conversation_id stringlengths 13 17 | prompt stringlengths 0 2.28k | response stringlengths 648 79.9k | messages listlengths 2 2 | metadata dict | type stringclasses 4
values | meta_answer stringlengths 0 139 | oumi_answer stringlengths 0 194 | is_match bool 1
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metamathqa_20012 | Determine the interval of all x values for which both 2x and 3x are within the range of (1,2). | <think>
Okay, so I have this problem: Determine the interval of all x values for which both 2x and 3x are within the range of (1,2). Hmm, let me think. Alright, first I need to understand what exactly the question is asking. It says that both 2x and 3x have to be between 1 and 2. So, I need to find all x such that when... | [
{
"content": "Determine the interval of all x values for which both 2x and 3x are within the range of (1,2).",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem: Determine the interval of all x values for which both 2x and 3x are within the range of (1,2). Hmm, let me think. Alri... | {
"is_complete": true
} | MATH_Rephrased | (\frac{1}{2},\frac{2}{3}) | \left( \frac{1}{2}, \frac{2}{3} \right) | false |
metamathqa_20032 | What is the sum of the greatest common factor of 3 and X and the least common multiple of 3 and 6? The answer is 9. What is the value of unknown variable X? | <think>
Okay, let's try to solve this problem. The question says:
"What is the sum of the greatest common factor of 3 and X and the least common multiple of 3 and 6? The answer is 9. What is the value of unknown variable X?"
Hmm, let's break this down step by step. First, I need to recall what GCF (Greatest Common Fa... | [
{
"content": "What is the sum of the greatest common factor of 3 and X and the least common multiple of 3 and 6? The answer is 9. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "<think>\nOkay, let's try to solve this problem. The question says:\n\n\"What is the sum of the ... | {
"is_complete": true
} | MATH_SV | 6 | 9 | false |
metamathqa_20040 | Let $f(x)$ be a polynomial of degree 2006 with real coefficients, and let its roots be $r_1,$ $r_2,$ $\dots,$ $r_{2006}.$ There are exactly 1006 distinct values among
\[|r_1|, |r_2|, \dots, |r_{2006}|.\]What is the minimum number of real roots that $f(x)$ can have? | <think>
Hmm, let's see. The problem is about finding the minimum number of real roots a polynomial of degree 2006 can have, given that there are exactly 1006 distinct absolute values among its roots. The roots can be real or complex, but the coefficients of the polynomial are real. Since the coefficients are real, any ... | [
{
"content": "Let $f(x)$ be a polynomial of degree 2006 with real coefficients, and let its roots be $r_1,$ $r_2,$ $\\dots,$ $r_{2006}.$ There are exactly 1006 distinct values among\n\\[|r_1|, |r_2|, \\dots, |r_{2006}|.\\]What is the minimum number of real roots that $f(x)$ can have?",
"role": "user"
},
... | {
"is_complete": true
} | MATH_AnsAug | 6 | 4 | false |
metamathqa_20066 | Given $\mathbf{a} = \begin{pmatrix} -7 \\ 0 \\ 1 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 4 \\ 2 \\ -1 \end{pmatrix},$ find $\mathbf{a} - 3 \mathbf{b}.$ | <think>
Alright, let me tackle this problem. Okay, we have two vectors here, a and b. Vector a is given as (-7, 0, 1) and vector b is (4, 2, -1). The question asks me to find a minus three times b, so that's a - 3b. Let me remember how vector subtraction and scalar multiplication work.
First, let's recall that when yo... | [
{
"content": "Given $\\mathbf{a} = \\begin{pmatrix} -7 \\\\ 0 \\\\ 1 \\end{pmatrix}$ and $\\mathbf{b} = \\begin{pmatrix} 4 \\\\ 2 \\\\ -1 \\end{pmatrix},$ find $\\mathbf{a} - 3 \\mathbf{b}.$",
"role": "user"
},
{
"content": "<think>\nAlright, let me tackle this problem. Okay, we have two vectors her... | {
"is_complete": true
} | MATH_AnsAug | \begin{pmatrix}-19\-6\4\end{pmatrix} | \begin{pmatrix} -19 \\ -6 \\ 4 \end{pmatrix} | false |
metamathqa_20096 | Find the domain of the rational function $g(x) = \frac{x^3-2x^2+4x+3}{x^2-4x+3}$. Express your answer as a union of intervals. | <think>
Okay, so I need to find the domain of the rational function g(x) = (x³ - 2x² + 4x + 3)/(x² - 4x + 3). Alright, the domain of a rational function is all real numbers except where the denominator is zero because you can't divide by zero. So, my job is to figure out when the denominator equals zero and exclude ... | [
{
"content": "Find the domain of the rational function $g(x) = \\frac{x^3-2x^2+4x+3}{x^2-4x+3}$. Express your answer as a union of intervals.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the domain of the rational function g(x) = (x³ - 2x² + 4x + 3)/(x² - 4x + 3). Alright, t... | {
"is_complete": true
} | MATH_AnsAug | (-\infty,1)\cup(1,3)\cup(3,\infty) | (-\infty, 1) \cup (1, 3) \cup (3, \infty) | false |
metamathqa_20100 | The perimeter of a particular square and the circumference of a particular circle are equal. What is the ratio of the area of the square to the area of the circle? Express your answer as a common fraction in terms of $\pi$. | <think>
Alright, so the problem here is about a square and a circle that have the same perimeter (or circumference for the circle). I need to find the ratio of the area of the square to the area of the circle, expressed as a common fraction in terms of Ï. Let's break this down step by step.
First, let's recall some f... | [
{
"content": "The perimeter of a particular square and the circumference of a particular circle are equal. What is the ratio of the area of the square to the area of the circle? Express your answer as a common fraction in terms of $\\pi$.",
"role": "user"
},
{
"content": "<think>\nAlright, so the pr... | {
"is_complete": true
} | MATH_AnsAug | \frac{\pi}{4} | \dfrac{\pi}{4} | false |
metamathqa_20144 | Find the sum of the solutions to the equation $(3x+5)(2x-9) = 0$, expressed as a common fraction. | <think>
Okay, so I need to find the sum of the solutions to the equation (3x + 5)(2x - 9) = 0. Hmm, let's see. I remember from algebra that when you have a quadratic equation in factored form like this, the solutions are found by setting each factor equal to zero. So, basically, if the product of two things is zero, th... | [
{
"content": "Find the sum of the solutions to the equation $(3x+5)(2x-9) = 0$, expressed as a common fraction.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the sum of the solutions to the equation (3x + 5)(2x - 9) = 0. Hmm, let's see. I remember from algebra that when you have... | {
"is_complete": true
} | MATH_Rephrased | \frac{17}{6} | \dfrac{17}{6} | false |
metamathqa_20189 | "How many polynomials $P(x)$ of degree at most 3, with coefficients from the set $\\{0, 1, 2, 3, 4, (...TRUNCATED) | "<think>\nOkay, let's tackle this problem step by step. The question is asking how many polynomials (...TRUNCATED) | [{"content":"How many polynomials $P(x)$ of degree at most 3, with coefficients from the set $\\{0, (...TRUNCATED) | {
"is_complete": true
} | MATH_Rephrased | 220 | D | false |
metamathqa_20198 | Determine the coordinates of the midpoint of the segment with endpoints (7, -6) and (-3, 4). | "<think>\nOkay, so I need to find the midpoint of the segment between the points (7, -6) and (-3, 4)(...TRUNCATED) | [{"content":"Determine the coordinates of the midpoint of the segment with endpoints (7, -6) and (-3(...TRUNCATED) | {
"is_complete": true
} | MATH_Rephrased | (2,-1) | (2, -1) | false |
metamathqa_20199 | Compute $\arcsin \frac{1}{\sqrt{2}}.$ Express your answer in radians. | "<think>\nOkay, so I need to compute arcsin(1/â2). Hmm. Let me first recall what arcsin is. Arc(...TRUNCATED) | [{"content":"Compute $\\arcsin \\frac{1}{\\sqrt{2}}.$ Express your answer in radians.","role":"user(...TRUNCATED) | {
"is_complete": true
} | MATH_AnsAug | \frac{\pi}{4} | \dfrac{\pi}{4} | false |
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