",
        "gt_answers": "\\frac { \\sqrt { 3 } - \\vert a \\vert } { 2 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5795.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is: 5x2+3x2\u2212x23x2+x25x2\u2212x25x2\u2212x24x2+x25x2\u2212x25x2\u2212x25x2\u2212x24x2+x25x2\u2212x25x2\u2212x25x2\u2212x24x2+x25x2\u2212x25x2\u2212x25x2\u2212x25x2\u2212x25x2\u2212x25x2\u2212",
        "gt_answers": "1 - \\frac { 1 } { 5 } - \\frac { 3 } { 5 } = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5796.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\u222b \u222b f ( x ) dx = \u222b \u222b f ( x ) dx\n\nThis equation represents the indefinite integral of f(x) with respect to x. The left-hand side of the equation represents the definite integral of f(x) with respect to x from a to b, while the right-hand side represents the definite integral of f(x) with respect to x from c to d.",
        "gt_answers": "\\frac { D E } { O D } = \\frac { B D } { D E }\n",
        "image_path": "./data/HME100K/test_images/test_5797.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\frac{1}{x^2 - 5x + 6}$.",
        "gt_answers": "2 \\times 1 0 \\div 5 = 4 ( k m / h )\n",
        "image_path": "./data/HME100K/test_images/test_5798.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not clear as it is written in a language other than English. Please provide the equation in English or a clear image so I can assist you.",
        "gt_answers": "\\angle C O D = 4 \\angle E O D\n",
        "image_path": "./data/HME100K/test_images/test_5799.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\frac{4 + 3i}{5 - 2i}\n\nThis can be written in LaTeX format as:\n\n\\frac{4 + 3i}{5 - 2i}",
        "gt_answers": "x _ { 1 } = 2 \\sqrt [ 4 ] { 8 } - 1 \\approx 2 . 3 6 4\n",
        "image_path": "./data/HME100K/test_images/test_5800.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:\n\n$$\\begin{aligned} \\frac{a}{b} - \\frac{c}{d} = \\frac{ad-bc}{bd} \\end{aligned}$$\n\nwhere a, b, c, and d are positive integers.",
        "gt_answers": "x = \\frac { 1 7 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5801.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\n<latex>1+1=2</latex>",
        "gt_answers": "1 8 0 0 > 1 5 0 0\n",
        "image_path": "./data/HME100K/test_images/test_5803.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:$$\\text{m} = \\frac{\\text{d} \\cdot \\text{r}}{\\text{t}\\cdot \\text{s}}$$where:* $\\text{m}$ is the number of moles of CO2 produced in the combustion reaction* $\\text{d}$ is the density of air in liters per kilogram* $\\text{r}$ is the number of moles of air consumed in the reaction* $\\text{t}$ is the time it takes to consume the air in seconds* $\\text{s}$",
        "gt_answers": "\\Delta A E H \\cong \\Delta C G F ( S A S )\n",
        "image_path": "./data/HME100K/test_images/test_5805.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is a representation of a function f(x) = 2x - 3. The expression for this function can be written as:",
        "gt_answers": "x ^ { 2 } = \\frac { 5 0 \\times ( 1 8 \\times 1 5 - 8 \\times 9 ) } { \\partial 6 \\times \\partial 4 \\times \\partial 7 \\times \\partial 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5806.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image can be represented as follows:\n\n$$\\frac{3x^2+4x+1}{2x+1}=\\frac{3(2x+1)^2+4(2x+1)+1}{2(2x+1)}=\\frac{3(4x+2)+4}{2(2x+1)}=\\frac{11x+4}{2x+1}=5\\frac{x+2}{x+1}=\\frac{2}{1}=2$$\n\nThis expression represents the equation of a parabola with an axis",
        "gt_answers": "\\frac { 9 } { x + y } + \\frac { 6 } { x - y } = 3\n",
        "image_path": "./data/HME100K/test_images/test_5807.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$x = \\frac{a^2 + b^2}{a + b}$$",
        "gt_answers": "\\frac { 3 } { 4 } = \\frac { 1 } { 8 } = x : \\frac { 4 } { 9 }\n",
        "image_path": "./data/HME100K/test_images/test_5808.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{r}{v}=\\frac{v\\_{d}}{v}$.",
        "gt_answers": "G H = \\frac { 1 } { 6 } D C\n",
        "image_path": "./data/HME100K/test_images/test_5809.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write out the expression for the formula in the image using LaTeX format.\n\nHere is the formula in LaTeX format:\n\n$$\\begin{aligned} 3x + 4y &= 11 \\  \\\\ 2x - 5y &= -3 \\end{aligned}$$\n\nAnd here is the image:\n\n[image](https://i.imgur.com/qM6o4e2.png)",
        "gt_answers": "\\vert - 3 \\vert - ( 3 - \\pi ) ^ { \\circ } - 2 \\sin 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5810.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by:$$ 3x^4 + 9x^3 + 4x^2 + 1x + 4 $$",
        "gt_answers": "x = 8 \\sqrt { 3 } - 1 4\n",
        "image_path": "./data/HME100K/test_images/test_5811.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: y = x + 2xy. The variable x is the input to the formula and the variable y is the output.",
        "gt_answers": "6 . x + y = 5\n",
        "image_path": "./data/HME100K/test_images/test_5812.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:\n\n$$\\text{Area} = \\text{width}\\times\\text{height}$$\n\nwhere the width and height are given by:\n\n$$\\text{width} = \\text{12 cm}$$\n$$\\text{height} = \\text{15 cm}$$\nSubstituting these values into the formula, we get:\n\n$$\\text{Area} = \\text{12 cm} \\times \\text{15 cm} = \\text{180 cm}^2$$\nThus, the area of",
        "gt_answers": ": \\Delta A E D \\sim \\Delta A D B\n",
        "image_path": "./data/HME100K/test_images/test_5813.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I do not have access to the image you provided. Could you please provide a different image or a mathematical expression for me to work with?",
        "gt_answers": "2 7 8 \\div 5 = 5 5 \\cdots 3\n",
        "image_path": "./data/HME100K/test_images/test_5814.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by:\n\nA = \u03c0r^2, where r is the radius of the circle.\n\nIn this case, the radius is given by the expression:\n\nr = \u221a(x^2 + y^2)\n\nSo the formula for the area of the circle is:\n\nA = \u03c0[\u221a(x^2 + y^2)]^2\n\nAnd the formula for the length of the hypotenuse is:\n\nh = \u221a(x^2 + y^2)\n\nThis means that the",
        "gt_answers": "( \\sqrt { 7 } ) ^ { 2 } = ( a - \\frac { 1 } { a } )\n",
        "image_path": "./data/HME100K/test_images/test_5815.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\documentclass{article}\n\\usepackage{amsmath}\n\n\\begin{document}\n\nThe formula for the area of a rectangle is:\n\n$$A = \\text{base} \\times \\text{height}$$\n\nwhere $\\text{base}$ is the length of the rectangle's base and $\\text{height}$ is the height of the rectangle.\n\nFor example, if the base of a rectangle is 5 units long and the height is 7 units tall, the area of the rectangle is:\n\n$$A = 5 \\times 7 = 35",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n\\begin{aligned}\n&4x^2+12x-15 \\\n\\end{aligned}\n\nThis formula can be rewritten as:\n\n$$4x^2 + 12x - 15 = 4(x^2 + 3x) - 15$$\n\nExpanding the parentheses on the right side, we get:\n\n$$4x^2 + 12x - 15 = 4(x^2 + 3x) - 15 =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that. The image shows a mathematical expression in LaTeX format. The expression is:\n\n\\begin{center}\nx^2 + y^2 = r^2\n\\end{center}\n\nwhere x and y are variables and r is a constant. This is the formula for the distance between two points in a two-dimensional space. To solve for x and y, we can substitute the values of r into the equation and solve for each variable separately. For example, if r = 5, we can solve for x and y as follows:\n\n\\begin{center",
        "gt_answers": "x = \\pm 1 2\n",
        "image_path": "./data/HME100K/test_images/test_5818.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I do not have access to the image you provided. Can you please provide the image or a description of the expression you want to write out using LaTeX?",
        "gt_answers": "\\angle A B E = 3 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5819.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image provided shows a mathematical expression for calculating the average of two numbers. The formula is given as:2(a+b)/2where a and b are the two numbers being averaged. The expression can be written in LaTeX format as:$\\frac{2(a + b)}{2}$The expression is read as \"the average of a and b is equal to two times the sum of a and b divided by two.\"",
        "gt_answers": "= \\frac { 2 } { 3 } \\pi\n",
        "image_path": "./data/HME100K/test_images/test_5820.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius r is given by:\n\nA = (\u03c0r^2) / 4\n\nThe area of a circle with radius 2 is given by:\n\nA = (\u03c0(2)^2) / 4\n= (\u03c0 \\* 4) / 4\n= \u03c0 / 2\n\nTherefore, the area of the circle with radius 2 is \u03c0 / 2.",
        "gt_answers": "v = \\sqrt { 1 0 } m / s\n",
        "image_path": "./data/HME100K/test_images/test_5821.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you with that!\n\nHere's the LaTeX code for the given expression:\n\n$$\\frac{a^2+b^2}{2ab}=\\frac{a^2+b^2}{2b\\sqrt{a^2+b^2}}=\\sqrt{\\frac{a^4+2a^2b^2+b^4}{2a^2b^2}}=\\sqrt{\\frac{a^2(a^2+2b^2)+b^2(a^2+b^2)}{2b^2a^2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by the formula 4x + 2y = 6, where x and y are integers.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle can be written as:\n\nA = lw\n\nwhere l is the length of the rectangle and w is the width of the rectangle.\n\nIn LaTeX format, this equation can be written as:\n\n$ A = lw $",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a formula written in LaTeX format.\n\nThe formula is:\n\n![Formula](https://latex.codecogs.com/svg.image?%5B%5BImg%5D%5D&svg=true&emoji=true&width=400&height=400)\n\nWhere,\n\nx = number to be represented\nn = positive integer\n\nThe formula represents the nth integer in the sequence of numbers that have the property that the nth digit is zero. For example, the first integer in the sequence is 102",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{a^2+b^2}{2ab}$$where a and b are the side lengths of the square. The formula calculates the area of the square.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a function of the number of terms in a sequence, given by the sum of the first n terms. The formula is written as follows:\n\n$$\\sum\\_{i=1}^{n} i = \\frac{n(n+1)}{2}$$\n\nwhere n is the number of terms in the sequence. The formula states that the sum of the first n terms in a sequence is equal to the sum of the first n odd numbers, which can be written as n(n+1)/2.\n\nNote: The above formula is based on the assumption that the terms in",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```css\n\n\\begin{equation}\n    f(x) = \\frac{1}{x^2 + 2}\n\\end{equation}\n```\nThe above formula represents the given image of the function f(x) = 1/x^2 + 2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n$$ 4\\_{0} + 0\\_{0} = 4\\_{0} $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{x^2 + y^2}{x^2 - y^2}$. This is the formula for the distance between two points in a two-dimensional space. The formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In the formula, x and y represent the coordinates of the two points in the plane, and the numerator and denominator represent the sum and difference of",
        "gt_answers": "\\angle G H D = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5831.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n&#x3B2;xn&#x2212;1\" role=\"presentation\">\u0394xn\u22121\u0394xn\u22121\\Delta x\\_{n-1} = \\frac{x\\_n - x\\_{n-1}}{x\\_{n-1}}\u0394xn\u200b\u22121\u200b=xn\u200b\u2212xn\u22121\u200bx\\_n - x\\_{n-1}xn\u200b\u2212xn\u22121\u200bx\\_n - x\\_{n-1} \\frac{x\\_n",
        "gt_answers": "8 c m = 8 0 0 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_5833.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{a^2+b^2}{2ab}$$\n\nThis formula represents the geometric mean of two numbers, a and b. The numerator is the sum of the squares of a and b, while the denominator is the product of a and b.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$ \\frac{b+d}{2} $$\n\nwhere b and d are the values of the variables in the formula.",
        "gt_answers": "\\therefore \\widehat { B D } = \\widehat { C D }\n",
        "image_path": "./data/HME100K/test_images/test_5836.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is:A=\u03c0r^2where r is the radius of the circle.",
        "gt_answers": "1 . 7 2 - 7 . 1 x = 0 . 3\n",
        "image_path": "./data/HME100K/test_images/test_5837.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$\\mathrm{d}x = \\frac{3}{2} \\times \\frac{x^2 + 6x + 8}{x^2 - 6x + 8}$. This formula is used to calculate the derivative of a quadratic function.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 5x + 4y + 3z = 40.",
        "gt_answers": "x = \\frac { 5 } { 4 8 }\n",
        "image_path": "./data/HME100K/test_images/test_5841.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:$$\\begin{aligned}x &= \\frac{3b^2 - 9ab + 3b}{2(2b - 3a)}\\\\y &= \\frac{3ab - 3b^2 + 2b}{2(2b - 3a)}\\\\z &= \\frac{3ab - 3b^2 + 2b}{2(2b - 3a)}\\end{aligned}$$",
        "gt_answers": "1 2 ( 3 0 0 - 3 x ) + ( 1 2 - b )\n",
        "image_path": "./data/HME100K/test_images/test_5842.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 4cm is A = \u03c0r^2, where r is the radius of the circle. Using the formula, the area of the circle is \u03c0 x 4^2 = 50.4\u03c0cm^2.\n\nThe volume of a sphere with a diameter of 10cm is V = 4/3\u03c0r^3, where r is the radius of the sphere. Using the formula, the volume of the sphere is 4/3 x \u03c0 x 10^3 = 14,328",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\frac{P\\_f}{P\\_i}=\\frac{1-\\rho}{1-\\rho\\frac{P\\_i}{P\\_f}}$$\nwhere $P\\_i$ is the price level in the initial period, $P\\_f$ is the price level in the final period, and $\\rho$ is the elasticity of demand for the good in question.",
        "gt_answers": "O E \\bot D C\n",
        "image_path": "./data/HME100K/test_images/test_5844.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is a formula written in LaTeX format for the expression of the formula in the image.\n\n![](https://latex.codecogs.com/img?s=P&v=2.0)\n\n![](https://latex.codecogs.com/img?s=P&v=2.0)\n\n![](https://latex.codecogs.com/img?s=P&v=2.0)\n\n![](https://latex.codecogs.com/img?s=P&v=2.0)\n\n![](https://",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression for the formula d = a/b, which can be written as follows in LaTeX format:\n\n$$d = \\frac{a}{b}$$\n\nThe expression states that the value of d is equal to the ratio of a to b.",
        "gt_answers": "\\frac { O D } { O E } = \\frac { O A } { O C }\n",
        "image_path": "./data/HME100K/test_images/test_5846.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image can be written as follows: $\\frac{30}{2}\\times\\frac{20}{2}\\times\\frac{5}{2}=120$\n\nNote: In LaTeX, the multiplication symbol is represented by the juxtaposition of the characters `2' and `\\*'.",
        "gt_answers": "\\frac { 3 0 } { x } - \\frac { 3 2 } { x + 3 } = 2\n",
        "image_path": "./data/HME100K/test_images/test_5847.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\\begin{equation}\n\nn^2 = 702\n\\end{equation}",
        "gt_answers": "7 0 1 2 \\approx 7 0 0 0\n",
        "image_path": "./data/HME100K/test_images/test_5849.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX code for the image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\node at (0,0)[inner sep=0pt, outer sep=0pt, font=\\tiny] {$ $};\n\\draw (0,0) circle (2);\n\\filldraw (0,0) circle (0.5pt);\n\\node at (0.5,0.5)[anchor=center] {$ s $};\n\\end{tikzpicture}\n\\end{center}\n\nThis LaTeX code generates the following image:\n\n![Image of formula",
        "gt_answers": "S _ { 1 } = S _ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5850.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$x + y = 2$$This equation represents the addition of the variables x and y and the result is 2.",
        "gt_answers": "y _ { c } = 8\n",
        "image_path": "./data/HME100K/test_images/test_5853.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\begin{aligned} & (1)\\ d\\_i = \\frac{e^{m\\_i}}{e^{m\\_f}}\\cdot r\\_i + \\frac{e^{m\\_i}}{e^{m\\_f}}\\cdot r\\_j + \\frac{e^{m\\_j}}{e^{m\\_f}}\\cdot r\\_i \\\n\\end{aligned}$$\n\nwhere $d\\_i$ is the number of infected individuals in compartment $i$ at time $t$, $m\\_i$ is the",
        "gt_answers": "\\angle D F B = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5854.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length l and width w is given by:\n\nA = l \\* w\n\nThe formula for the area of a square with side length s is given by:\n\nA = s^2\n\nThe formula for the area of a circle with radius r is given by:\n\nA = \u03c0r^2\n\nThe formula for the volume of a rectangular prism with length l, width w, and height h is given by:\n\nV = l \\* w \\* h\n\nThe formula for the volume of a cylinder with radius",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression:$$\\frac{1}{\\sqrt{10}}$$In this formula, the numerator is $\\frac{1}{\\sqrt{10}}$, which can be simplified to $\\frac{1}{5}$. The denominator is $\\sqrt{10}$, which can be simplified to $\\sqrt{10}$. The fraction line is $\\frac{\\frac{1}{\\sqrt{10}}}{\\sqrt{10}}$, which simplifies to $\\frac{1}{5}\\sqrt{10}$. The final answer is $\\frac{1}{5}\\sqrt{10",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given below:\n\n$$c = \\frac{v^2}{4a}$$\n\nIn this formula, 'c' represents the velocity of the car when it reaches the top of the hill, 'v' represents the velocity of the car at the bottom of the hill, 'a' represents the acceleration of the car, and '4' is a constant factor used to simplify the formula.",
        "gt_answers": "\\angle A D C = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5857.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the formula for the mean of two independent random variables with a common mean of 5. The equation is:",
        "gt_answers": "W = - x ^ { 2 } + 7 x + 4 8\n",
        "image_path": "./data/HME100K/test_images/test_5859.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is 2x - 2y + 5z.",
        "gt_answers": "x = - \\frac { 6 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5860.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the image:\n\n\\begin{center}\\begin{tikzpicture}\\draw[black, thick] (0,0) -- (2,2);\\draw[black, thick] (0,2) -- (2,0);\\draw[black, thick] (0,0) -- (0,2);\\draw[black, thick] (2,0) -- (2,2);\\draw[black, thick] (1,1) -- (1,3);\\draw[black, thick] (1,3) -- (1,",
        "gt_answers": "x = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5861.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:$$(a+b) \\cdot (c+d) = ac + bd$$The formula is a product of two binomials, each of which is a sum of two numbers.",
        "gt_answers": "= 1 + 2 y _ { 2 } = 1 - 3 .\n",
        "image_path": "./data/HME100K/test_images/test_5863.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:$$ \\frac{2 \\cdot (4 + 5) \\cdot (8 - 3)}{6 - 1}$$",
        "gt_answers": "y = - \\frac { 1 5 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5864.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![ImageContent](https://cdn.sparkfun.com/datasheets/Dev/Arduino/Shields/WolfsonWM8731.pdf)\n\n![ImageContent](https://cdn.sparkfun.com/datasheets/Dev/Arduino/Shields/WolfsonWM8731.pdf)\n\n![ImageContent](https://cdn.sparkfun.com/datasheets/Dev/Arduino/Shields/WolfsonWM8731.pdf)",
        "gt_answers": "O P \\bot C D\n",
        "image_path": "./data/HME100K/test_images/test_5865.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the formula in the image:\n\n$$ \\frac{4250 - 3250}{250} = \\frac{1000}{250} = 4 $$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not clear. Please provide more context or details about the image to help me understand the expression.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the image:\n\n$$\\begin{aligned}\n&\\frac{1}{2}\\left(\\frac{1}{1 + \\sqrt{3}} + \\frac{1}{1 - \\sqrt{3}}\\right) - \\frac{1}{2} \\left(\\frac{1}{\\sqrt{2}} + \\frac{1}{\\sqrt{2}}\\right) + \\frac{1}{2}\\left(\\frac{1}{\\sqrt{3}} + \\frac{1}{\\sqrt{3}}\\right) - \\frac{1}{2}\\left(\\frac",
        "gt_answers": "\\angle E K G = 1 8 0 ^ { \\circ } - 9 0 ^ { \\circ } - 3 0 ^ { \\circ } = 6 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_5868.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, I am unable to see the image as it is not provided. Please provide the image so that I can assist you with the LaTeX format.",
        "gt_answers": "\\cos x \\in [ \\frac { 1 } { 2 } , 1 ]\n",
        "image_path": "./data/HME100K/test_images/test_5869.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is an equation in LaTeX format, which represents a quadratic equation with the solution of x = 2. The equation is x^2 + 2x - 4 = 0.",
        "gt_answers": "\\frac { 1 } { x } - ( - 2 ) = 2 x\n",
        "image_path": "./data/HME100K/test_images/test_5870.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX equation for the formula:\n\n$$\\begin{aligned}x^2+2x-4&=0\\Rightarrow x=2-2i\\end{aligned}$$\n\nThis equation represents a quadratic equation with roots of x = 2 - 2i, which can be verified by factoring the equation as $(x - 2)(x + 2i) = 0$ and solving for x. The solution is x = 2 - 2i.",
        "gt_answers": "x ^ { 2 } - 2 x - 1 = ( x - 1 - \\sqrt { 2 } ) ( x - 1 + \\sqrt { 2 } )\n",
        "image_path": "./data/HME100K/test_images/test_5871.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$E = mc^2$\n\nwhere $E$ is the energy of the system, $m$ is the mass of the electron, $c$ is the speed of light in a vacuum, and $^2$ is the square of the speed of light.",
        "gt_answers": "I _ { 1 } = \\frac { V } { R _ { 1 } } = \\frac { 1 2 V } { 2 0 \\Omega } = 0 . 6 A\n",
        "image_path": "./data/HME100K/test_images/test_5872.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the expression for the given image:\n\n$$\\frac{a+b}{c+d}=\\frac{a+d}{b+c}$$",
        "gt_answers": "R = \\frac { U } { I }\n",
        "image_path": "./data/HME100K/test_images/test_5873.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write the expression of the formula in the image using LaTeX format, you can use the following code:\n\n$$\\frac{m}{m + 2}$$\n\nThis expression represents the percentage of marks obtained by a student in a test with 20 marks, given that the maximum marks obtainable are 100.",
        "gt_answers": "\\frac { P D } { D C } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5875.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2x + 5y = 12.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is the ratio of the area of the rectangle to the width of the rectangle.\n\nLet A be the width of the rectangle and b be the height of the rectangle. Then, the area of the rectangle is given by the formula:\n\nA = (1/2) \\* b \\* h\n\nwhere h is the height of the rectangle.\n\nThe ratio of the area of the rectangle to the width of the rectangle is given by the formula:\n\nA / w = b / (w/2)\n\nwhere w is the width of the rectangle.\n\nSub",
        "gt_answers": "y _ { 1 } = \\frac { 1 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5878.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image can be written as:\n\n\\begin{align}\nP &= \\frac{1}{n} \\sum\\_{i=1}^{n} x\\_i \\\n&= \\frac{1}{4} \\left( 2 + 4j - 5k \\right) \\\n&= \\frac{1}{4} \\left( 2 + 4j + 5k \\right) \\\n&= \\frac{1}{2} \\left( x\\_1 + x\\_2 \\right) \\\n&= \\frac{1}{2}",
        "gt_answers": "\\angle 2 = \\frac { 1 } { 2 } \\angle A B C\n",
        "image_path": "./data/HME100K/test_images/test_5879.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by: $ y = \\frac{b}{2} + \\frac{c}{2} $ where $b$ and $c$ are the sides of the triangle with hypotenuse $a$.\n\nThe image shows a triangle with sides $a = 5$, $b = 6$, and $c = 5$. Using the equation, we can calculate the height of the triangle: $y = \\frac{b}{2} + \\frac{c}{2} = \\frac{6}{2} + \\frac{5}{2} = 4 +",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "B O = \\frac { 1 } { 2 } B D = 1 c m\n",
        "image_path": "./data/HME100K/test_images/test_5883.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can write the expression of the formula in the image using LaTeX format.\n\nHere's the formula for the given image:\n\n$$\\text{Im}\\_{g\\_{45}} = \\frac{1}{2} \\cdot \\frac{1}{2} \\cdot \\frac{1}{4} \\cdot \\frac{1}{3} = \\frac{1}{12}$$\n\nThe expression can be read as follows: the imaginary part of the fourth root of 45 is equal to 1/12.",
        "gt_answers": "y _ { 2 } = - \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5884.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can follow these steps:\n\n1. Identify the variables and constants in the formula.\n2. Write the formula in LaTeX format using the variables and constants identified in step 1.\n3. Simplify the formula if possible.\n\nThe formula in the image is given by:\n\n$$2x + 5y = 10$$\n\nwhere x and y are the variables.\n\nTherefore, the LaTeX format for the formula is:\n\n$$2x + 5y = 10$$",
        "gt_answers": "\\frac { 1 2 ( x + 1 ) \\vert } { 3 } - 2 ( x + 2 ) =\n",
        "image_path": "./data/HME100K/test_images/test_5885.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$b = \\frac{h \\times i}{j}$$\n\nwhere $h$, $i$, and $j$ are the height, width, and diagonal length of the rectangle, respectively.",
        "gt_answers": "B _ { 2 } = \\frac { \\pi } { 2 } + B _ { 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5886.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula written in LaTeX format is:\n\n$$\\text{f(x) = (x - 3)(x + 2)}$$\n\nThis formula represents a quadratic equation with a leading coefficient of 1, and two terms, one of which is x^2 and the other is -x^3. The constant term is 3x^2 - 6x + 8.",
        "gt_answers": "U _ { r } = \\sqrt { P \\cdot R _ { 1 } } = \\sqrt { 4 W \\times 1 \\Omega } = 2 V\n",
        "image_path": "./data/HME100K/test_images/test_5887.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $ 2x^2 - 5x + 3 $.",
        "gt_answers": "x = \\frac { 2 } { 3 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5889.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image provided is not clear enough to determine the expression of the formula in LaTeX format. Can you please provide a clearer image?",
        "gt_answers": "\\frac { C D } { C P } = \\frac { C P } { C B }\n",
        "image_path": "./data/HME100K/test_images/test_5890.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\begin{aligned}I=\\int\\_{0}^{L}\\frac{dI}{dt}=\\frac{V\\_{dc}}{L}\\end{aligned}$$\n\nwhere $I$ is the current flowing through the inductor, $L$ is the inductance of the inductor, $V\\_{dc}$ is the DC voltage applied to the inductor, and the integral symbol $\\int$ denotes the time integral of the current with respect to time.",
        "gt_answers": "1 \\times ( - 3 ) = \\frac { c } { a }\n",
        "image_path": "./data/HME100K/test_images/test_5891.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write out the expression of the formula in the image using LaTeX format.\n\nThe image shows a geometric sequence, where the first term is 3, and each subsequent term is half of the previous term. The common ratio is 0.5. Therefore, the nth term of the sequence is given by:\nan = 3(0.5)^(n - 1)\nSo, the expression for the nth term can be written as:\nan = 3(0.5)^(n - 1)\nTo evaluate this expression for n = 4,",
        "gt_answers": "\\frac { 3 } { 7 } \\times 9 = \\frac { 2 7 } { 6 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5892.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a graph with three points: (0, 0), (1, 1), and (1, 2).\n\nUsing the given image and the equation y = x2 + 2x + 1, find the slope of the tangent line to the graph at each of the three points.\n\nFor the point (0, 0), the slope of the tangent line is:\n\nd(y)/d(x) = 2\n\nFor the point (1, 1), the slope of the tangent line is:\n\nd(y)/d(",
        "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": "MiniGPT4"
    },
    {
        "question": "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 - 4x + 2 = 0",
        "gt_answers": "\\frac { x + 1 } { 2 } - \\frac { 3 x - 1 } { 4 } = 1\n",
        "image_path": "./data/HME100K/test_images/test_5894.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the probability that a random number between 1 and 4 is greater than 3, we can use the following formula: P(x > 3) = P(x \u2264 3)P(x > 3) = P(x \u2264 3)P(x > 3) = P(x \u2264 3)P(x > 3) = P(x \u2264 3)P(x > 3) = P(x \u2264 3)P(x > 3) = P(x \u2264 3)P(x >",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the formula in the image using LaTeX format, follow these steps:\n\n1. First, select the text in the image and copy it to your clipboard.\n2. Next, open a LaTeX editor, such as Overleaf or ShareLaTeX.\n3. Paste the copied text into the editor and format it as follows:\n\n<img src=\"https://www.example.com/image.png\" alt=\"Image Content\">\n4. Save the LaTeX code and display it to see the formula in the image format.\n\nNote: In the LaTeX code, the `src` attribute",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{2x + 3}{x - 1}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the area of the circle in the image is given by the formula:\n\nA = \u03c0r^2,\n\nwhere r is the radius of the circle. In the image, r = 4 cm. So, the area of the circle is:\n\nA = \u03c0(4 cm)^2 = \u03c0(16 cm)^2 = 50.26 cm^2.",
        "gt_answers": "6 0 \\div 4 \\div 5 = 3 ( c m )\n",
        "image_path": "./data/HME100K/test_images/test_5898.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for a parabola with equation y = ax^2 + bx + c is given by: y = ax^2 + bx + c. This equation can be derived from the derivative of y with respect to x, which is given by: dy/dx = 2ax + b. Substituting a, b, and c into this equation, we get: dy/dx = 2a(x^2) + bx + c. Taking the derivative again with respect to x, we get: d/dx ( dy/dx ) = 2ax + b. Finally",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a radius of 5.3 cm is $\\frac{3.14 \\times 3.14}{2}$. This formula can be written as $A = \\frac{3.14 \\times 3.14}{2}$ or $A = 3.14^2$ in LaTeX format.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n15x^4 + 3x^3 - 5x^2 - 10x + 8\n\nThis formula is a polynomial function of degree 4, which means that it has 4 terms. The first term is 15x^4, the second term is 3x^3, the third term is -5x^2, and the fourth term is -10x. The constant term is 8.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX formula for the expression in the image:\n\n$a + 3b - 2b = 7$\n\n$a = \\frac{7 - 2b}{3}$\n\n$b = \\frac{7 - a}{3}$\n\nThus, the solution to the equation is $\\frac{7 - 2\\times 3}{3} = 4$, and $\\frac{7 - 4}{3} = 2$.",
        "gt_answers": "t = \\frac { 5 \\sqrt { 3 } } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5903.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To express the formula in the image using LaTeX format, you would write:\n\n\\begin{center}\n\\( \\frac{1}{4}(x + 2y) = 12 \\)\n\\end{center}\n\nThis formula represents the equation of a line in slope-intercept form, with a slope of 1/4 and a y-intercept of 12. The image shows the equation of the line, with the x-coordinate of the point where the line intersects the x-axis marked as 0 and the y-coordinate of the point where the line intersects",
        "gt_answers": "\\sin \\theta = \\frac { y } { r } = - \\frac { 3 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5904.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle with sides of 5cm and 12cm is:\n\nA = (1/2) \\* h \\* w\n\nwhere h is the height of the triangle and w is the width of the triangle.\n\nSubstituting the given values into the formula, we get:\n\nA = (1/2) \\* 12 \\* 5\nA = 30\n\nTherefore, the area of the triangle is 30 square centimetres.",
        "gt_answers": "x = \\frac { 5 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5905.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ y = \\frac{a \\cdot x^2 - 3 \\cdot b \\cdot x + 5}{2 \\cdot a - 5 \\cdot b} $$\n\nThis is a quadratic equation with the variables $x$ and $y$. The solutions to the equation can be found by solving for the values of $x$ that make the equation true. These values are the roots of the quadratic equation.\n\nTo solve the equation, we can use the quadratic formula:\n\n$$ x = \\frac{-b \\pm \\sqrt{b",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I apologize for the mistake. I'll try to correct the formula for the expression shown in the image using LaTeX format. Here's the corrected formula:\n\n$$x = \\frac{a\\cdot b}{c\\cdot d}$$\n\nIn this formula, the variables a, b, c, and d represent the given measurements, and the expression x represents the solution.\n\nHere's the corrected LaTeX code:\n\n$$x = \\frac{a \\cdot b}{c \\cdot d}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n\\begin{align\\*}\n    y & = mx + b \\\\\n    x^2 & = ax^2 + bx + c \\\\\n    y & = \\frac{ax^2 + bx + c}{2m} + \\frac{m}{2} \\\\\n    \\frac{y - \\frac{ax^2 + bx + c}{2m} - \\frac{m}{2}}{x^2} & = \\frac{1}{a} \\\\\n    y - \\",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:$$\\frac{4x^3+7x^2+9x+12}{x+6}$$In LaTeX format, this is written as:$$\\frac{4x^3+7x^2+9x+12}{x+6}$$Note that the fraction bar is used to separate the numerator and denominator.",
        "gt_answers": "\\frac { 1 } { 2 } x = 4 7 - 1 3\n",
        "image_path": "./data/HME100K/test_images/test_5910.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the following LaTeX expression:\n\n$$x = \\frac{y - 5}{2}$$\n\nThis formula represents the equation of a line in the form of y = mx + b. The variable x is on the left side of the equation, and the variable y is on the right side of the equation. The coefficient for x is 1, and the constant term is -5/2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{100}{\\sqrt{x^2 + 4x + 8}}$$This formula represents a quadratic equation in the form of y = ax^2 + bx + c, where a = 100, b = 2, and c = 4. The radical in the denominator is represented by the \"sqrt\" function in LaTeX, which produces the square root of a number.",
        "gt_answers": "\\frac { 4 } { 5 } \\textcircled { > } \\frac { 5 } { 7 }\n",
        "image_path": "./data/HME100K/test_images/test_5913.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows the equation 2x2 - 5x + 3 = 1, with the variable x representing the independent variable. The equation is a linear equation in one variable, with a constant term of 3 and a linear term of - 5x. The solution to this equation is x = 1, which is the point where the equation is satisfied. The equation can be rewritten in slope-intercept form as y = 2x + 3, with a slope of - 5 and a y-intercept of 3.",
        "gt_answers": "9 \\times \\frac { 1 } { 3 } = 3\n",
        "image_path": "./data/HME100K/test_images/test_5914.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$2 + 3x = 5$$\n\nwhere x is the variable representing the number of people in the room.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{6000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation shown in the image can be expressed as:\n\n\u222b \u222b \u222b \u222b \u222b \u222b (x + y + z) dx dy dz = \u222b \u222b \u222b \u222b \u222b \u222b (x + y + z) dx dy dz\n\nwhere the lower integrals are evaluated over the given regions. The integrals are evaluated as:\n\u222b \u222b \u222b \u222b \u222b \u222b (x + y + z) dx dy dz = \u222b \u222b \u222b \u222b \u222b \u222b (x + y + z) dx dy dz = \u222b \u222b",
        "gt_answers": "y = - \\frac { 1 9 } { 2 } \\times \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5918.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "\\{ a \\vert 0 < a < 1 r i g h t \\}\n",
        "image_path": "./data/HME100K/test_images/test_5920.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is:\n\n$$ \\frac{a + b}{2} = \\frac{b + c}{2} = \\frac{c + d}{2} = \\frac{d + e}{2} = \\frac{e + f}{2} = 2 $$\n\nWhere a, b, c, d, e, and f are the values of the points on the image.",
        "gt_answers": "6 \\times \\frac { 1 } { 4 } T = 2 5\n",
        "image_path": "./data/HME100K/test_images/test_5921.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\begin{aligned} \\frac{10\\left(10-\\frac{4}{3}\\right)^4}{2\\left(2-\\frac{1}{2}\\right)^4} \\end{aligned}$$This is a numerical expression for the formula in the image.\n\n![ImageContent](https://www.sciencedirect.com/science/article/abs/pii/S2212665920300619)",
        "gt_answers": "S _ { \\Delta A B C } = \\frac { 1 } { 2 } \\times B C \\times A D = 4\n",
        "image_path": "./data/HME100K/test_images/test_5922.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the expression of the formula in the image:\n\n$$\\begin{aligned}\\text{b} = \\frac{a^2 + 2ab + b^2}{2(a + b)}\\\\\\text{b} = \\frac{a^2 + 2ab + b^2}{2(a + b)}\\\\\\text{b} = \\frac{a^2 + 2ab + b^2}{2(a + b)}\\\\\\text{b} = \\frac{a^2 + 2ab + b^",
        "gt_answers": "a ^ { 2 } + b ^ { 2 } \\geqslant \\frac { ( a + b ) ^ { 2 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5923.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: x - y = 10 \\* sqrt(x^2 + y^2) - 5.\n\nHere is how to derive the formula using LaTeX format:\n\nx - y = \u222b(sqrt(x^2 + y^2))dx - 5\n\nThe integral sign (\u222b) is used to denote the definite integral, which represents the area under the curve of the function from x = 0 to x = 10. The function is sqrt(x^2 + y^2), which is the square root of",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is: a = - b \\* 3c.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is given by:\n\nA = \u03c0r^2, where r is the radius of the circle.\n\nUsing the formula, we can calculate the area of the circle with a radius of 4.5cm:\n\nA = \u03c0(4.5)^2 = 34.14(4.5)^2 = 59.9585cm^2\n\nTherefore, the area of the circle is 59.9585cm^2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by:\n\n\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b\u222b",
        "gt_answers": "x = \\frac { 7 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5927.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is as follows:\n\n$$ \\text{ImageContent} = \\frac{3\\times4\\times5\\times6\\times7\\times8}{2\\times3\\times4\\times5\\times6\\times7} $$\n\nThis formula can be read as: `the sum of 3, 4, 5, 6, 7, and 8, divided by the product of 2, 3, 4, 5, 6, and 7.`",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n\\begin{center}\n\\frac{1}{2}(a+b)\\left(\\frac{1}{2}(c+d)\\right)\n\\end{center}\n\nwhere a, b, c, and d are the lengths of the sides of the squares in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: x^2 - 8x + 9.",
        "gt_answers": "x = 4 0 \\times \\frac { 8 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5930.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows an equation for the number of fractions in the number 6, using the formula 6 / 1 = 6. The formula is written in LaTeX format as: $\\frac{6}{1} = 6$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given below in LaTeX format.\n\n\\begin{align\\*}\nf(x) &= \\int\\_a^x t^2dt + \\frac{1}{4}\\int\\_a^x t^4dt + \\frac{1}{8}\\int\\_a^x t^6dt + \\frac{1}{16}\\int\\_a^x t^8dt \\\n&= \\frac{1}{3}x^3 + \\frac{1}{2}x^4 + \\frac{1}{4!}x^5 + \\",
        "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": "MiniGPT4"
    },
    {
        "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 in LaTeX format:\n\n\\begin{equation}\nE = mc^2\n\\end{equation}\n\nwhere E represents energy, m represents mass, and c represents the speed of light in a vacuum.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the given formula:\n\n\\begin{align\\*}\n2x^2 + 4x + 2 &= 4x^2 + 4x + 2 \\\n&= 4x(x + 1) \\\n&= 4x^2 - 4x + 4 \\\n&= 4x^2 - 4x - 2\n\\end{align\\*}",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle is 1/2 \\* base \\* height. In the image, the base is 5 and the height is 10. Therefore, the area of the triangle is 1/2 \\* 5 \\* 10 = 50.\n\nThe sum of the areas of the two smaller triangles is 25 + 12.5 = 37.5. The sum of the areas of the two larger triangles is 50 + 50 = 100. The sum of the areas of the four triangles",
        "gt_answers": "y = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5938.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{2}{5}\\cdot\\frac{20}{25}$$This formula is derived by dividing the number 2 by 5, then multiplying the result by 20 and dividing by 25. The result is the fraction 4/5, which is simplified to 0.8 in decimal form.",
        "gt_answers": "\\frac { 2 } { C _ { 6 } ^ { 2 } } = \\frac { 2 } { 1 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5939.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{R} = \\frac{1}{2}\\left(\\frac{1}{a} + \\frac{1}{b}\\right)$$\n\nwhere $\\text{R}$ is the result, $\\frac{1}{a}$ and $\\frac{1}{b}$ are the probabilities of the events $\\text{A}$ and $\\text{B}$, respectively. The probability of event $\\text{A}$ is $\\frac{1}{2}$, and the probability of event $\\text{B}$ is also $\\frac{1}{",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle is A = \u03c0r^2, where r is the radius of the circle. Using this formula, we can calculate the area of the circle in the image as follows:A = \u03c0(25)^2 = 529\u03c0\\text{A = } \\pi r^2, \\text{ where } r \\text{ is the radius of the circle}. Using this formula, we can calculate the area of the circle in the image as follows:A = \u03c0(25)\u00b2 = 529\u03c0\u03c0\u200br\u00b2\u200b, where r",
        "gt_answers": "x _ { 1 } = \\frac { \\sqrt { m ^ { 2 } + 1 } } { m ^ { 2 } + 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5943.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: $\\frac{2x + 3y - 4z}{x + 2y - 3z}$.",
        "gt_answers": "x _ { 1 } = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5944.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the given image:\n\n\\begin{center}\n\\begin{minipage}{0.5\\textwidth}\n\\begin{equation}\n\\text{The number of rectangles that can be made from the given image is} \\quad \\text{6.}\n\\end{equation}\n\\end{minipage}\n\\end{center}\n\nThis is the LaTeX formula for the given image, which states that there are 6 rectangles that can be made from the image.",
        "gt_answers": "A C / / B D\n",
        "image_path": "./data/HME100K/test_images/test_5945.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{3}{4} + \\frac{1}{2} = \\frac{7}{4}$$This equation shows that the sum of the fractions $\\frac{3}{4}$ and $\\frac{1}{2}$ is equal to the fraction $\\frac{7}{4}$.",
        "gt_answers": "\\frac { 2 4 } { 3 2 } = \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5946.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "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\\begin{align\\*}\ny = 3x^2 + 2x - 4\n\\end{align\\*}",
        "gt_answers": "\\frac { 3 1 } { 3 } k = - \\frac { 2 9 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_5947.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the expression of the formula in the image is given by:",
        "gt_answers": "\\frac { 1 } { x + y } = 2\n",
        "image_path": "./data/HME100K/test_images/test_5948.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is:\n\n$$ 1 - \\frac{a^2}{b^2} $$\n\nwhere $a$ and $b$ are constants.",
        "gt_answers": "( x + 3 + x ) ^ { 2 } - ( 2 x + 3 + x ) = 4 0\n",
        "image_path": "./data/HME100K/test_images/test_5949.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is given by:\n\nf(x) = (x - 1) / (x + 2)\n\nThis is a rational function with a pole at x = 1, which is a double root of the denominator. The graph of this function has a vertical asymptote at x = 1 and a horizontal asymptote at y = 1/2.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{100 \\times 100}{45}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: 3(4 - x) + x + 3 = 11. \n\nIn LaTeX format, this expression can be written as:\n\n\\begin{align\\*}\n3(4 - x) + x + 3 &= 11 \\\n\\end{align\\*}\n\nwhere the `&=` symbol is used to indicate equality, and the `\\*` symbol is used to indicate multiplication.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX format for the given expression:\n\n\\begin{align\\*}\n 5x^2 + 10x - 12 = 0\n\\end{align\\*}",
        "gt_answers": "f ^ { \\prime } ( x ) = 2 a x - \\frac { 1 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_5954.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{R} = \\frac{mgh}{2}$$\n\nwhere m is the mass of the object being lifted, g is the acceleration due to gravity, and h is the height of the object being lifted.",
        "gt_answers": "( m + n ) ^ { 2 } - 4 m n = ( m - n ) ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5955.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:x2+y2=r2\\*sin&#x2061;x2+y2=r2&#x2212;sin&#x2061;x2+y2=r2&#x2212;sin&#x2061;x2+y2=r2&#x2212;sin&#x2061;x2+y2=r2\\sin(x2+y2)=r2\\sin\\left(x2+y2\\right",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: 2\\*g(b) / d.\n\nHere is the LaTeX format for the expression:\n\n\\[2\\*g(b) / d\\]",
        "gt_answers": "\\frac { G F } { B D } = \\frac { A F } { A D . }\n",
        "image_path": "./data/HME100K/test_images/test_5957.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\frac{a+b+c}{5}=\\frac{a+b+c+d}{6}$",
        "gt_answers": "( 5 ) \\frac { 3 } { 5 } - x = \\frac { 1 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_5958.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is: 3x2 + 5x + 11x + 9. This formula is written in LaTeX format as follows:\n\n3x2 + 5x + 11x + 9.",
        "gt_answers": "\\frac { 1 } { 2 } : \\frac { 2 } { 7 } = \\frac { 2 } { 3 } : x\n",
        "image_path": "./data/HME100K/test_images/test_5960.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{8}{3}$$\n\nThis is because the image shows the formula for the volume of a sphere, which is given by the formula:\n\n$$V = \\frac{4}{3} \\pi r^3$$\n\nwhere r is the radius of the sphere. To find the radius of the sphere in the image, we can use the formula:\n\n$$r = \\sqrt{\\frac{V}{4/3 \\pi}}$$\n\nSubstituting the given volume of 8 cubic units into",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX format for the expression in the image:\n\n$$\\begin{aligned} \\frac{5\\sin(x)}{3}+\\frac{4\\cos(x)}{5}\\end{aligned}$$\n\nNote: This formula uses the identity $\\sin(x)^2 + \\cos(x)^2 = 1$, which is a common identity in trigonometry.",
        "gt_answers": "t = \\frac { 3 2 } { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5963.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image is an equation for a circle with center (5, 5) and radius 3. The equation can be written as:\n\n(x - 5)^2 + (y - 5)^2 = 9\n\nwhich can be simplified to:\n\nx^2 + y^2 = 9\n\nTherefore, the equation of the circle is x^2 + y^2 = 9.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: $\\text{sin} \\left( \\frac{\\text{x}}{\\text{a}} \\right) + \\text{cos} \\left( \\frac{\\text{x}}{\\text{a}} \\right) = \\text{sin} \\left( \\frac{\\text{x}}{\\text{a}} \\right) - \\text{cos} \\left( \\frac{\\text{x}}{\\text{a}} \\right)$",
        "gt_answers": "x _ { 2 } = \\frac { - 1 - \\sqrt { 5 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5965.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}\n\\draw (0,0) rectangle (2,1.5);\n\\draw (0,0) -- (2,1.5);\n\\node[right] at (2,1) {$x$};\n\\node[above] at (1,0.5) {$y$};\n\\draw[dotted] (0,0) -- (0.5,0);\n\\draw[dotted] (1.5,0) -- (2,",
        "gt_answers": "x = \\frac { 2 } { 1 3 } \\div 4\n",
        "image_path": "./data/HME100K/test_images/test_5966.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX formula for the image:\n\n\\begin{center}\n\\begin{aligned}\n\\frac{dV}{dt} &= \\frac{dV}{dx} \\cdot \\frac{dx}{dt} \\\n&= -\\frac{V^2}{2} \\cdot \\frac{dx}{dt} \\\n&= -\\frac{V^2}{2} \\cdot \\frac{d^2x}{dt^2} \\\n&= -\\frac{V^2}{2} \\cdot \\frac{a}{m} \\\n&= -\\frac{V^2",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is not shown. The image shows a piece of paper with numbers and letters written on it.\n\nThe expression for the formula in the image is not clear.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 644.133\\*85.455+111.815\\*201.458+119.366\\*50.952+76.865\\*73.948+34.278\\*15.777+93.388\\*2.947+77.355\\*0.579+56.628\\*1.977+",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "This is the expression of the formula in the image using LaTeX format:\n\n$$\\frac{x^2}{x+4}$$",
        "gt_answers": "x = \\frac { 1 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5970.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is: 3x^2 - 9x + 5.\n\nThe formula is written as follows:\n\n3(x^2) - 9(x) + 5\n\nThe formula is written in the LaTeX format as follows:\n\n\\begin{align\\*} 3x^2 - 9x + 5 \\end{align\\*}",
        "gt_answers": "y _ { 3 } = \\frac { 2 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_5971.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n\\frac{5 + 4\\*4}{9 + 5\\*5} = \\frac{5 + 16}{9 + 25} = \\frac{21}{34}\n\nwhich simplifies to 0.6185.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\frac{A+B}{2C+D}$$where $A$ is the area of the triangle with vertices at the origin, $(0,0)$ and $(1,2)$; $B$ is the area of the triangle with vertices at the origin, $(0,0)$ and $(0,4)$; $C$ is the area of the triangle with vertices at the origin, $(0,0)$ and $(2,0)$; and $D$ is the area of the triangle with vertices at the origin, $(0,0",
        "gt_answers": "\\angle A N C = \\angle M B C (\n",
        "image_path": "./data/HME100K/test_images/test_5973.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX formula for the expression:\n\n$$\\frac{\\frac{\\left(\\frac{x}{a}\\right)^2+\\left(\\frac{y}{b}\\right)^2-\\left(\\frac{x+y}{c}\\right)^2}{\\left(\\frac{x}{a}\\right)^2+\\left(\\frac{y}{b}\\right)^2}$$\n\nIn this formula, x, y, a, b, and c are variables.",
        "gt_answers": "x _ { 1 } = - \\frac { 1 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5974.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\frac{dV}{dt} = \\frac{Q}{t} - \\frac{V}{t^2}\n\\end{center}\n\nThis formula represents the rate of change of voltage with respect to time, assuming that the current is constant. The left-hand side of the equation represents the derivative of voltage with respect to time, and the right-hand side represents the rate of charge entering or leaving the capacitor, divided by the time constant of the capacitor.\n\nNote that",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is the area of a square with side length $\\sqrt{5}$. To find the area, we can use the formula for the area of a square, which is $A = s^2$, where $s$ is the side length of the square. Substituting $\\sqrt{5}$ for $s$, we get $A = \\sqrt{5}^2 = 5$. Therefore, the area of the square is 5 square units.",
        "gt_answers": "\\frac { 1 } { a - 1 } + \\frac { 1 } { a ^ { 2 } - 1 }\n",
        "image_path": "./data/HME100K/test_images/test_5977.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is x + 2y = 6. To write it in LaTeX format, we can use the following code:\n\nx + 2y = 6x + 2y=6\u200bwhere x and y are variables representing the coordinates of the points in the plane. The equation states that the sum of the coordinates of any point in the plane is equal to 6.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression of the formula in the image using LaTeX format:\n\n$$ \\frac{1}{4}(x^4 + 3x^3y + 4x^2y^2 + xy^3 + y^4) $$",
        "gt_answers": "w = \\frac { 3 } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_5979.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I cannot see the image as it is not provided. Please provide the image so I can help you with the LaTeX formula.",
        "gt_answers": "( a + b ) \\times c = a \\times c + b \\times c\n",
        "image_path": "./data/HME100K/test_images/test_5980.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the image is given by: 0. 383 x + 1. 626 x + 0. 075 x = 0. 494 x.\n\nThis equation represents the linear regression line that fits the data in the image. The equation has a slope of 0. 383 and an intercept of 1. 626. The y-intercept is 0. 075.\n\nThe R-squared value for this regression line is 0. 494, indicating that the regression line explains",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $\\text{sin}(x) + \\frac{1}{2}\\text{sin}(x) = \\frac{1}{2}\\text{sin}(2x)$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given expression is $\\frac{m \\times 2+3}{6}$.\n\nThe expression can be simplified as $\\frac{m\\times 5}{3}$.",
        "gt_answers": "m ^ { 2 } + ( - \\frac { 2 } { 3 } m + 3 ) ^ { 2 } = 9\n",
        "image_path": "./data/HME100K/test_images/test_5983.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression in the image is not specified, so I cannot provide the LaTeX format. Can you please provide more information or context about the image?",
        "gt_answers": "3 \\times 1 x < - 1 , . x > 2 3\n",
        "image_path": "./data/HME100K/test_images/test_5984.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:\n\nad dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( ) dc dc = - ( )",
        "gt_answers": "\\frac { A D } { D G } = \\frac { A F } { C F }\n",
        "image_path": "./data/HME100K/test_images/test_5985.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image can be expressed as follows:\n\n$$ \\frac{2(x+2)}{x-1} = \\frac{2(2)}{1-1} = \\frac{4}{0} = \\infty $$\nThis is an indeterminate form, so it is not possible to solve for x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by:\n\n$f(x) = \\left \\{\\begin{array}{ccc} 1 & x & x^2 \\\\ 0 & 1 & 0 \\end{array}\\right \\}$\n\nwhere $x$ is an arbitrary real number.",
        "gt_answers": "2 5 V + 3 V = 6 . 7 5 V\n",
        "image_path": "./data/HME100K/test_images/test_5987.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the formula in the image:\n\n$ f = \\frac{300}{200 + 300} $\n\nThis formula calculates the value of f, which is equal to 300 divided by 200 plus 300. The result is 1.5.",
        "gt_answers": "F _ { 1 } = 3 0 0 N\n",
        "image_path": "./data/HME100K/test_images/test_5989.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here's the LaTeX expression for the given image:\n\n\\begin{center}\n\\begin{tikzpicture}[scale=0.5]\n\\draw (0,0) -- (1,0) node[midway, above] {$ $};\n\\draw (1,0) -- (2,0) node[midway, above] {$ $};\n\\draw (2,0) -- (3,0) node[midway, above] {$ $};\n\\draw (3,0) -- (4,0) node[midway, above] {$ $};",
        "gt_answers": "\\frac { 1 } { x - y } = b\n",
        "image_path": "./data/HME100K/test_images/test_5990.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by:\n\n$$\\text{x}\\sin\\left(\\frac{\\text{t}}{2}\\right) + \\text{y}\\cos\\left(\\frac{\\text{t}}{2}\\right) = \\text{v}t$$\n\nwhere $\\text{x}$ and $\\text{y}$ are the initial velocity and displacement of the object, respectively, $\\text{v}$ is the acceleration of the object, and $\\text{t}$ is time.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation shown in the image is: $\\frac{a}{b+c}$.\n\nHere is the LaTeX code for the equation: $\\frac{a}{b+c}$",
        "gt_answers": "3 . x > 5 0\n",
        "image_path": "./data/HME100K/test_images/test_5993.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression of the formula in the image:\n\n$$ \\text{Image Content} = \\frac{2}{x^2 + 4x + 100} $$\n\nIn this expression, the variable x is used to represent the input value for the formula. The numerator 2 is the constant term, and the denominator $x^2 + 4x + 100$ is the polynomial function. This expression can be used to calculate the image content for any given input value of x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image is 2x2 - 4x - 8.\n\nHere is the LaTeX code for the expression:\n\n$$ 2x^{2} - 4x - 8 $$\n\nIn the formula, $x$ represents the independent variable and $-4$ and $-8$ represent the constants. The exponent $2$ represents the power of $x$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression of the formula in the image:\n\n$$\\frac{a\\sin\\theta + b\\cos\\theta}{c}$$",
        "gt_answers": "2 a + b = \\frac { 7 } { 6 }\n",
        "image_path": "./data/HME100K/test_images/test_5997.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is a mathematical expression for the derivative of a function f(x) with respect to x.\n\nThe formula is written as f'(x), which is the symbol for the derivative of a function. The prime symbol indicates that the derivative is taken with respect to x.\n\nThe formula is used in calculus to find the rate of change of a function at a given point. It is a fundamental concept in calculus and is used to find the maximum or minimum values of a function, as well as to determine the concavity of a function.",
        "gt_answers": "0 x = 1 y = \\pm 2\n",
        "image_path": "./data/HME100K/test_images/test_5998.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:$\\frac{\\frac{x^2+y^2}{2}}{x+y}=\\frac{x^2+y^2}{2x+2y}$",
        "gt_answers": "\\frac { x } { 1 5 } = \\frac { 1 . 5 } { 0 . 5 }\n",
        "image_path": "./data/HME100K/test_images/test_5999.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n\u222b \u222b \u222b (2x + 3y) dx + (x - 5y) dy\n\nThis formula represents the double integral of the function f(x,y) = (2x + 3y) over the region bounded by the x-axis, the y-axis, the curve y = x - 5, and the x-axis.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is pi^2.",
        "gt_answers": "\\pi + \\sqrt { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_6001.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, I can help you write out the expression of the formula in the image using LaTeX format.\n\nThe formula in the image is given by:\n\n$$\\frac{1}{a + b}$$\n\nwhere a and b are constants.",
        "gt_answers": "u = \\frac { 1 } { x \\div y }\n",
        "image_path": "./data/HME100K/test_images/test_6002.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX format for the formula in the image:\n\n$$\\begin{aligned} \\text{number of squares} &= \\text{total number of dots} - \\text{total number of triangles} \\ \\ \\ \\\\ &= \\text{32} - \\text{6} \\ \\ \\ \\\\ &= \\text{26} \\end{aligned}$$\n\nThis formula calculates the number of squares in the image by subtracting the total number of triangles from the total number of dots. The result is 26, which is the number of squares in the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\ce{Ca(2+)\\over2mO}$$\n\nHere, the equation represents a chemical reaction between calcium ion (Ca2+) and diphosphate ion (2mO) to form calcium diphosphate (Ca(2+)\\over2mO).",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is 16 - 5 \\* 3 + 4 \\* 1.",
        "gt_answers": "= - \\frac { 5 } { 4 } a\n",
        "image_path": "./data/HME100K/test_images/test_6007.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image: $\\frac{2m}{a^2+b^2}=\\sqrt{a^2+b^2}$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n![Formula for the formula in the image](https://i.imgur.com/n5fTcwz.png)\n\nThis formula is written in LaTeX format, with the variables x and y representing the points on the coordinate plane, and the variable t representing the time at which the points are reached. The function f(x,y) represents the velocity of the object at time t.",
        "gt_answers": "9 + a ^ { 2 } = 4 a ^ { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_6009.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is x^2 + y^2 = r^2.\n\nIn LaTeX format, this equation can be written as follows:\n\n\\begin{align\\*} x^2 + y^2 &= r^2 \\end{align\\*}\n\nNote that the `align\\*` environment is used to align the equation on the right margin. The `=` symbol is used to indicate the equality of the equation. The `\\*` environment is used to create an unnumbered equation.",
        "gt_answers": "x _ { 1 } = \\frac { 1 } { b }\n",
        "image_path": "./data/HME100K/test_images/test_6010.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the given image is: x + 4y = 16.\n\nTo write the equation in LaTeX format, we can use the following code:\n\n$$\\begin{aligned} x + 4y &= 16 \\end{aligned}$$\n\nThis code will display the equation with the correct formatting, including the plus sign, the equal sign, and the subscript for the variable x.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$ \\text{T} = \\frac{\\text{I}}{\\text{V}} $$\n\nwhere T is the temperature in Kelvin, I is the current in amperes, and V is the voltage in volts.",
        "gt_answers": "( 2 x + y ) ( x - 3 y ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_6012.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: xy + 2y - xy^2 + x^2y + 2xy - xy - 2xy + 2x^2 - xy^2 - 2x^2y - 2x^2y + 2x^2y - 2x^2 - x^2 + 2xy - xy + 2x^2y - 2x^2y + 2x^2y - 2x^2y + 2x^2 - x^2 + 2xy",
        "gt_answers": "( x - \\frac { 2 - \\sqrt { 6 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_6013.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$\\frac{1}{2} \\left( x^2 + y^2 \\right) = \\frac{1}{2} \\left( 2x + 2y \\right)$$",
        "gt_answers": "x + \\frac { \\pi } { 4 } = \\frac { 2 } { 4 } + 2 k \\pi\n",
        "image_path": "./data/HME100K/test_images/test_6014.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is: ln(x3x2x1)/x3x2x1. This can be written in LaTeX format as follows: $\\frac{\\ln(x\\_3x\\_2x\\_1)}{x\\_3x\\_2x\\_1}$.\n\nHere is an explanation of the formula:\n\nln(x3x2x1) represents the logarithm of the product of x3, x2, and x1. This is a measure of the number of times the base value (e.g., 10) must be multiplied to",
        "gt_answers": "( 1 - P ) ^ { 7 } p ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_6016.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n\\documentclass[a4paper, 12pt]{article}\n\n\\usepackage{amsmath}\n\n\\begin{document}\n\nThe equation for the area of a rectangle is given by:\n\n$$ A = l \\times w $$\n\nwhere l is the length and w is the width. For example, if the length is 4 cm and the width is 3 cm, the area of the rectangle is:\n\n$$ A = 4 \\times 3 = 12 \\ cm^2 $$\n\nThe area of the image can be calculated by finding the length",
        "gt_answers": "4 4 \u3001 B\n",
        "image_path": "./data/HME100K/test_images/test_6017.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here's the LaTeX format for the expression in the image:\n\n\\begin{center}\n\\begin{equation}\nx^2 + 3x - 5 = 0\n\\end{equation}\n\\end{center}\n\nThis equation represents a parabolic equation with one variable, where the coefficient of the squared term is 3 and the constant term is -5. The solutions to this equation are the roots, which can be found using the quadratic formula:\n\nx = (-b +/- sqrt(b^2 - 4ac)) / (2a)",
        "gt_answers": "\\frac { ( 5 + 6 ) ( 5 - 6 ) } { 5 + 6 } + \\cdots +\n",
        "image_path": "./data/HME100K/test_images/test_6019.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a triangle with a base of a and a height of b is given by: A = (1/2)ab. In this case, a = 3 and b = 4, so the area is A = (1/2) \\* 3 \\* 4 = 6.",
        "gt_answers": "\\frac { A C } { B C } = 2\n",
        "image_path": "./data/HME100K/test_images/test_6021.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image using LaTeX format is:\n\n$$\\begin{aligned} x &= \\frac{1}{2}\\left( \\frac{1}{3}x^2 + 10\\right) + \\frac{1}{2}\\left( \\frac{1}{4}x^2 + 20\\right) \\\n?$$\n\nThis is the formula for a quadratic function with two maxima and one minimum. The first term corresponds to the coefficient of x^2, the second term corresponds to the constant term, and the third term corresponds to the coefficient of x.",
        "gt_answers": "0 = 1 - \\frac { m x } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_6023.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{6^2}{256+6^2} = \\frac{36}{332}$$",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a triangle can be written as:\n\nA = (1/2)bh, where b is the base of the triangle, h is the height, and A is the area.\n\nThe formula for the area of a trapezoid can be written as:\n\nA = (1/2)bh + (1/2)dh, where b is the base, h is the height, d is the distance between the parallel sides, and A is the area.\n\nThe formula for the area of a rectangle can be written as:\n\nA = l",
        "gt_answers": "\\frac { 3 } { 4 } \\cdot 1 2 0 = 9 0 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_6026.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is given by the equation: 2x2 + 3x + 5 = 11, where x is the variable representing the number of apples in the basket.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\na + 3b + 5c = 7a + 2b + 4c = 9b + 5c = 10c = 5a + 3b + 5c = 8a + 2b + 4c = 9b + 5c = 10c = 5c = 5c = 5a + 3b + 5c = 8a + 2b + 4c = 9b + 5c =",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a rectangle with a base of 3 and height of 4 is:\n\nA = 3h = 3 \\* 4 = 12 cm^2\n\nThe area of a rectangle is given by the formula:\n\nA = l \\* w\nWhere l is the length and w is the width.\n\nSo, the area of the rectangle in the image is 3 \\* 4 = 12 cm^2.",
        "gt_answers": "3 a = - \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_6030.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is not clear as the image is not showing any mathematical expression. Please provide the mathematical expression for the equation in the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation is a simple linear regression line. The equation can be written as:\n\ny = b0 + b1\\*x\n\nwhere b0 is the intercept and b1 is the slope.\n\nThe equation can be derived from the given image by drawing a line of best fit through the data points. The slope of the line is given by the change in y for a unit change in x. The intercept is given by the y-value where x=0.\n\nThe values of b0 and b1 can be found by solving the equation for x and y, respectively. The equation can be written",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\text{number of heads in a coin toss} = \\frac{1}{2} \\times \\frac{1}{2} + \\frac{1}{2} \\times \\frac{1}{2} + \\frac{1}{2} \\times \\frac{1}{2} = \\frac{1}{2} \\times \\frac{1}{2} + \\frac{1}{2} \\times \\frac{1}{2} + \\frac{1}{2} \\times \\frac{1}{2",
        "gt_answers": "\\vert - 4 \\vert + \\vert + 7 \\vert + \\vert - 9 \\vert + \\vert + 8 \\vert + \\vert + 6 \\vert + \\vert - 4 \\vert + \\vert - 3 \\vert = 4 \\vert ( k m )\n",
        "image_path": "./data/HME100K/test_images/test_6034.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is: $\\frac{100}{36}\\cdot\\frac{60}{60}\\cdot\\frac{15}{10}\\cdot\\frac{20}{10}=\\frac{15}{4}\\cdot\\frac{5}{2}=\\frac{75}{4}$.",
        "gt_answers": "\\angle P A C = \\angle A P B + \\angle P B D\n",
        "image_path": "./data/HME100K/test_images/test_6035.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$ E = mc^2 $$\n\nwhere E represents the energy of the object, m represents its mass, and c represents the speed of light in a vacuum. This equation shows that energy and mass are directly related to each other, and that the total energy of an object is equal to its mass multiplied by the speed of light squared.",
        "gt_answers": "\\therefore \\angle O Q A = \\angle O C A Q = 6 2 ^ { \\circ }\n",
        "image_path": "./data/HME100K/test_images/test_6036.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a mathematical expression that is written in LaTeX format.\n\nThe expression is: \u222b(\u222bx\u00b2dx) \\* (\u222bx\u221a(2)dx) \\* (\u222bx\u221a(3)dx) \u222bx2dx \u222bx\u221a(2)dx \u222bx\u221a(3)dx.\n\nThe variable x is integrated from 0 to 1 in the first and third integrals, and from 0 to \u221a(2) in the second integral.\n\nThe limits of integration are written using the integral sign, represented by the double integral symbol.",
        "gt_answers": "x = \\frac { 2 3 - 3 P ^ { 1 } } { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_6037.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$\\text{ImageContent}$$This formula represents the value of the image.",
        "gt_answers": "y = \\frac { 4 } { x }\n",
        "image_path": "./data/HME100K/test_images/test_6039.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is: 5x^2 + 10x + 5.\n\nHere's how to write it in LaTeX format:\n\n\\begin{align\\*}\n5x^2 + 10x + 5\n\\end{align\\*}",
        "gt_answers": "= \\frac { 1 } { 2 } A O \\cdot C M\n",
        "image_path": "./data/HME100K/test_images/test_6040.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX code for the expression:\n\n\\begin{equation}\n\\text{Image content} = \\text{Some text}\n\\end{equation}\n\nIn this equation, `\\text{Image content}` represents the image content, and `\\text{Some text}` represents some text that is related to the image.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is not written in LaTeX format. It appears to be a mathematical expression that has been written out in words.\n\nThe expression is: 5 + (2/3) \\* (1 + 1/4) = 5 + (2/3) \\* (1.25) = 5 + (2/3) \\* 1.25 = 5 + 2/3 = 7.66666666666666666666666666666666",
        "gt_answers": "e \\geq \\frac { c } { a } \\geq \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_6042.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$f(x) = \\left(\\frac{a}{b}\\right)^x$$\n\nwhere $a$ and $b$ are constants.",
        "gt_answers": "y ^ { 2 } - 2 0 y + 1 0 0 - 4 y - 2 0 = 0\n",
        "image_path": "./data/HME100K/test_images/test_6043.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is given by: 3x + 4y = 10.\n\nTo find the solution, we can substitute the values of x and y into the equation:\n\n3(1) + 4(2) = 10\n\nSubstituting the values, we get:\n\n3 + 8 = 10\n\nThus, the solution is x = 3 and y = 2.",
        "gt_answers": "N a _ { 2 } C O _ { 3 } + H _ { 2 } S O _ { 4 } = N a _ { 2 } S O _ { 4 } + H _ { 2 } O + C O _ { 3 } \\uparrow\n",
        "image_path": "./data/HME100K/test_images/test_6044.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The image shows a calculation in LaTeX format.\n\nThe expression is given by:\n\n$$\\text{c}\\_{2}=\\frac{2\\text{V}}{\\text{r}}\\text{c}$$\n\nwhere c2 is the capacitance of the capacitor, V is the voltage across the capacitor, r is the resistance of the resistor, and c is the capacitance of the capacitor.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following steps:\n\n1. Select the text that represents the formula in the image and copy it to the clipboard.\n2. Paste the copied text into the LaTeX editor.\n3. Format the text as follows:\n`$\\text{Expression for }x^2+3x+5$`\n4. Insert the expression for x^2+3x+5 into the formula in the image, replacing the variable x with the expression we just created in step 3. The resulting formula in LaTeX format would",
        "gt_answers": "x \\div 3 \\times 3 = 2 . 1 \\times 3\n",
        "image_path": "./data/HME100K/test_images/test_6049.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image is:x=2y2+4y2=5x2\u2212y2=2x2y2=3x2\u2212y2=22x2\u2212y2=32x2y2=5x2\u2212y2=32x2\u2212y2=22x2\u2212y2=33x2y2=5x2\u2212y2=33x2\u2212y2=22x2\u2212y2=33x2y2=5x2\u2212y2=33x2\u2212y2=2",
        "gt_answers": "\\frac { 1 0 } { 2 0 0 } = \\frac { 1 } { 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_6050.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image given in LaTeX format is: $\\frac{3\\times 4\\times 5}{2\\times 3\\times 4} = \\frac{60}{6} = 10$\n\nThis is the formula to find the sum of the three numbers 3, 4, and 5, with a denominator of 2 times 3 times 4. The numerator is 3 times 4 times 5, and the sum is 10.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the image is given by the equation:\n\n$$ \\text{y} = 2x + 1 $$\n\nwhere x is the input and y is the output.",
        "gt_answers": "y = \\frac { 3 } { 4 } + \\frac { 1 } { 4 } \\cos 4 x\n",
        "image_path": "./data/HME100K/test_images/test_6054.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is given by:\n\n$$\\text{Number of points scored by team A} = \\frac{x}{y} \\times 4 \\times 3$$\n\nwhere x and y are the number of goals scored by team A and team B respectively.",
        "gt_answers": "x _ { 4 } = - \\sqrt { 5 }\n",
        "image_path": "./data/HME100K/test_images/test_6055.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression of the formula in the image using LaTeX format is:\n\n$$ \\sin(x) = \\frac{e^{-x}}{\\sqrt{1+e^{-2x}}}$$",
        "gt_answers": "2 m - 1 = 0 , n - 3 = 0\n",
        "image_path": "./data/HME100K/test_images/test_6056.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$c = \\frac{t^2 - d^2}{2t}$$",
        "gt_answers": "A C \\bot B D\n",
        "image_path": "./data/HME100K/test_images/test_6057.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is $\\frac{a+b}{c+d}$.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "1. For the given image, find the area of the triangle with vertices at the points (1, 4), (3, 6), and (2, 5).\n\nThe triangle has one base with length 5 and one height with length 3. The area of the triangle is given by the formula:\n\nArea = (1/2) \\* base \\* height\n= (1/2) \\* 5 \\* 3\n= 3.75\n\nTherefore, the area of the triangle is 3.75.\n\n2. Find the",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with a diameter of 4 is $\\sqrt {4r^2}$ where r is the radius of the circle. The formula for the volume of a cylinder with a height of 8 and a radius of 4 is $\\pi r^2 h$ where r is the radius of the cylinder and h is the height. The formula for the volume of a cone with a height of 6 and a radius of 4 is $\\frac{1}{3} \\pi r^2 h$ where r is the radius of the cone and h is the height. The formula for",
        "gt_answers": "m ^ { 2 } - 4 = - 1\n",
        "image_path": "./data/HME100K/test_images/test_6060.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a circle with radius $r$ is $\\text{area = } \\frac{r^2}{4}$.",
        "gt_answers": "a > \\frac { 1 } { 2 } a\n",
        "image_path": "./data/HME100K/test_images/test_6061.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{mg}{60}$$\n\nwhere m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and 60 is the time in seconds that the object falls from rest to the ground.",
        "gt_answers": "\\cdot S _ { \\Delta } P D C = \\frac { 1 } { 2 } \\times 4 \\times y\n",
        "image_path": "./data/HME100K/test_images/test_6062.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Here is the LaTeX expression for the formula in the image:\n\n\\begin{center}\n\\begin{equation}\n4x^2 + 4y^2 = 0\n\\end{equation}\n\\end{center}\n\nThe equation represents a parabola with an equation of 4x\u00b2 + 4y\u00b2 = 0, which has no solutions in real numbers. The x\u00b2 and y\u00b2 terms represent the squared distance from the origin, and the equation represents the set of all points that are equidistant from the origin.",
        "gt_answers": "x - 2 = - \\frac { 4 } { k }\n",
        "image_path": "./data/HME100K/test_images/test_6064.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:\n\n$$x^2+3x-5=0$$\n\nTo solve for x, we can use the quadratic formula:\n\n$$x = (-b \u00b1 \u221a(b^2 - 4ac)) / 2a$$\n\nPlugging in the values, we have:\n\n$$x = \\left(\\frac{-3 \\pm \\sqrt{3^2 - 4(1)(2)}}{2(1)}\\right) = \\left(\\frac{-3 \u00b1 \\sqrt{13}}{2}\\right)$$",
        "gt_answers": "x ^ { 2 } - x - \\frac { 3 } { 4 } < 0\n",
        "image_path": "./data/HME100K/test_images/test_6065.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression for the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n\\begin{center}\n$ \\frac{x + 2}{x - 1} = \\frac{x^2 + 3x + 2}{x^2 - 2x + 1} $\n\\end{center}\n\nThis code produces the following output:\n\n\\begin{center}\n$ \\frac{x + 2}{x - 1} = \\frac{x^2 + 3x + 2}{x^2 -",
        "gt_answers": "x + \\frac { 3 } { 4 } = \\pm \\frac { 3 } { 4 }\n",
        "image_path": "./data/HME100K/test_images/test_6067.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To find the expression for the image, we can write out the following equation:\n\n\\begin{align}\nx = \\frac{bh}{2a}\ny = \\frac{ah}{2b}\nz = \\frac{ch}{2d}\n\\end{align}\n\nwhere a, b, c, and d are the lengths of the sides of the image. Plugging in the values from the image, we get:\n\n\\begin{align}\nx &= \\frac{2.5cm}{2 \\* 4.5cm} = 1.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "To write out the expression of the formula in the image using LaTeX format, we can use the following LaTeX code:\n\n\\begin{align}\nx + 2y - 3z &= 5 \\notag \\\n\\end{align}\nHere, the `align` environment is used to align the equation horizontally, and the `notag` environment is used to denote the equation's number. The equation is written in the usual mathematical notation, where `x`, `y`, and `z` are variables, and `=` is used to denote equality.\n\nNote that this equation is",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the expression for the formula in the image using LaTeX format:\n\n$$\\begin{aligned} x + 2 &= 7 \\\n\\frac{x - 1}{2} &= 3 \\\n\\frac{x - 2}{3} &= 1 \\\nx &= \\frac{13}{3} \\\n\\end{aligned}$$\n\nThe formula is asking to find the value of $x$ that satisfies the given conditions. The first equation states that $x + 2 = 7$, the second equation states that $\\frac{x - 1}{2",
        "gt_answers": "\\frac { 7 } { 1 2 } \\times \\frac { 1 } { 3 } = \\frac { 7 \\times 1 } { 1 2 \\times 3 } = \\frac { 7 } { 3 6 }\n",
        "image_path": "./data/HME100K/test_images/test_6071.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the given image is given by:",
        "gt_answers": "- \\frac { 1 } { 5 } , - \\sqrt [ 3 ] { \\alpha 7 } , - 5 . 1 \\alpha 3 4 5 \\cdot\n",
        "image_path": "./data/HME100K/test_images/test_6072.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the area of a triangle with legs of length 10 and 5 is:",
        "gt_answers": "t = \\frac { n } { 1 2 0 }\n",
        "image_path": "./data/HME100K/test_images/test_6073.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the area of a rectangle with length l and width w is A = lw.\n\nIn LaTeX format, the formula can be written as:\n\n\\[ A = lw \\]\n\nwhere l and w are the length and width of the rectangle, respectively.",
        "gt_answers": "x = \\frac { 4 } { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_6074.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:$$m\\_{th} = \\frac{1}{2}(a + b) - \\frac{1}{2}(a - b)$$This formula represents the midpoint between two points $a$ and $b$. The midpoint is the point that is equidistant from both $a$ and $b$. The formula is derived by finding the average of the two points, $a + b$, and then subtracting the average of the two points, $a - b$, to find the midpoint.",
        "gt_answers": "m ^ { 2 } + m - \\frac { 3 } { 4 } = 0\n",
        "image_path": "./data/HME100K/test_images/test_6075.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be $\\frac{1000\\times 20}{50}$. This is because the image shows the number 1000, which is multiplied by 20 to get 2000, then divided by 50 to get 40.\n\nAlternatively, if you would like to express the formula in the image using the variable x, the expression would be $\\frac{1000\\times x}{50}$. This is because x represents the number of items in the list, and the expression shows",
        "gt_answers": "2 x + 1 0 0 = 2 \\times 1 2 0 0 + 1 0 0 = 2 5 0 0\n",
        "image_path": "./data/HME100K/test_images/test_6076.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is:\n\n$$\\frac{x + 2y}{2x - y}$$\n\nThis formula can be read as \"the ratio of x plus two y to two x minus y.\" The denominator, 2x - y, is the difference between two values of x and y. The numerator, x + 2y, is the sum of x and two times y. The expression can be interpreted as finding the ratio of the sum of x and two times y to the difference between two values of x and y.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format is: $ f(x) = \\frac{1}{x} $\n\nThe formula is a basic one, which states that the derivative of a function with respect to x is equal to 1 divided by x. This is a linear function, meaning that the slope of the tangent line at any point on the graph is equal to the derivative of the function at that point.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image using LaTeX format would be: $ E = mc^2 $ where E is the energy of the object, m is its mass and c is the speed of light in a vacuum.\n\nNote: LaTeX is a typesetting system for mathematical and scientific documents. It provides a variety of commands and symbols for writing equations, formulas, and other mathematical expressions.",
        "gt_answers": "b _ { 1 } + b _ { 2 } + \\cdots + b _ { n } = 2 ^ { n + 1 } - 2\n",
        "image_path": "./data/HME100K/test_images/test_6081.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here's the LaTeX expression for the image you provided:\n\n\\begin{center}\n$x = \\frac{9}{5} + 2$\n\\end{center}\n\nHere's a breakdown of the expression:\n\n* The $\\frac{}$ symbol is used to denote a fraction, with the numerator (the top part of the fraction) being 9 and the denominator (the bottom part of the fraction) being 5.\n* The addition symbol ($+$) is used to combine the numerator and denominator, resulting in the fraction $\\frac{9",
        "gt_answers": "8 \\div 0 . 2 5 = 3 2\n",
        "image_path": "./data/HME100K/test_images/test_6082.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is:$$\\frac{p}{q}$$where p and q are positive integers.",
        "gt_answers": "B P = \\sqrt { 9 + ( 1 - y ) ^ { 2 } }\n",
        "image_path": "./data/HME100K/test_images/test_6083.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$\\frac{16}{2} = \\frac{8}{1} + \\frac{8}{1}$$\n\nThe numerator is 16, which is the sum of 8 and 8. The denominator is 2, which is the sum of 1 and 1.\n\nSo, the simplified expression is:\n\n$$\\frac{8}{1} + \\frac{8}{1}$$\n\nwhich is equal to 8.\n\nTherefore, the image represents the equation 8 = 8.\n##",
        "gt_answers": "\\frac { 8 } { 1 1 } \\div 2 \\textcircled { < } \\frac { 8 } { 1 1 }\n",
        "image_path": "./data/HME100K/test_images/test_6084.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula for the expression in the image is given by the following LaTeX equation: $\\frac{x^2}{a^2 + b^2}$ where $a$ and $b$ are the lengths of the hypotenuse and legs of the right triangle.",
        "gt_answers": "\\frac { x } { 1 5 } = \\frac { 1 . 5 } { 0 . 5 }\n",
        "image_path": "./data/HME100K/test_images/test_6086.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the formula in the image is:\n\nbe = bf / f\n\nwhere bf is the slope of the line passing through the point of tangency of the curve with the x-axis, and f is the x-coordinate of that point.",
        "gt_answers": "\\frac { B E } { E F } = \\frac { E G } { B E }\n",
        "image_path": "./data/HME100K/test_images/test_6087.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure, here is the LaTeX expression of the formula in the image:\n\n$$m=\\frac{a^2+b^2}{2ab}$$",
        "gt_answers": "\\overrightarrow { x } = 1 . 6 m ^ { 3 }\n",
        "image_path": "./data/HME100K/test_images/test_6088.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "Sure! Here is the expression in LaTeX format:\n\n$$\\begin{align\\*}\n\\frac{10\\left(\\frac{10^3-10^2}{10^3+10^2}\\right)+20\\left(\\frac{20^3-20^2}{20^3+20^2}\\right)}{50+20}=\\frac{200\\left(\\frac{20^3-20^2}{20^3+20^2}\\right)+10\\left(\\frac{10",
        "gt_answers": "( x ^ { 2 } + 4 x ) ( x ^ { 2 } + 4 x + 8 ) = 0\n",
        "image_path": "./data/HME100K/test_images/test_6089.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the formula in the image is:$$\\frac{2x + 5}{x + 3} = \\frac{x + 2}{x + 3} - \\frac{x + 2}{x - 2}$$\n\nwhere $x$ is any real number. This formula is derived from the fact that the slope of the line passing through the points $(0,2)$ and $(2,5)$ is the same as the slope of the line passing through the points $(1,4)$ and $(3,6)$.",
        "gt_answers": "x = \\frac { 2 . 4 \\times 3 } { 1 2 } = 0 . 6\n",
        "image_path": "./data/HME100K/test_images/test_6090.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation in the image can be written as:\n\n$$\\text{Imaginary part of } Z = \\frac{1}{2}\\left(\\frac{1+i}{2}\\right) + \\frac{1}{2}\\left(\\frac{3+i}{2}\\right) = \\frac{3+i}{4}$$\n\nwhere $Z$ is the impedance of the circuit, and the real and imaginary parts of $Z$ are denoted by $Z\\_r$ and $Z\\_i$, respectively.",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation for the height of a cone can be represented as follows:\n\nh = r \\* v / (3 \\* pi)\n\nwhere h is the height of the cone, r is the radius of the base of the cone, v is the volume of the cone and pi is the mathematical constant that is approximately equal to 3.14.",
        "gt_answers": "t = \\frac { S } { V }\n",
        "image_path": "./data/HME100K/test_images/test_6092.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The expression for the given image is:\n\n$$ f(x, y) = \\frac{x^2 + 3xy + y^2}{x^2 + 5x + 3y^2} $$",
        "gt_answers": "F e + C u S O _ { 4 } = F e S O _ { 4 } + + C u\n",
        "image_path": "./data/HME100K/test_images/test_6093.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula is given as follows:\n\n$$\\text{image content}$$",
        "gt_answers": "y = x \\pm \\sqrt { 2 }\n",
        "image_path": "./data/HME100K/test_images/test_6094.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The formula in the image is 43.264 + 1.428\\*2 + 0.166\\*12 = 59.058.\n\nThe LaTeX format is: 43.264 + 1.428\\*2 + 0.166\\*12 = 59.058.",
        "gt_answers": "\\Delta = 3 6 m + 1 6\n",
        "image_path": "./data/HME100K/test_images/test_6095.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "I'm sorry, but I am not able to see the image you provided as it is not accessible. Can you please provide me with a different image that I can see and work with?",
        "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": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "```\n\n$$\n   \\frac{a + b}{c + d}\n= \\frac{(c + d) \\* (a + b)}{(a + b) \\* (c + d)}\n= \\frac{cd + ad + bd + bc}{cd + ab + bd + ac}\n= \\frac{1}{2} \\* \\frac{a + b + c + d}{a + b + c + d}\n$$\n```\nThis is the expression of the formula in the image using LaTeX format.",
        "gt_answers": "\\frac { C G } { A G } = 1\n",
        "image_path": "./data/HME100K/test_images/test_6097.jpg",
        "model_name": "MiniGPT4"
    },
    {
        "question": "Please write out the expression of the formula in the image using LaTeX format.",
        "answer": "The equation written in the image is:\n\n$$y = \\frac{50000}{20000 + 1000x}$$\n\nThe variable x represents the number of hours studied per day, and y represents the number of days studied per week. The expression states that the number of days studied per week is equal to the number of hours studied per day multiplied by the number of days studied per week.",
        "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": "MiniGPT4"
    }
]