instruction_seed stringlengths 18 2k | source stringclasses 1
value | r1_distill_70b_response sequencelengths 3 9 | __original_row_idx int64 1 6k | r1_distill_70b_extracted_answer sequencelengths 3 9 | _majority_responses sequencelengths 1 9 | verified_r1_distill_70b_response stringlengths 365 72.1k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|---|
The areas of two similar regular hexagons are in the ratio $49:81$. What is the ratio of their perimeters? Express your answer in the form $a:b$. | tiger_math | [
"<think>\nOkay, so I'm trying to solve this problem where the areas of two similar regular hexagons are in the ratio 49:81, and I need to find the ratio of their perimeters. Hmm, I remember that when dealing with similar figures, especially regular polygons, the ratios of their corresponding linear measures (like s... | 8 | [
"7:9",
"7:9",
"7:9"
] | [
"<think>\nOkay, so I'm trying to solve this problem where the areas of two similar regular hexagons are in the ratio 49:81, and I need to find the ratio of their perimeters. Hmm, I remember that when dealing with similar figures, especially regular polygons, the ratios of their corresponding linear measures (like s... | <think>
Okay, so I'm trying to solve this problem where the areas of two similar regular hexagons are in the ratio 49:81, and I need to find the ratio of their perimeters. Hmm, I remember that when dealing with similar figures, especially regular polygons, the ratios of their corresponding linear measures (like side le... | [
{
"from": "human",
"value": "The areas of two similar regular hexagons are in the ratio $49:81$. What is the ratio of their perimeters? Express your answer in the form $a:b$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I'm trying to solve this problem where the areas of two similar regular ... |
The areas of two similar regular hexagons are in the ratio $49:81$. What is the ratio of their perimeters? Express your answer in the form $a:b$. | tiger_math | [
"<think>\nOkay, so I'm trying to solve this problem where the areas of two similar regular hexagons are in the ratio 49:81, and I need to find the ratio of their perimeters. Hmm, I remember that when dealing with similar figures, especially regular polygons, the ratios of their corresponding linear measures (like s... | 8 | [
"7:9",
"7:9",
"7:9"
] | [
"<think>\nOkay, so I'm trying to solve this problem where the areas of two similar regular hexagons are in the ratio 49:81, and I need to find the ratio of their perimeters. Hmm, I remember that when dealing with similar figures, especially regular polygons, the ratios of their corresponding linear measures (like s... | <think>
Alright, so I've got this problem here about two similar regular hexagons. The areas are in the ratio 49:81, and I need to find the ratio of their perimeters, expressing it as a:b. Hmm, okay, so similar figures, hexagons in this case. Hmm.
First off, I remember that when two figures are similar, their correspo... | [
{
"from": "human",
"value": "The areas of two similar regular hexagons are in the ratio $49:81$. What is the ratio of their perimeters? Express your answer in the form $a:b$."
},
{
"from": "gpt",
"value": "<think>\nAlright, so I've got this problem here about two similar regular hexagons. The ar... |
The areas of two similar regular hexagons are in the ratio $49:81$. What is the ratio of their perimeters? Express your answer in the form $a:b$. | tiger_math | [
"<think>\nOkay, so I'm trying to solve this problem where the areas of two similar regular hexagons are in the ratio 49:81, and I need to find the ratio of their perimeters. Hmm, I remember that when dealing with similar figures, especially regular polygons, the ratios of their corresponding linear measures (like s... | 8 | [
"7:9",
"7:9",
"7:9"
] | [
"<think>\nOkay, so I'm trying to solve this problem where the areas of two similar regular hexagons are in the ratio 49:81, and I need to find the ratio of their perimeters. Hmm, I remember that when dealing with similar figures, especially regular polygons, the ratios of their corresponding linear measures (like s... | <think>
Alright, so I've got this problem about similar regular hexagons, right? The areas are in a ratio of 49 to 81, and I need to find the ratio of their perimeters. Hmm, okay. Let me think about how to approach this.
First off, I remember that when dealing with similar shapes, especially polygons, their correspond... | [
{
"from": "human",
"value": "The areas of two similar regular hexagons are in the ratio $49:81$. What is the ratio of their perimeters? Express your answer in the form $a:b$."
},
{
"from": "gpt",
"value": "<think>\nAlright, so I've got this problem about similar regular hexagons, right? The area... |
"Convert the point $(\\rho,\\theta,\\phi) = \\left( 2, \\frac{2 \\pi}{3}, \\frac{\\pi}{4} \\right)$ (...TRUNCATED) | tiger_math | ["<think>\nOkay, so I need to convert a point from spherical coordinates to rectangular coordinates.(...TRUNCATED) | 1 | ["( -\\frac{\\sqrt{2}}{2}, \\frac{\\sqrt{6}}{2}, \\sqrt{2} )","( -\\frac{\\sqrt{2}}{2}, \\frac{\\sqr(...TRUNCATED) | ["<think>\nOkay, so I need to convert a point from spherical coordinates to rectangular coordinates.(...TRUNCATED) | "<think>\nOkay, so I need to convert a point from spherical coordinates to rectangular coordinates. (...TRUNCATED) | [{"from":"human","value":"Convert the point $(\\rho,\\theta,\\phi) = \\left( 2, \\frac{2 \\pi}{3}, \(...TRUNCATED) |
"Convert the point $(\\rho,\\theta,\\phi) = \\left( 2, \\frac{2 \\pi}{3}, \\frac{\\pi}{4} \\right)$ (...TRUNCATED) | tiger_math | ["<think>\nOkay, so I need to convert a point from spherical coordinates to rectangular coordinates.(...TRUNCATED) | 1 | ["( -\\frac{\\sqrt{2}}{2}, \\frac{\\sqrt{6}}{2}, \\sqrt{2} )","( -\\frac{\\sqrt{2}}{2}, \\frac{\\sqr(...TRUNCATED) | ["<think>\nOkay, so I need to convert a point from spherical coordinates to rectangular coordinates.(...TRUNCATED) | "<think>\nAlright, so I have this problem here where I need to convert a point from spherical coordi(...TRUNCATED) | [{"from":"human","value":"Convert the point $(\\rho,\\theta,\\phi) = \\left( 2, \\frac{2 \\pi}{3}, \(...TRUNCATED) |
"Convert the point $(\\rho,\\theta,\\phi) = \\left( 2, \\frac{2 \\pi}{3}, \\frac{\\pi}{4} \\right)$ (...TRUNCATED) | tiger_math | ["<think>\nOkay, so I need to convert a point from spherical coordinates to rectangular coordinates.(...TRUNCATED) | 1 | ["( -\\frac{\\sqrt{2}}{2}, \\frac{\\sqrt{6}}{2}, \\sqrt{2} )","( -\\frac{\\sqrt{2}}{2}, \\frac{\\sqr(...TRUNCATED) | ["<think>\nOkay, so I need to convert a point from spherical coordinates to rectangular coordinates.(...TRUNCATED) | "<think>\nOkay, so I have this point in spherical coordinates, which is (ρ, θ, φ) = (2, 2π/3, π(...TRUNCATED) | [{"from":"human","value":"Convert the point $(\\rho,\\theta,\\phi) = \\left( 2, \\frac{2 \\pi}{3}, \(...TRUNCATED) |
"Below is a portion of the graph of a quadratic function, $y=q(x)=ax^2+bx+c$:\n\n[asy]\nimport graph(...TRUNCATED) | tiger_math | ["<think>\nOkay, so I have this quadratic function y = q(x) = ax² + bx + c, and there's a graph sho(...TRUNCATED) | 12 | [
"-5",
"-5",
"-5"
] | ["<think>\nOkay, so I have this quadratic function y = q(x) = ax² + bx + c, and there's a graph sho(...TRUNCATED) | "<think>\nOkay, so I have this quadratic function y = q(x) = ax² + bx + c, and there's a graph show(...TRUNCATED) | [{"from":"human","value":"Below is a portion of the graph of a quadratic function, $y=q(x)=ax^2+bx+c(...TRUNCATED) |
"Below is a portion of the graph of a quadratic function, $y=q(x)=ax^2+bx+c$:\n\n[asy]\nimport graph(...TRUNCATED) | tiger_math | ["<think>\nOkay, so I have this quadratic function y = q(x) = ax² + bx + c, and there's a graph sho(...TRUNCATED) | 12 | [
"-5",
"-5",
"-5"
] | ["<think>\nOkay, so I have this quadratic function y = q(x) = ax² + bx + c, and there's a graph sho(...TRUNCATED) | "<think>\nOkay, so I have this quadratic function q(x) = ax² + bx + c, and I know that the graph pa(...TRUNCATED) | [{"from":"human","value":"Below is a portion of the graph of a quadratic function, $y=q(x)=ax^2+bx+c(...TRUNCATED) |
"Below is a portion of the graph of a quadratic function, $y=q(x)=ax^2+bx+c$:\n\n[asy]\nimport graph(...TRUNCATED) | tiger_math | ["<think>\nOkay, so I have this quadratic function y = q(x) = ax² + bx + c, and there's a graph sho(...TRUNCATED) | 12 | [
"-5",
"-5",
"-5"
] | ["<think>\nOkay, so I have this quadratic function y = q(x) = ax² + bx + c, and there's a graph sho(...TRUNCATED) | "<think>\nAlright, so I need to figure out the value of q(16) for the quadratic function q(x) = ax²(...TRUNCATED) | [{"from":"human","value":"Below is a portion of the graph of a quadratic function, $y=q(x)=ax^2+bx+c(...TRUNCATED) |
If $y = \displaystyle\frac{1}{3x+1}$, what is the value of $x$ when $y = 2$? | tiger_math | ["<think>\nTo solve for \\( x \\) when \\( y = 2 \\) in the equation \\( y = \\frac{1}{3x + 1} \\), (...TRUNCATED) | 25 | [
"-\\frac{1}{6}",
"-\\frac{1}{6}",
"-\\frac{1}{6}"
] | ["<think>\nTo solve for \\( x \\) when \\( y = 2 \\) in the equation \\( y = \\frac{1}{3x + 1} \\), (...TRUNCATED) | "<think>\nTo solve for \\( x \\) when \\( y = 2 \\) in the equation \\( y = \\frac{1}{3x + 1} \\), I(...TRUNCATED) | [{"from":"human","value":"If $y = \\displaystyle\\frac{1}{3x+1}$, what is the value of $x$ when $y =(...TRUNCATED) |
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