id
stringlengths 6
6
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061459 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, determine the ratio of the cycle lengths of f(x) and g(x)."
},
{
"from": "gpt",
"value": "By observing the graphs, one cycle of f(x) completes at 360° while g(x) completes its cycle at 720°. To find the scaling factor or ratio, you would divide the cycle length of g(x) by that of f(x), giving 720° / 360°. So the answer is 2\nThe answer is 2"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/061459.png | 061459 |
087055 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: The number line below shows 3 wholes split in to 1/8 size pieces.\nIf 3 is divided into pieces that are 1/8 of a whole each, how many pieces are there in total?"
},
{
"from": "gpt",
"value": "If each whole is split up into eighths, $\\frac{1}{8}$, how many eighths make up each whole?\n We can see that each whole is split up into eight pieces. \n So how many pieces are there if we have 3 wholes?\n Number of pieces $=3 \\times 8$\n Evaluate the multiplication using an appropriate strategy.\n Number of pieces $=24$ So the answer is 24\nThe answer is 24"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/087055.png | 087055 |
075924 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Does the function $y=\\log_2(x+3)$ have a maximum output value?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "The analysis states that the $y$-values stretch slowly upwards towards positive infinity as $x$ increases, indicating no maximum output value. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/075924.png | 075924 |
027524 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the y-intercept of the line represented by the graph of the equation $y = -4x$?\nChoices:\nA. 0\nB. 1\nC. -1\nD. 4"
},
{
"from": "gpt",
"value": "In the equation of a line $y = mx + b$, the y-intercept is represented by $b$. Here, since the equation is $y = -4x$, the intercept $b = 0$. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/027524.png | 027524 |
034735 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the angular range encompassing the region of interest?\nChoices:\nA. $0$ to $\\pi$\nB. $-\\pi/6$ to $7\\pi/6$\nC. $\\pi/6$ to $3\\pi/2$\nD. $0$ to $2\\pi$"
},
{
"from": "gpt",
"value": "The region is defined from the angle where $\\sin\\theta = -\\frac{1}{2}$. These angles which mark the limits of the region of interest are $\\theta = -\\frac{\\pi}{6}$ and $\\theta = \\frac{7\\pi}{6}$, effectively creating the necessary angular bounds. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/034735.png | 034735 |
006242 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, is the diagonal bisected by the other diagonal?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "In a parallelogram, each diagonal bisects the other, meaning they cut each other into equal parts. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/006242.png | 006242 |
024818 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what would be the total parking cost for 3 hours?\nChoices:\nA. 3 pounds\nB. 6 pounds\nC. 9 pounds\nD. 12 pounds"
},
{
"from": "gpt",
"value": "Using the hourly rate from the analysis:\nHourly rate = 2 pounds.\nCost for 3 hours = 3 * 2 pounds = 6 pounds So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/024818.png | 024818 |
025270 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what property does the curve show?\nChoices:\nA. Periodicity\nB. Asymptotic behavior\nC. Discontinuity\nD. Linear progression"
},
{
"from": "gpt",
"value": "The curve in the image repeats at regular intervals, showing periodicity. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/025270.png | 025270 |
080188 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Identify the part of a circle shown in the diagram.\nChoices:\nA. Radius\nB. Arc\nC. Tangent\nD. Circumference"
},
{
"from": "gpt",
"value": "What is the name of the perimeter of a circle?\n\nCircumference So the answer is D\nAnswer: Circumference"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/080188.png | 080188 |
064098 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the total number of hours Alfred spends traveling each week?"
},
{
"from": "gpt",
"value": "Examine Alfred's pie chart and count the total number of sections, as each section corresponds to one hour of travel time. So the answer is 5 hours\nThe answer is 5 hours"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/064098.png | 064098 |
056489 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, if angle STW is 119 degrees, what must be the measure of angle XWT?"
},
{
"from": "gpt",
"value": "Given that angle STW is 119 degrees and if angle STW and angle XWT are alternate interior angles (meaning they are equal due to their placement relative to parallel lines and a transversal), then angle XWT also measures 119 degrees. So the answer is Angle XWT measures 119 degrees.\nThe answer is Angle XWT measures 119 degrees."
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/056489.png | 056489 |
027926 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, if $x = -1$, which line would have a smaller $y$-value?\nChoices:\nA. The black line\nB. The gray line\nC. Both have the same y-value\nD. Cannot be determined"
},
{
"from": "gpt",
"value": "For $x = -1$, since the gray line is below the black line, it will have the smaller $y$-value. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/027926.png | 027926 |
072376 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: For a triangle where the angles are determined to follow the ratio 5:12:13, does angle B measure 72 degrees?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Given angle A measures 30 degrees from the calculated ratio, multiplying 30 by 12/5 as found from A/B = 5/12 gives B = 72 degrees. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/072376.png | 072376 |
059067 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how would the surface area calculation change if only one face of each pair was considered?"
},
{
"from": "gpt",
"value": "The total surface area is then twice the sum of your answers to parts (a), (b) and (c). So the answer is It would be necessary to multiply the sum of the areas of one face from each pair by two.\nThe answer is It would be necessary to multiply the sum of the areas of one face from each pair by two."
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/059067.png | 059067 |
085363 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: The graph represents Yvonne's distance from home over a 9 minute interval.When she first started to move, did she travel towards or away from home?\nChoices:\nA. Away\nB. Towards"
},
{
"from": "gpt",
"value": "At the beginning of the graph, Yvonne's distance from home decreased. \n Towards So the answer is B\nAnswer: Towards"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/085363.png | 085363 |
062106 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, is each x-value mapped to precisely one y-value in the graph?"
},
{
"from": "gpt",
"value": "Examine the graph for each value of x. Check if any x-value corresponds to more than one y-value by observing intersections of vertical lines with the graph. So the answer is Each x-value is mapped to precisely one y-value.\nThe answer is Each x-value is mapped to precisely one y-value."
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/062106.png | 062106 |
029046 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, does every $x$ value have only one corresponding $y$ value?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "The graph suggests a relation where some $x$ values have more than one corresponding $y$ value. Therefore, it is not a function. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/029046.png | 029046 |
027142 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what transformation can be done to graph f(x) to obtain graph g(x)?\nChoices:\nA. Multiply each y-coordinate by 4\nB. Divide each y-coordinate by 4\nC. Translate the function 2 units left\nD. Stretch the function by 2 units\nE. Reflect the function in the x-axis"
},
{
"from": "gpt",
"value": "From the analysis, we know that each y-coordinate of function f(x) is multiplied by 4 to get the corresponding coordinates for function g(x). Hence, to transform f(x) to g(x), we multiply each y-coordinate by 4. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/027142.png | 027142 |
045808 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the decimal equivalent of the shaded columns?\nChoices:\nA. 0.1\nB. 0.2\nC. 0.5\nD. 1"
},
{
"from": "gpt",
"value": "5 of the 10 columns are shaded. This means 5 tenths or 0.5. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/045808.png | 045808 |
072848 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Are angles AOB and BOC adjacent, given they share side OB and vertex O?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Sharing a side and a vertex means angles AOB and BOC are adjacent. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/072848.png | 072848 |
011780 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how long is the sum of the lengths of $\\overline{AC}$ and $\\overline{BC}$ in $\\triangle ABC$?\nChoices:\nA. 12\nB. 6\nC. 18\nD. 24"
},
{
"from": "gpt",
"value": "Since $\\overline{AC} = 6$ and $\\overline{BC} = 6$, their sum = $12$. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/011780.png | 011780 |
065807 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, observe and report the number of games won by the Greenville team in 2011?"
},
{
"from": "gpt",
"value": "According to the data presented in the image for 2011, the Greenville baseball team’s win total was:\n$$\n\\begin{aligned}\n22 \\text{ games}\n\\end{aligned}\n$$ So the answer is 22 games\nThe answer is 22 games"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/065807.png | 065807 |
076317 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Can $h(x)$ be evaluated at $x=-2$?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "With no specific mention of exceptions at $x=-2$, it is assumed that $h(-2)$ is defined. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/076317.png | 076317 |
002259 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the expression for the area of the triangle in terms of side $b$ and $\\theta$?\nChoices:\nA. \\frac{1}{2}ac\nB. \\frac{1}{2}ab\nC. \\frac{1}{2}bc\nD. \\frac{1}{2}ba\\sin(\\theta)"
},
{
"from": "gpt",
"value": "The area of a right-angled triangle can be expressed as $\\frac{1}{2}ba\\sin(\\theta)$, where $b$ is one leg and $a$ is the leg adjacent to $\\theta$. So the answer is D\nAnswer: D"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/002259.png | 002259 |
061785 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, which expressions represent a cubic function with a double root?"
},
{
"from": "gpt",
"value": "The cubic function graphed exhibits a double root at one point. A double root in a cubic function can be represented by two identical factors. Thus, expressions that have a squared factor (indicating a repeated root) alongside another linear factor (indicating the third root) would represent this situation. So the answer is $y=a(x-p)(x+q)^{2}$ and $y=a(x-p)^{2}(x-q)$\nThe answer is $y=a(x-p)(x+q)^{2}$ and $y=a(x-p)^{2}(x-q)$"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/061785.png | 061785 |
033168 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, if point B has a y-coordinate of $b$, what is point C’s y-coordinate for $b = 1$?\nChoices:\nA. -1\nB. 0\nC. 1\nD. 2"
},
{
"from": "gpt",
"value": "From the problem's givens, and solving through, point C’s coordinates are defined as $(10b, -b)$. With $b=1$, the y-coordinate of point C therefore maps to $-1$. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/033168.png | 033168 |
025901 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which coordinate is equivalent to $\\cos (360^\\circ)$?\nChoices:\nA. $y$-coordinate of point A$\nB. $x$-coordinate of point B$\nC. $y$-coordinate of point C$\nD. $x$-coordinate of point A$\nE. $x$-coordinate of point C$"
},
{
"from": "gpt",
"value": "At $360^\\circ$, the unit circle completes a full rotation and returns to its starting point at $(1, 0)$, where the $x$-coordinate represents $\\cos (360^\\circ)$, which is 1. So the answer is D\nAnswer: D"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/025901.png | 025901 |
001155 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, find the hypotenuse length if one leg is 5 units in a right triangle.\nChoices:\nA. 5 units\nB. 10 units\nC. 7.07 units\nD. 12.07 units"
},
{
"from": "gpt",
"value": "Using Pythagoras' theorem, if one leg is 5 in a 1:1 root 2 ratio triangle, the hypotenuse would be 5*sqrt(2) or approximately 7.07 units. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/001155.png | 001155 |
087201 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: In the game of chess, the Knight can make any of the moves displayed in the diagram to the right. If a Knight is the only piece on the board, what is the greatest number of spaces from which not all 8 moves are possible?\nChoices:\nA. 8\nB. 24\nC. 38\nD. 48\nE. 56"
},
{
"from": "gpt",
"value": "Since we are looking for the greatest number of spaces from which not all 8 moves are possible, we can eliminate the greatest number, 56. Now, clearly not all 8 moves are possible from the outer squares, and there are 28 outer squares—not 32. Also, not all 8 moves are possible from the next to outer squares, and there are 20 of them—not 24. All 8 moves are possible from the remaining squares. Hence, the answer is 28 + 20 = 48. The answer is 48. Notice that 56, (32 + 24), is given as an answer-choice to catch those who don’t add carefully. So the answer is D\nAnswer: 48"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/087201.png | 087201 |
019316 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, identify the smaller surface area pair of the box dimensions?\nChoices:\nA. 25x33\nB. 20x33\nC. 25x20\nD. 33x25"
},
{
"from": "gpt",
"value": "Calculating the area of each face, dimensions 25x20 form the smallest product (500 units each). Since these faces are identical and less in area compared to the other faces, they represent the smaller surface area pairs. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/019316.png | 019316 |
030595 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how would you calculate the radius of the circle?\nChoices:\nA. Using circumference\nB. By measuring the diameter\nC. Using the area formula\nD. Calculating the hypotenuse of a triangle inside the circle"
},
{
"from": "gpt",
"value": "To find the radius from the image, one can measure the diameter shown and divide it by two, as the radius is half of the diameter. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/030595.png | 030595 |
065809 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how does the wait time in April compare to the wait time in March?"
},
{
"from": "gpt",
"value": "To compare wait times, observe the y-values for each month on the graph. The difference between these values demonstrates an increase or decrease. So the answer is By subtracting the wait time of March from the wait time of April, one can calculate the change in wait time.\nThe answer is By subtracting the wait time of March from the wait time of April, one can calculate the change in wait time."
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/065809.png | 065809 |
044150 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, to which specific age group does this blood lead trend pertain?\nChoices:\nA. Newborns\nB. Teenagers\nC. Preschoolers\nD. Adults"
},
{
"from": "gpt",
"value": "The vertical axis label on the left shows that the preschool blood lead trend is indicated by the dashed curve and the top time series (1940–1990). So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/044150.png | 044150 |
044020 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the approximate average annual increase in revenue per store from 2005 to 2012?\nChoices:\nA. $43,750\nB. $50,000\nC. $56,250\nD. $62,500"
},
{
"from": "gpt",
"value": "The total increase from 2005 to 2012 is $350,000 over 7 years. Therefore, the average annual increase is $350,000 / 7 = $50,000. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/044020.png | 044020 |
004577 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which trigonometric value is specifically used in the context of rhombus diagonal calculation?\nChoices:\nA. sin 73.8 degrees\nB. cos 73.8 degrees\nC. tan 73.8 degrees\nD. sec 73.8 degrees"
},
{
"from": "gpt",
"value": "The cosine of angle 73.8 degrees is explicitly mentioned as being used in the cosine rule to calculate the diagonal of the rhombus, as shown in the calculations d^2=200-200*cos(73.8 degrees). So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/004577.png | 004577 |
060262 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what can be inferred about the rate of water leakage over time?"
},
{
"from": "gpt",
"value": "If the line is linear and downward, it indicates a constant rate of water leakage over time. So the answer is constant rate of leakage\nThe answer is constant rate of leakage"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/060262.png | 060262 |
002633 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the measure of the angle opposite to side $a$?\nChoices:\nA. 30 degrees\nB. 45 degrees\nC. 60 degrees\nD. 90 degrees"
},
{
"from": "gpt",
"value": "The triangle includes a right angle, and the side $a$ opposite this angle must be part of the 90 degree angle. So the answer is D\nAnswer: D"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/002633.png | 002633 |
062085 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, does each output value of the function correspond to exactly one input value?"
},
{
"from": "gpt",
"value": "A function that associates each output value with exactly one input value is one-to-one. By applying the horizontal line test to the function in the image, we can verify if each horizontal line intersects the curve at most once. This would confirm that each value in the range corresponds to a unique value in the domain. So the answer is Yes or No depending on the horizontal line test\nThe answer is Yes or No depending on the horizontal line test"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/062085.png | 062085 |
033352 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what value is substituted in the definite integral to calculate the area?\nChoices:\nA. $x=0$ and $x=2$\nB. $y=0$ and $y=4$\nC. $x=-1$ and $x=1$\nD. $y=-2$ and $y=2$"
},
{
"from": "gpt",
"value": "To determine the area, the definite integral uses the integration bounds where the curves intersect and where the requisite x-values are substituted, which are $x=0$ and $x=2$. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/033352.png | 033352 |
080875 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: What is the value of g?"
},
{
"from": "gpt",
"value": "Add the measures of the supplementary angles and set the sum equal to $180^{\\circ}$. Then solve for $g$.\n$$\n\\begin{aligned}\ng+73^{\\circ} & =180^{\\circ} \\\\\ng & =180^{\\circ}-73^{\\circ} \\\\\ng & =107^{\\circ}\n\\end{aligned}\n$$\n\nSo, $g=107^{\\circ}$. So the answer is $107^{\\circ}$\nThe answer is $107^{\\circ}$"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/080875.png | 080875 |
075988 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Can the equation of the line be written as $y=-7$ for all its points?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Since the equation of a horizontal line is given by $y=k$ where $k$ is a constant, and it's stated that for all points on this line $y=-7$, therefore it's correct to write the line equation as $y=-7$. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/075988.png | 075988 |
086579 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: A real estate agent counted the number of offices per floor in the building he is selling.\nHow many floors have at least 20 offices?"
},
{
"from": "gpt",
"value": "Count all the leaves in the rows with stems 2, 3, 4, 5, 6, and 7.\nCount all the leaves in the rows with stems 2, 3, 4, 5, 6, and 7. So the answer is 10\nThe answer is 10"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/086579.png | 086579 |
032343 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how many x-intercepts does h(x) have?\nChoices:\nA. None\nB. One\nC. Two\nD. Three"
},
{
"from": "gpt",
"value": "By counting the points where h(x) crosses the x-axis, the number of x-intercepts for this function can be pinpointed. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/032343.png | 032343 |
021232 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the resulting shape from the cut portion used to create the frustum?\nChoices:\nA. Pyramid\nB. Cylinder\nC. Cuboid\nD. Conical"
},
{
"from": "gpt",
"value": "The portion removed was the top of a pyramid, thus maintaining a pyramid shape, albeit smaller. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/021232.png | 021232 |
043915 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the general trend of fossil fuel energy consumption from 1950 to 2010?\nChoices:\nA. Steady increase\nB. Fluctuating\nC. Steady decrease\nD. Rapid increase, then decrease"
},
{
"from": "gpt",
"value": "The slope of the line connecting 1950 and 2010 shows a general upward or downward trend based on its angle. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/043915.png | 043915 |
034093 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the limit of the function as x approaches 1?\nChoices:\nA. 2\nB. 3\nC. 4\nD. 5"
},
{
"from": "gpt",
"value": "We analyze the graph at the point where x equals 1. Observing the behavior of the function as x approaches 1 from both the left and right shows that the function approaches the same value, hence the limit exists. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/034093.png | 034093 |
081511 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: An entomologist can model the number of mosquitos in a forest as a function of rainfall.\n\nThe function $f(x)=5 x-x^2$, where $x$ represents rainfall (in centimeters), gives the number of mosquitos in the forest (in millions). What is another rainfall amount that relates to 2 million mosquitos?\nRound your answer to the nearest half centimeter.\n\nAbout _ centimeters of rainfall"
},
{
"from": "gpt",
"value": "The following statements are equivalent:\nThere are 2 million $\\quad x=k$ is a solution to $\\quad$\\begin{tabular}{c}\nThe graphs of $y=f(x)$ \\\\\nmosquitos when \\\\\n$x=k$.\n\\end{tabular}$\\quad$ the equation $f(x)=2 . \\quad$\\begin{tabular}{c}\nand $y=2$ intersect at \\\\\n$x=k$.\n\\end{tabular}\n\nSince we are asked to find a rainfall amount that relates to 2 million mosquitos, we need to find $k$.\n\nWe can either do that by solving $5 x-x^2=2$ or by looking for the intersection point of the graphs $y=f(x)$ and $y=2$. The second option is easier, so we will go with that!\n\nHere is the graph of $f$ along with the graph of $y=2$.\n\nThe graphs seem to intersect where $x \\approx 0.5$ and $x \\approx 4.5$.\n\nWe were told that there are 2 million mosquitos when there is approximately $0.5 \\mathrm{~cm}$ of rainfall.\n\nSo another rainfall amount that relates to 2 million mosquitos is about 4.5 centimeters of rainfall. \\n 4.5 So the answer is 4.5\nThe answer is 4.5"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/081511.png | 081511 |
025757 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, at which times t=k does the equation f(t)=g(t) hold true?\nChoices:\nA. Only at noon\nB. Multiple specific times\nC. Continually over a period\nD. Only in the morning"
},
{
"from": "gpt",
"value": "Graphical intersections indicate that the equation f(t)=g(t) holds at multiple specific moments, denoted as times 't=k', where the graphs of both airplane altitudes meet. It would not hold 'Only at noon', 'Continually over a period', or 'Only in the morning' unless those were the only times shown with intersections, which is not suggested. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/025757.png | 025757 |
069646 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how many flowers in the diagram are neither red nor thorny?"
},
{
"from": "gpt",
"value": "The image includes a Venn diagram representing different categories of flowers. The section that denotes flowers which are both non-red and thornless contains a specific number. So the answer is 10\nThe answer is 10"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/069646.png | 069646 |
032483 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which function appears to be a quadratic function?\nChoices:\nA. f(x)\nB. g(x)\nC. h(x)"
},
{
"from": "gpt",
"value": "Observe the curvature of each graph to identify the quadratic function, characterized by its parabolic shape. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/032483.png | 032483 |
049411 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, at what time does the radius equal the initial rate of increase multiplied by 4?\nChoices:\nA. 1 s\nB. 2 s\nC. 3 s\nD. 4 s"
},
{
"from": "gpt",
"value": "Set $r(t) = 7t$ equal to $7*4 = 28$ and solve for t. So the answer is D\nAnswer: D"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/049411.png | 049411 |
057475 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, verify if the boundary of surface $S$ forms a closed loop."
},
{
"from": "gpt",
"value": "The boundary $C$ of the hemisphere surface $S$ is a circle, lying in the plane $y=0$ and centered at the origin. Being a circle, it is a closed loop. So the answer is closed loop\nThe answer is closed loop"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/057475.png | 057475 |
070980 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: If the values for length and width are swapped, does the area of the rectangle remain 28 square centimeters?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Swapping the values of length and width (7 cm and 4 cm) does not affect the calculation: 4 x 7 = 28 cm^2. Thus, the area remains 28 square centimeters. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/070980.png | 070980 |
007602 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, if the tent door is h centimeters tall, calculate the total height of the tent structure.\nChoices:\nA. h+9\nB. h+11\nC. h+12\nD. h+13"
},
{
"from": "gpt",
"value": "The door is h cm tall and above that, the tent extends further up by 9 cm as shown. Thus, the entire tent’s height would be the sum of the height of the door plus 9 cm. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/007602.png | 007602 |
021159 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, identify the geometric shapes that make up the solid.\nChoices:\nA. Cubes and cylinders\nB. Two pyramids\nC. Pyramids and prisms\nD. Cones and pyramids"
},
{
"from": "gpt",
"value": "The solid in the image consists of two pyramids, one nested on top of the other with congruent square bases. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/021159.png | 021159 |
070385 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Is the division portrayal via area model right if the widths are 1 and 9 with heights also 1 and 9, and they display correct area products as 1, 9, 9, 81 but a bottom total different than 100?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Even though the areas of multiplication are directly correct (1, 9, 9, 81), the total shown in the bottom which differs from their sum, 100, points to an incorrect representation in terms of total area. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/070385.png | 070385 |
005106 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what mathematical operation is applied after finding the cosine of the angle?\nChoices:\nA. Addition to the hypotenuse\nB. Subtraction from the hypotenuse\nC. Multiplication with the hypotenuse\nD. Division by the hypotenuse"
},
{
"from": "gpt",
"value": "After obtaining the cosine value of the angle, it is multiplied with the hypotenuse to solve for the y-coordinate. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/005106.png | 005106 |
084672 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: What is the area of this square?"
},
{
"from": "gpt",
"value": "Find the side length of the square.\nside: $3 \\mathrm{~m}$\n\nUse this number in the formula.\n$$\n\\begin{aligned}\n\\text { area } & =\\text { side } \\cdot \\text { side } \\\\\n& =3 \\cdot 3 \\\\\n& =9\n\\end{aligned}\n$$\n\nNow find the units. The lengths are measured in meters, so the area is measured in square meters.\n\nThe area is 9 square meters. So the answer is 9\nThe answer is 9"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/084672.png | 084672 |
058222 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, is this 3D figure classified according to the shape of its base?"
},
{
"from": "gpt",
"value": "This is a type of prism and prisms are classified according to the shapes of their bases. So the answer is Yes\nThe answer is Yes"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/058222.png | 058222 |
051163 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, ascertain whether angles x and y are complementary."
},
{
"from": "gpt",
"value": "Referring to details from the image: given the rule that an angle at the centre (AOC) is twice an angle at the circumference from the same chord, AOC measures 2y. In the isosceles triangle ACO, the base angles, OCA, and OAC are equal and noted as x. The equation formed by calculating the interior angles of the triangle results in 2y + 2x = 180, leading to the finding that x and y, when simplified, add up to 90. So the answer is x+y=90\nThe answer is x+y=90"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/051163.png | 051163 |
034718 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what mathematical substitution is avoided by reversing the order of integration?\nChoices:\nA. Polynomial substitution\nB. Quadratic substitution\nC. Trig substitution\nD. Logarithmic substitution"
},
{
"from": "gpt",
"value": "The analysis hints at avoiding a trigonometric substitution by reversing the order of integration which simplifies the computation required. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/034718.png | 034718 |
056780 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, find the ratio of the longer leg to the shorter leg in the depicted triangle."
},
{
"from": "gpt",
"value": "In the given triangle, which follows the properties of a 30-60-90 triangle, the ratio of the longer leg ($t$) to the shorter leg is determined by the relationship between their lengths. For every 30-60-90 triangle, this ratio is $\\sqrt{3}:1$. Considering the shorter leg as 3 cm, the longer leg therefore would be $3\\sqrt{3}$ cm, demonstrating the ratio of $\\sqrt{3}:1$ between the longer and shorter legs. So the answer is $\\sqrt{3}:1\nThe answer is $\\sqrt{3}:1"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/056780.png | 056780 |
022726 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the formula to compute the volume of the cylinder in the grain silo?\nChoices:\nA. pi r^2 * 12\nB. pi r^2 * 6\nC. pi r^2 * 18\nD. pi r * 12"
},
{
"from": "gpt",
"value": "The cylinder's volume formula is being calculated as π r^2 multiplied by its height, which is 12 meters. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/022726.png | 022726 |
031129 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the tangent of the marked angle?\nChoices:\nA. 1\nB. 0\nC. \\(\\sqrt{3}/3\\)\nD. \\(\\sqrt{3}\\)"
},
{
"from": "gpt",
"value": "Tangent is the ratio of the sine to the cosine of a given angle. Information from the diagram will supply the sine and cosine values necessary for this calculation. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/031129.png | 031129 |
011891 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the radius of the circumscribed circle around the square with a side length of 5 units?\nChoices:\nA. 2.5 units\nB. 5 units\nC. 7.5 units\nD. \\(2.5\\sqrt{2}\\) units"
},
{
"from": "gpt",
"value": "The radius of the circumscribed circle around a square is \\(\\frac{diagonal}{2}\\). For a side of 5 units, the diagonal is \\(5\\sqrt{2}\\) units, making the radius \\(2.5\\sqrt{2}\\) units. So the answer is D\nAnswer: D"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/011891.png | 011891 |
030346 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, does the graph of y=4^x contain any sharp turns or vertices?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "The curve of y=4^x is smooth, showing continuous growth without any breaks, sharp turns, or vertices. The nature of exponential functions assures smooth and continuous curvature without angular points. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/030346.png | 030346 |
075548 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Is the function not defined at x = 7.5?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "The domain ends at x = 7, therefore at x = 7.5 the function is not defined. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/075548.png | 075548 |
044039 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, by how much did the revenue of the least earning store increase from 2005 to 2006?\nChoices:\nA. $20,000\nB. $50,000\nC. $80,000\nD. $100,000"
},
{
"from": "gpt",
"value": "The least earning store had a revenue increase from $180,000 in 2005 to $200,000 in 2006, amounting to a $20,000 increase. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/044039.png | 044039 |
006527 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the remaining angle $a$ if an adjacent angle on a straight line measures 93 degrees?\nChoices:\nA. 87 degrees\nB. 93 degrees\nC. 180 degrees\nD. None of these"
},
{
"from": "gpt",
"value": "The remaining angle $a$ is supplementary to the given 93 degree angle as they reside on the same straight line. Given their relationship,\n\n$a = 180^\\circ - 93^\\circ = 87^\\circ$. This follows the idea of angles on a straight line summing to 180 degrees, which is illustrated in the image. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/006527.png | 006527 |
025911 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which coordinate equals $\\cos (180^\\circ)$?\nChoices:\nA. $x$-coordinate of point B$\nB. $y$-coordinate of point B$\nC. $x$-coordinate of point A$\nD. $y$-coordinate of point C$\nE. $x$-coordinate of point C$"
},
{
"from": "gpt",
"value": "At $180^\\circ$ on the unit circle, which is the opposite side of the starting point $(1, 0)$, the $x$-coordinate, -1, fully describes $\\cos (180^\\circ)$. So the answer is E\nAnswer: E"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/025911.png | 025911 |
054761 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the length of side AD?"
},
{
"from": "gpt",
"value": "Applying the Pythagorean Theorem to the triangle ADB, since triangle ABC has been verified to be a right triangle with AC as hypotenuse, then triangle ADB will also be right angled at angle B. Thus, applying the theorem: AD^2 = AB^2 + BD^2. Using the relationship that BD = BC + CD, and the substitution of numerical values, results in AD^2 = 8^2 + 15^2, hence AD is found by calculating the square root of 289, which yields 17. So the answer is 17\nThe answer is 17"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/054761.png | 054761 |
055595 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, if the lengths of the legs of the triangle are 5 and 12, calculate the length of the side opposite the right angle."
},
{
"from": "gpt",
"value": "Applying the Pythagorean theorem to calculate the side opposite the right angle, given as $x$: \n$$\n5^2 + 12^2 = x^2 \\\n25 + 144 = x^2 \\\n169 = x^2 \\\nx = \\sqrt{169} \\\nx = 13\n$$ So the answer is 13\nThe answer is 13"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/055595.png | 055595 |
026983 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, does the graph of the function f appear to be unchanged when mirrored across the vertical axis?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "If the graph of function f appears to remain the same when mirrored across the y-axis, the function is even. Check the graph to validate this characteristic. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/026983.png | 026983 |
074742 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: For the point (-2, 3), does it lie inside the shaded region under the constraints of the given inequalities?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "With $x<1$ and $y \\leq 3$ being the inequalities for the shaded region, the point (-2, 3) satisfies these as $-2 < 1$ and $3 \\leq 3$ are both correct. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/074742.png | 074742 |
087011 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: What proportion of the diagram is shaded blue. Express your answer in decimal form."
},
{
"from": "gpt",
"value": "Divide the number of blue squares by the total number of squares.\n$$\n=\\frac{5}{10}\n$$\n\nWhen converting a fraction to a decimal, the number of zeros in the denominator is equal to the number of decimal places.\n\nThere is 1 zero in the denominator, hence there is 1 decimal place. E.g. $\\frac{4}{10}=0.4$\n$$\n=0.5\n$$ So the answer is 0.5\nThe answer is 0.5"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/087011.png | 087011 |
038475 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the increment step of the y-axis in the graph?\nChoices:\nA. 5 units\nB. 10 units\nC. 15 units\nD. 20 units"
},
{
"from": "gpt",
"value": "Checking the scale marked on the y-axis of the graph, the scale increases by increments of 10 units. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/038475.png | 038475 |
047756 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what happens to the height of the water as it moves horizontally from the spout?\nChoices:\nA. Increases\nB. Decreases\nC. Remains the same\nD. Cannot be determined"
},
{
"from": "gpt",
"value": "The equation of the motion of the water is a quadratic equation with a negative coefficient of $x^2$. This indicates that as $x$ (the horizontal distance) increases, the height $h(x)$ decreases from its initial point from the spout. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/047756.png | 047756 |
062359 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, determine the transformation applied to the parent function $y = 3^x$ to obtain the function $y = 2 - 3^x$."
},
{
"from": "gpt",
"value": "Compared to the parent function $y = 3^x$, the function $y = 2 - 3^x$ can be viewed as $y = -3^x$ shifted upwards by 2 units. This reflects the graph across the x-axis and then raises it. So the answer is Reflection across the x-axis and upward shift of 2 units\nThe answer is Reflection across the x-axis and upward shift of 2 units"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/062359.png | 062359 |
064934 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the monthly construction rate of new schools?"
},
{
"from": "gpt",
"value": "The image provides information on the number of schools built per month, which is 5 from the analysis. So the answer is 5 schools per month\nThe answer is 5 schools per month"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/064934.png | 064934 |
044204 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which five-year period ends with a violent crime rate close to the base line?\nChoices:\nA. 1953-1958\nB. 1958-1963\nC. 1963-1968\nD. 1968-1973"
},
{
"from": "gpt",
"value": "At the end of this period, crime rates are shown to return near to initial observed values, suggesting a circular trend. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/044204.png | 044204 |
074618 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Can the distance from point A to B be determined at the exact time Ken leaves point A?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "The analysis states that the vertical axis denotes the distance from point B and Ken's departure from point A at 9 am allows us to determine the distance at that time, which is 120 km. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/074618.png | 074618 |
019158 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what numerical method is utilized to find the surface area of the shape?\nChoices:\nA. Differentiation\nB. Integration\nC. Algebraic manipulation\nD. Geometric approximation"
},
{
"from": "gpt",
"value": "The surface area of the elliptic paraboloid's portion above $z=1$ is calculated using integration, as set up in the given analysis with specifics on converting to polar coordinates for the actual integration process. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/019158.png | 019158 |
067046 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how many terms are plotted in the arithmetic sequence?"
},
{
"from": "gpt",
"value": "The total number of terms in the sequence that are plotted can be counted directly from the graph, which corresponds to the number of distinct points. So the answer is The count of distinct points plotted\nThe answer is The count of distinct points plotted"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/067046.png | 067046 |
062771 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how many watermelons can Boris buy if he buys 6 pineapples to fulfill his two conditions?"
},
{
"from": "gpt",
"value": "In the image, we can therefore focus on the line labeled $P = 6$. This line shows the combinations where Boris buys 6 pineapples. By examining the points on this line, we need to find which points lie within the shaded area representing Boris's constraints. The intersections of $P = 6$ with the shaded area would determine the range of watermelons Boris can buy while meeting both the number of fruits and budget constraints. So the answer is Boris can buy between 10 and 12 watermelons.\nThe answer is Boris can buy between 10 and 12 watermelons."
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/062771.png | 062771 |
074454 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Is the volume of this object equal to 4 cubic units?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Based on the structure, there is 1 row with 4 cubes. Each cube represents 1 cubic unit, resulting in a total of 4 cubic units. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/074454.png | 074454 |
057684 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the radius of the cylindrical top piece?"
},
{
"from": "gpt",
"value": "In the image setup, the cylinder is attached to a rectangular prism. Identifying the radius of the cylinder is key as it is used to compute both surface area and volume of the cylinder. The radius directly affects the outcome of formulas like the area of a circle ($\\pi r^2$) or the volume of a cylinder ($\\pi r^2 h$). So the answer is The radius of the cylindrical top piece is 5 mm\nThe answer is The radius of the cylindrical top piece is 5 mm"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/057684.png | 057684 |
077639 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Does the function k(m) = -m^2 - 10m + 21 yield k(3) = 0?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "By substituting m=3 into k(m)=-m^2-10m+21, we calculate -3^2-10(3)+21=-9-30+21=-18, which is not 0. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/077639.png | 077639 |
085380 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Ken starts travelling at 9 am from point A and moves towards point B in a straight line.The distance between Ken and point B at various times in his journey is shown on the graph below.What is the total distance travelled by Ken from 9 am to 4 pm?"
},
{
"from": "gpt",
"value": "Add up all the distances travelled in each time interval.Notice that he travels away from point B between 10 am and 12 pm. This distance is also a part of the total distance travelled.= 50+30+60+40 km.Evaluate the sum. \n 180 km So the answer is 180 km\nThe answer is 180 km"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/085380.png | 085380 |
084810 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Find the area of $\\triangle T U V$."
},
{
"from": "gpt",
"value": "You are given two angle measures ( $m \\angle T$ and $m \\angle V)$ and the length of one of their opposite sides $(v)$. To find the area of $\\triangle T U V$, you must know two side lengths and the measure of their included angle.\n\nSo, find $m \\angle U$. Then use the Law of Sines to find $t$, the length of the side opposite $\\angle T$.\nFind $\\boldsymbol{m} \\angle \\boldsymbol{U}$.\nSolve for $m \\angle U$ using the fact that the angle measures of a triangle sum to $180^{\\circ}$.\n$$\n\\begin{aligned}\nm \\angle T+m \\angle V+m \\angle U & =180^{\\circ} \\\\\n122^{\\circ}+26^{\\circ}+m \\angle U & =180^{\\circ} \\\\\n148^{\\circ}+m \\angle U & =180^{\\circ} \\\\\nm \\angle U & =32^{\\circ}\n\\end{aligned}\n$$\n\nSo, $m \\angle U=32^{\\circ}$.\nFind $\\boldsymbol{t}$.\nSince you know the measure of $\\angle V$, the length $v$ of its opposite side, and the measure of $\\angle T$, use the Law of Sines to find the length $t$ of the side opposite $\\angle T$.\n$$\n\\begin{aligned}\n\\frac{V}{\\sin (V)} & =\\frac{t}{\\sin (T)} \\\\\n\\frac{48}{\\sin 26^{\\circ}} & =\\frac{t}{\\sin 122^{\\circ}} \\\\\n\\frac{48}{0.4383 \\ldots} & =\\frac{t}{0.8480 \\ldots} \\\\\n109.4962 \\ldots & =\\frac{t}{0.8480 \\ldots} \\\\\n92.8580 \\ldots & =t\n\\end{aligned}\n$$\n\nSo, $t=92.8580 \\ldots \\mathrm{m}$.\nFind the area.\nNow that you know two side lengths of the triangle and the measure of the included angle $(t$, $v$, and $m \\angle U$ ), plug the values into the area formula.\n$$\n\\text { Area of } \\begin{aligned}\n\\triangle T U V & =\\frac{1}{2} t v \\sin (U) \\\\\n& =\\frac{1}{2} \\cdot 92.8580 \\ldots \\cdot 48 \\sin 32^{\\circ} \\\\\n& =\\frac{1}{2} \\cdot 92.8580 \\ldots \\cdot 48 \\cdot 0.5299 \\ldots \\\\\n& =1,180.9750 \\ldots\n\\end{aligned}\n$$\n\nTo the nearest tenth, the area of $\\triangle T U V$ is $1,181.0$ square meters. So the answer is 1,181.0\nThe answer is 1,181.0"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/084810.png | 084810 |
073438 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: The area would remain 40 square inches if we change the height to 6 inches?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "If we change the height to 6 inches, but keep the bases as 10 and 6 inches, the area would not remain at 40 square inches. The larger the height, the larger the area is. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/073438.png | 073438 |
018864 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the lower limit of the x integration?\nChoices:\nA. 0\nB. -1\nC. 1\nD. 2x"
},
{
"from": "gpt",
"value": "The integral for calculating the solid's volume involves setting limits for x and y. According to the image description, the x-integration starts at x=0, which is the natural boundary set by the $x=0$ plane also forming part of the enclosed 3D region. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/018864.png | 018864 |
032076 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, identify the formula for the slope of the line.\nChoices:\nA. m = (y2 - y1) / (x2 - x1)\nB. m = x2 - x1\nC. m = y2 + y1\nD. m = (x2 + x1) / (y2 - y1)"
},
{
"from": "gpt",
"value": "Using two distinct points on the line from the image and applying the slope formula, the correct expression is m = (y2 - y1) / (x2 - x1). So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/032076.png | 032076 |
081834 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Find the value of $\\sin \\theta$. Rationalise the denominator if necessary."
},
{
"from": "gpt",
"value": "In a right-angled triangle, $\\sin \\theta$ is a ratio given by\n\n$\\sin \\theta=\\frac{\\text { opposite }}{\\text { hypotenuse }}$.\n\nWhat is the directed length of the side opposite to $\\theta$ ?\n\nWhat is the length of the hypotenuse?\n\nThe directed length of the opposite side is -6 .\n\nThe length of the hypotenuse is $2 \\sqrt{13}$.\n\n$\\sin \\theta=\\frac{-6}{2 \\sqrt{13}}$\n\nCancel out any common factors of the numerator and denominator.\n\n$\\sin \\theta=\\frac{-3}{\\sqrt{13}}$\n\nThe denominator is irrational, so we need to 'rationalise the denominator' by multiplying both the numerator and denominator by the same value so that the denominator becomes an integer.\n\n$\\sin \\theta=\\frac{-3}{\\sqrt{13}} \\times \\frac{\\sqrt{13}}{\\sqrt{13}}$\n\nSimplify.\n\n$\\sin \\theta=\\frac{-3 \\sqrt{13}}{13}$ So the answer is $\\sin \\theta=\\frac{-3 \\sqrt{13}}{13}$\nThe answer is $\\sin \\theta=\\frac{-3 \\sqrt{13}}{13}$"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/081834.png | 081834 |
015272 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, are the two regions, one shaded and one unshaded, together form a square?\nChoices:\nA. yes\nB. no"
},
{
"from": "gpt",
"value": "The image shows a square that has been divided into two regions: a shaded region and an unshaded region. Therefore, it can be concluded that together, these two regions make up the entire square So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/015272.png | 015272 |
030973 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, describe the end behavior of the graph as $x$ approaches infinity.\nChoices:\nA. Approaches zero\nB. Approaches 5\nC. Goes to infinity\nD. Approaches negative infinity"
},
{
"from": "gpt",
"value": "Observe and describe how the function behaves on the graph as $x$ values become large and positive. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/030973.png | 030973 |
066526 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how many jumps were longer than 160 cm?"
},
{
"from": "gpt",
"value": "Look at the table in the image and sum the frequencies of class intervals that represent jumps longer than 160 cm. So the answer is sum of frequencies for jumps over 160 cm\nThe answer is sum of frequencies for jumps over 160 cm"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/066526.png | 066526 |
056774 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how do you calculate the hypotenuse when the shorter leg's length is known?"
},
{
"from": "gpt",
"value": "The length of the hypotenuse in a right triangle can be found using the relationship that it is double the length of the shorter leg. Formulate an equation and put in the known value of the shorter leg to find the hypotenuse. So the answer is The length of the hypotenuse is 16 meters.\nThe answer is The length of the hypotenuse is 16 meters."
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/056774.png | 056774 |
084936 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Let $E$ be the region bounded below by the cone $z=\\sqrt{x^2+y^2}$ and above by the sphere $z=x^2+y^2+z^2 \\quad$ (Figure 15.5.10). Set up a triple integral in spherical coordinates and find the volume of the region using the following orders of integration:\na. $d \\rho d \\phi d \\theta$\n"
},
{
"from": "gpt",
"value": "a. Use the conversion formulas to write the equations of the sphere and cone in spherical coordinates.\n\nFor the sphere:\n$$\n\\begin{array}{r}\nx^2+y^2+z^2=z \\\\\n\\rho^2=\\rho \\cos \\varphi \\\\\n\\rho=\\cos \\varphi .\n\\end{array}\n$$\n\nFor the cone:\n$$\n\\begin{array}{r}\nz=\\sqrt{x^2+y^2} \\\\\n\\rho \\cos \\varphi=\\sqrt{\\rho^2 \\sin ^2 \\varphi \\cos ^2 \\phi} \\\\\n\\rho \\cos \\varphi=\\sqrt{\\rho^2 \\sin ^2 \\varphi\\left(\\cos ^2 \\phi+\\sin ^2 \\phi\\right)} \\\\\n\\rho \\cos \\varphi=\\rho \\sin \\varphi \\\\\n\\cos \\varphi=\\sin \\varphi \\\\\n\\varphi=\\pi / 4 .\n\\end{array}\n$$\n\nHence the integral for the volume of the solid region $E$ becomes\n$$\nV(E)=\\int_{\\theta=0}^{\\theta=2 \\pi} \\int_{\\varphi=0}^{\\varphi=\\pi / 4} \\int_{\\rho=0}^{\\rho=\\cos \\varphi} \\rho^2 \\sin \\varphi d \\rho d \\varphi d \\theta .\n$$ So the answer is $V(E)=\\int_{\\theta=0}^{\\theta=2 \\pi} \\int_{\\varphi=0}^{\\varphi=\\pi / 4} \\int_{\\rho=0}^{\\rho=\\cos \\varphi} \\rho^2 \\sin \\varphi d \\rho d \\varphi d \\theta$\nThe answer is $V(E)=\\int_{\\theta=0}^{\\theta=2 \\pi} \\int_{\\varphi=0}^{\\varphi=\\pi / 4} \\int_{\\rho=0}^{\\rho=\\cos \\varphi} \\rho^2 \\sin \\varphi d \\rho d \\varphi d \\theta$"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/084936.png | 084936 |
024588 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which slope values correspond to the lines marking the boundaries of the shaded region?\nChoices:\nA. 1, -1\nB. 1, 1\nC. -1, -1\nD. 0, undefined"
},
{
"from": "gpt",
"value": "Look at the directional slope indicated by the lines forming boundaries. Analyze if these slopes show a positive, negative, or neutral (horizontal/vertical) inclination as required by the equations $y=x$ and $y=-x$. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/024588.png | 024588 |
033745 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, does the limit exist as $x$ approaches 3 in the function $f(x)$?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "By observing the graph, we can see that as we approach $x=3$ from both sides the graph is approaching the same value which means the function $f(x)$ is continuous at $x=3$ and hence the limit does exist. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/033745.png | 033745 |
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