conversation_id stringlengths 12 17 | prompt stringlengths 16 4.41k | response stringlengths 2.28k 13.3k | messages listlengths 2 2 | metadata dict | type stringclasses 4
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|---|---|---|---|---|---|
metamathqa_20000 | The cost of five pencils and one pen is $\$2.50$, and the cost of one pencil and two pens is $\$1.85$. What is the cost of two pencils and one pen? | <think>
Alright, let's try to solve this problem step by step. So, we have two equations here:
1. The cost of five pencils and one pen is $2.50.
2. The cost of one pencil and two pens is $1.85.
We need to find the cost of two pencils and one pen. Hmm, okay. So first off, let me assign variables to these things to mak... | [
{
"content": "The cost of five pencils and one pen is $\\$2.50$, and the cost of one pencil and two pens is $\\$1.85$. What is the cost of two pencils and one pen?",
"role": "user"
},
{
"content": "<think>\nAlright, let's try to solve this problem step by step. So, we have two equations here:\n\n1. ... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20008 | Cory has $3$ apples, $2$ oranges and $2$ bananas. If Cory eats one piece of his fruit per day for a week and the pieces of fruit within each category are indistinguishable, in how many orders can Cory eat the fruit? One such order is $AAAOOBB.$ | <think>
Alright, so I need to figure out the number of different orders Cory can eat his fruit over a week. He's got 3 apples, 2 oranges, and 2 bananas. Each day he eats one fruit, and the question is about the number of distinct sequences he can follow. The fruits of the same type are indistinct, meaning an apple is a... | [
{
"content": "Cory has $3$ apples, $2$ oranges and $2$ bananas. If Cory eats one piece of his fruit per day for a week and the pieces of fruit within each category are indistinguishable, in how many orders can Cory eat the fruit? One such order is $AAAOOBB.$",
"role": "user"
},
{
"content": "<think>... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20011 | What is the sum of all values of $x$ that are solutions to the equation $x^2 = 7x - 12$? | <think>
Okay, so I need to solve the equation x squared equals 7x minus 12 and then find the sum of all the solutions. Hmm, let's think. First, I remember that quadratic equations can often be solved by moving all terms to one side so that the equation equals zero. That way, I can factor them, complete the square, or u... | [
{
"content": "What is the sum of all values of $x$ that are solutions to the equation $x^2 = 7x - 12$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to solve the equation x squared equals 7x minus 12 and then find the sum of all the solutions. Hmm, let's think. First, I remember that qu... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20016 | Compute $\begin{pmatrix} -4 \\ -1 \end{pmatrix} \cdot \begin{pmatrix} 6 \\ X \end{pmatrix}$. The answer is -32. What is the value of unknown variable X? | <think>
Okay, let me try to figure out this problem step by step. So, the question is asking to compute the dot product of two vectors: the first vector is \(\begin{pmatrix} -4 \\ -1 \end{pmatrix}\) and the second vector is \(\begin{pmatrix} 6 \\ X \end{pmatrix}\). They told us that the result of this dot product is -3... | [
{
"content": "Compute $\\begin{pmatrix} -4 \\\\ -1 \\end{pmatrix} \\cdot \\begin{pmatrix} 6 \\\\ X \\end{pmatrix}$. The answer is -32. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "<think>\nOkay, let me try to figure out this problem step by step. So, the question is ask... | {
"is_complete": true
} | MATH_SV |
metamathqa_20020 | Determine the determinant of the matrix $\mathbf{R}$, which represents a counter-clockwise rotation about the origin by an angle of $58^\circ$. | <think>
Okay, so I need to find the determinant of the matrix R, which is a counter-clockwise rotation matrix by 58 degrees. Hmm, let me recall... Rotation matrices are part of linear transformations, right? When you rotate a point in the plane without changing its shape or size, the determinant should have something t... | [
{
"content": "Determine the determinant of the matrix $\\mathbf{R}$, which represents a counter-clockwise rotation about the origin by an angle of $58^\\circ$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the determinant of the matrix R, which is a counter-clockwise rotation ma... | {
"is_complete": true
} | MATH_Rephrased |
metamathqa_20025 | The areas of three squares are 16, 49 and 169. What is the average (mean) of their side lengths? | <think>
Okay, so I have this problem here that says: The areas of three squares are 16, 49, and 169. What is the average (mean) of their side lengths? Alright, let me think. I know that when we talk about the area of a square, it's calculated by side length squared. So to find the side length, we need to take the squar... | [
{
"content": "The areas of three squares are 16, 49 and 169. What is the average (mean) of their side lengths?",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem here that says: The areas of three squares are 16, 49, and 169. What is the average (mean) of their side lengths? Al... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20027 | What is the value of the expression $(37 + 12)^2 - (37^2 +12^2)$? | <think>
Okay, so Iâve got this math problem to solve: (37 + 12)² minus (37² + 12²). Hmm, let me figure this out step by step. First, maybe I should just compute each part separately? Let me try that.
Letâs start with the first part: (37 + 12)². Adding 37 and 12 gives me⦠wait, 37 + 12 is 49. So this part sim... | [
{
"content": "What is the value of the expression $(37 + 12)^2 - (37^2 +12^2)$?",
"role": "user"
},
{
"content": "<think>\nOkay, so Iâve got this math problem to solve: (37 + 12)² minus (37² + 12²). Hmm, let me figure this out step by step. First, maybe I should just compute each part separatel... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20037 | How many positive integer values of $x$ are solutions to the inequality $10 < -x + 13$? | <think>
Alright, let's try to figure out how many positive integer values of x satisfy the inequality 10 < -x + 13. Hmm, okay, so first off, the problem is asking for positive integers x such that when you plug them into this inequality, it holds true. Let me break it down step by step.
First, maybe I should solve the... | [
{
"content": "How many positive integer values of $x$ are solutions to the inequality $10 < -x + 13$?",
"role": "user"
},
{
"content": "<think>\nAlright, let's try to figure out how many positive integer values of x satisfy the inequality 10 < -x + 13. Hmm, okay, so first off, the problem is asking ... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20038 | The operation $\star$ is defined as $a \star b = a + \frac{a}{b}$. What is the value of $12 \star 3$? | <think>
Okay, let me try to figure out this math problem. The question is about an operation called "star" defined as a star b equals a plus a divided by b. So, written out, that's a star b = a + (a/b). And we need to find the value of 12 star 3. Hmm, let me break this down step by step.
First, let me make sure I unde... | [
{
"content": "The operation $\\star$ is defined as $a \\star b = a + \\frac{a}{b}$. What is the value of $12 \\star 3$?",
"role": "user"
},
{
"content": "<think>\nOkay, let me try to figure out this math problem. The question is about an operation called \"star\" defined as a star b equals a plus a ... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20039 | Out of a class of 40 students, 18 students said they liked apple pie, 15 students said they liked chocolate cake, and 12 students said they did not like either dessert. How many students in the class liked both apple pie and chocolate cake? | <think>
Alright, let's try to figure out this problem. So, we have a class of 40 students. Out of these, 18 like apple pie, 15 like chocolate cake, and 12 don't like either dessert. We need to find out how many students like both apple pie and chocolate cake. Hmm, okay, this sounds like a Venn diagram problem.
First, ... | [
{
"content": "Out of a class of 40 students, 18 students said they liked apple pie, 15 students said they liked chocolate cake, and 12 students said they did not like either dessert. How many students in the class liked both apple pie and chocolate cake?",
"role": "user"
},
{
"content": "<think>\nAl... | {
"is_complete": true
} | MATH_Rephrased |
metamathqa_20043 | How many integers $n$ satisfy $(n+3)(n-7) \le 0$? | <think>
Okay, so I need to figure out how many integers n satisfy the inequality (n + 3)(n - 7) ⤠0. Let me start by understanding what this inequality means.
First, I remember that when you have a product of two expressions, like (A)(B) ⤠0, this means that either one of them is positive and the other is negativ... | [
{
"content": "How many integers $n$ satisfy $(n+3)(n-7) \\le 0$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out how many integers n satisfy the inequality (n + 3)(n - 7) ⤠0. Let me start by understanding what this inequality means. \n\nFirst, I remember that when you hav... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20047 | Given the equation $y = \frac{3x}{2x^2 - 6x + 4}$, the domain is all real numbers except for $x = A$ and $x = B$. What is the sum of $A$ and $B$? | <think>
Okay, let's see. The problem is about finding the domain of the function y equals 3x divided by (2x² - 6x + 4). The domain is all real numbers except x = A and x = B, and I need to find the sum of A and B. Hmm, right. The domain of a function includes all the real numbers for which the function is defined. Sin... | [
{
"content": "Given the equation $y = \\frac{3x}{2x^2 - 6x + 4}$, the domain is all real numbers except for $x = A$ and $x = B$. What is the sum of $A$ and $B$?",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. The problem is about finding the domain of the function y equals 3x divided by ... | {
"is_complete": true
} | MATH_Rephrased |
metamathqa_20049 | Grandma gave Bryce and Carter some raisins. Bryce received 6 more raisins than Carter, and Carter received half the number of raisins Bryce received. How many raisins did Bryce receive? | <think>
Okay, so Grandma gave Bryce and Carter some raisins. The problem says Bryce received 6 more raisins than Carter, and Carter received half the number of raisins Bryce received. Hmm. I need to figure out how many raisins Bryce got. Let me break it down step by step.
First, let me translate the problem into math ... | [
{
"content": "Grandma gave Bryce and Carter some raisins. Bryce received 6 more raisins than Carter, and Carter received half the number of raisins Bryce received. How many raisins did Bryce receive?",
"role": "user"
},
{
"content": "<think>\nOkay, so Grandma gave Bryce and Carter some raisins. The ... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20050 | Evaluate $\left\lceil\sqrt{2}\,\right\rceil+\left\lceil\sqrt{22}\,\right\rceil+\left\lceil\sqrt{222}\,\right\rceil$. | <think>
Okay, so I need to evaluate the sum of three ceiling functions: the ceiling of the square root of 2, the ceiling of the square root of 22, and the ceiling of the square root of 222. Then add them all together. Hmm, ceiling function... right, that rounds a number up to the nearest integer. So even if the square ... | [
{
"content": "Evaluate $\\left\\lceil\\sqrt{2}\\,\\right\\rceil+\\left\\lceil\\sqrt{22}\\,\\right\\rceil+\\left\\lceil\\sqrt{222}\\,\\right\\rceil$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to evaluate the sum of three ceiling functions: the ceiling of the square root of 2, the cei... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20051 | In parallelogram $ABCD$, $AB = 38$ cm, $BC = 3y^3$ cm, $CD = 2x +4$ cm, and $AD = 24$ cm. What is the product of $x$ and $y$? | <think>
Okay, so I need to solve this problem about a parallelogram, right? Let me remember. In a parallelogram, opposite sides are equal. So, that means AB equals CD and BC equals AD. The problem gives me the measurements for each side. Let's list out what's given:
AB = 38 cm
BC = 3y³ cm
CD = (2x + 4) cm
AD = 24 ... | [
{
"content": "In parallelogram $ABCD$, $AB = 38$ cm, $BC = 3y^3$ cm, $CD = 2x +4$ cm, and $AD = 24$ cm. What is the product of $x$ and $y$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to solve this problem about a parallelogram, right? Let me remember. In a parallelogram, opposite sid... | {
"is_complete": true
} | MATH_AnsAug |
metamathqa_20062 | If a function f is defined as f(z) = i * (complex conjugate of z), where i^2 = -1 and z is a complex number, how many values of z satisfy the conditions |z| = 5 and f(z) = z? | <think>
Okay, let's see. I have this function f(z) defined as f(z) = i times the complex conjugate of z. And I need to find how many values of z satisfy both |z| = 5 and f(z) = z. Hmm, okay. Let me break this down step by step.
First, let's recall that a complex number z can be written in the form z = x + yi, where x ... | [
{
"content": "If a function f is defined as f(z) = i * (complex conjugate of z), where i^2 = -1 and z is a complex number, how many values of z satisfy the conditions |z| = 5 and f(z) = z?",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. I have this function f(z) defined as f(z) = i times... | {
"is_complete": true
} | MATH_Rephrased |
metamathqa_20069 | A rhombus has sides of length 51 units each and a shorter diagonal of length X units. What is the length, in units, The length of the longer diagonal is 90. What is the value of unknown variable X? | <think>
Okay, so I need to figure out the length of the shorter diagonal X of a rhombus. They told me that each side of the rhombus is 51 units long, and the longer diagonal is 90 units. Alright, let me remember the properties of a rhombus. All sides are equal, right? And the diagonals bisect each other at right angles... | [
{
"content": "A rhombus has sides of length 51 units each and a shorter diagonal of length X units. What is the length, in units, The length of the longer diagonal is 90. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out the length of t... | {
"is_complete": true
} | MATH_SV |
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