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<｜begin▁of▁sentence｜><｜User｜>If $x \cdot (x+y) = x^2 + 8$, what is the value of $xy$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this equation: x times (x plus y) equals x squared plus 8. I need to find the value of xy. Hmm, let's write that down ste... | deepscaler_teacher_vllm_clean_v4_conceptual | math | If $x \cdot (x+y) = x^2 + 8$, what is the value of $xy$? | 8 | <｜begin▁of▁sentence｜><｜User｜>If $x \cdot (x+y) = x^2 + 8$, what is the value of $xy$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this equation: x times (x plus y) equals x squared plus 8. I need to find the value of xy. Hmm, let's write that down step by step.
First, let's parse the equation: x*(x + y) = x² + 8.
I think I should start by expanding the left side. So, x*(x + y) is equal to x² + xy. That makes sense becaus... | official | v4_conceptual | 17,168 | 914 | 1f89263f69f12d84 | 8 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x \\cdot (x+y) = x^2 + 8$, what is the value of $xy$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this equation: x times (x plus y) equals x square... | 927 |
<｜begin▁of▁sentence｜><｜User｜>A square has two diagonals, and a convex pentagon has five diagonals. How many diagonals does a convex decagon have? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to figure out how many diagonals a convex decagon has. Hmm, ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | A square has two diagonals, and a convex pentagon has five diagonals. How many diagonals does a convex decagon have? | 35 | <｜begin▁of▁sentence｜><｜User｜>A square has two diagonals, and a convex pentagon has five diagonals. How many diagonals does a convex decagon have? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to figure out how many diagonals a convex decagon has. Hmm, I remember that the number of diagonals in a polygon can be found using a formula. Wait, let me recall... I think it's something like n(n-3)/2, where n is the number of sides. Let me verify that because I might be mixing it up with some... | official | v4_conceptual | 39,721 | 1,018 | 42cb164c3db33c88 | 35 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square has two diagonals, and a convex pentagon has five diagonals. How many diagonals does a convex decagon have?",
"role": "user"
},
{
"content": "<think>\nOkay,... | 1,031 |
<｜begin▁of▁sentence｜><｜User｜>Given the function $f(x) = \frac{m}{x} - m + \ln x$ (where $m$ is a constant).
1. Find the monotonic intervals of $f(x)$.
2. For what values of $m$ does $f(x) \geq 0$ hold true? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given the function $f(x) = \frac{m}{x} - m + \ln x$ (where $m$ is a constant).
1. Find the monotonic intervals of $f(x)$.
2. For what values of $m$ does $f(x) \geq 0$ hold true? | m = 1 | <｜begin▁of▁sentence｜><｜User｜>Given the function $f(x) = \frac{m}{x} - m + \ln x$ (where $m$ is a constant).
1. Find the monotonic intervals of $f(x)$.
2. For what values of $m$ does $f(x) \geq 0$ hold true? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this function f(x) = m/x - m + ln x, and I need to do two things: first, find its monotonic intervals, and second, determine for which values of m the inequality f(x) ≥ 0 holds. Hmm, let's start with the first part.
1. **Finding Monotonic Intervals:**
To find the monotonic intervals of f(x), I... | official | v4_conceptual | 14,716 | 3,028 | 5b56eb4dac6e25a5 | 1 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = \\frac{m}{x} - m + \\ln x$ (where $m$ is a constant).\n1. Find the monotonic intervals of $f(x)$.\n2. For what values of $m$ does $f(x) \\geq 0$ hold t... | 3,041 |
<｜begin▁of▁sentence｜><｜User｜>What is the value of the expression $x^2+ 5x-6$, when $x =-1$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this math problem here: I need to find the value of the expression \(x^2 + 5x - 6\) when \(x = -1\). Hmm, let me th... | deepscaler_teacher_vllm_clean_v4_conceptual | math | What is the value of the expression $x^2+ 5x-6$, when $x =-1$? | -10 | <｜begin▁of▁sentence｜><｜User｜>What is the value of the expression $x^2+ 5x-6$, when $x =-1$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this math problem here: I need to find the value of the expression \(x^2 + 5x - 6\) when \(x = -1\). Hmm, let me think about how to approach this step by step.
First, I remember that when you have an expression like this, you substitute the given value of \(x\) into the expression and then perf... | official | v4_conceptual | 17,054 | 1,501 | b9f61f50c5f07716 | -10 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of the expression $x^2+ 5x-6$, when $x =-1$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this math problem here: I need to find the v... | 1,514 |
<｜begin▁of▁sentence｜><｜User｜>Find the distance between the vertices of the hyperbola $9x^2 + 54x - y^2 + 10y + 55 = 0.$ Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the distance between the vertices of the hyperbola given by the equation \(9x^2... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Find the distance between the vertices of the hyperbola $9x^2 + 54x - y^2 + 10y + 55 = 0.$ | \frac{2}{3} | <｜begin▁of▁sentence｜><｜User｜>Find the distance between the vertices of the hyperbola $9x^2 + 54x - y^2 + 10y + 55 = 0.$ Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the distance between the vertices of the hyperbola given by the equation \(9x^2 + 54x - y^2 + 10y + 55 = 0\). Hmm, hyperbolas can be a bit tricky, but I remember that the standard form of a hyperbola is either \(\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1\) or \(\frac{(y-k)^2}{b^2} - \... | official | v4_conceptual | 18,183 | 3,050 | 5106d0236a805b5b | \dfrac{2}{3} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the distance between the vertices of the hyperbola $9x^2 + 54x - y^2 + 10y + 55 = 0.$",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the dist... | 3,063 |
<｜begin▁of▁sentence｜><｜User｜>Two numbers are independently selected from the set of positive integers less than or equal to 6. Exactly one of the numbers must be even. What is the probability that the sum of the two numbers is less than their product? Express your answer as a common fraction. Let's think step by step a... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Two numbers are independently selected from the set of positive integers less than or equal to 6. Exactly one of the numbers must be even. What is the probability that the sum of the two numbers is less than their product? Express your answer as a common fraction. | \frac{2}{3} | <｜begin▁of▁sentence｜><｜User｜>Two numbers are independently selected from the set of positive integers less than or equal to 6. Exactly one of the numbers must be even. What is the probability that the sum of the two numbers is less than their product? Express your answer as a common fraction. Let's think step by step a... | <think>
Okay, so I need to find the probability that the sum of two numbers is less than their product, given that exactly one of the numbers must be even when selecting two numbers from the set of positive integers less than or equal to 6. Let me break this down step by step.
First, let's understand the setup. The se... | official | v4_conceptual | 8,811 | 3,526 | 5ddf6f5b5588edbb | \dfrac{2}{3} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two numbers are independently selected from the set of positive integers less than or equal to 6. Exactly one of the numbers must be even. What is the probability that the sum of... | 3,539 |
<｜begin▁of▁sentence｜><｜User｜>A paperboy delivers newspapers to 11 houses along Main Street. He may skip delivering to any house, but he must not skip three consecutive houses to avoid losing his job. Determine the number of possible delivery sequences available to the paperboy under these conditions. Let's think step b... | deepscaler_teacher_vllm_clean_v4_conceptual | math | A paperboy delivers newspapers to 11 houses along Main Street. He may skip delivering to any house, but he must not skip three consecutive houses to avoid losing his job. Determine the number of possible delivery sequences available to the paperboy under these conditions. | 927 | <｜begin▁of▁sentence｜><｜User｜>A paperboy delivers newspapers to 11 houses along Main Street. He may skip delivering to any house, but he must not skip three consecutive houses to avoid losing his job. Determine the number of possible delivery sequences available to the paperboy under these conditions. Let's think step b... | <think>
Okay, so I have this problem about a paperboy delivering newspapers to 11 houses on Main Street. He can choose to skip delivering to any house, but he must not skip three consecutive houses. I need to figure out how many possible delivery sequences he can have under these conditions.
Hmm, let me try to underst... | official | v4_conceptual | 3,927 | 2,527 | 00fa760bcebe13d2 | 927 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A paperboy delivers newspapers to 11 houses along Main Street. He may skip delivering to any house, but he must not skip three consecutive houses to avoid losing his job. Determi... | 2,540 |
<｜begin▁of▁sentence｜><｜User｜>In a directed graph with $2013$ vertices, there is exactly one edge between any two vertices and for every vertex there exists an edge outwards this vertex. We know that whatever the arrangement of the edges, from every vertex we can reach $k$ vertices using at most two edges. Find the ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | In a directed graph with $2013$ vertices, there is exactly one edge between any two vertices and for every vertex there exists an edge outwards this vertex. We know that whatever the arrangement of the edges, from every vertex we can reach $k$ vertices using at most two edges. Find the maximum value of $k$ . | 2012 | <｜begin▁of▁sentence｜><｜User｜>In a directed graph with $2013$ vertices, there is exactly one edge between any two vertices and for every vertex there exists an edge outwards this vertex. We know that whatever the arrangement of the edges, from every vertex we can reach $k$ vertices using at most two edges. Find the ... | <think>
Okay, so I have this problem about a directed graph with 2013 vertices. The problem states that there's exactly one edge between any two vertices, which means it's a complete directed graph, right? Because in a complete graph, every pair of vertices is connected by a single edge. Now, it also says that for ever... | official | v4_conceptual | 30,823 | 2,187 | 1d0219bff9e081c0 | 2012 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a directed graph with $2013$ vertices, there is exactly one edge between any two vertices and for every vertex there exists an edge outwards this vertex. We know that whatev... | 2,200 |
"<｜begin▁of▁sentence｜><｜User｜>Simplify $\\sqrt{28x} \\cdot \\sqrt{15x} \\cdot \\sqrt{21x(...TRUNCATED) | deepscaler_teacher_vllm_clean_v4_conceptual | math | "Simplify $\\sqrt{28x} \\cdot \\sqrt{15x} \\cdot \\sqrt{21x}$. Express your answer in simplest radic(...TRUNCATED) | 42x\sqrt{5x} | "<｜begin▁of▁sentence｜><｜User｜>Simplify $\\sqrt{28x} \\cdot \\sqrt{15x} \\cdot \\sqrt{21x(...TRUNCATED) | "<think>\nOkay, so I need to simplify the expression √(28x) · √(15x) · √(21x). Hmm, let me t(...TRUNCATED) | official | v4_conceptual | 37,078 | 2,802 | 5e0383c43c78b5aa | 42x\sqrt{5x} | true | 1 | [{"content":"Please reason step by step, and put your final answer within \\boxed{}.","role":"system(...TRUNCATED) | 2,815 |
"<｜begin▁of▁sentence｜><｜User｜>Find $53\\cdot\\left(3\\frac{1}{5} - 4\\frac{1}{2}\\right)(...TRUNCATED) | deepscaler_teacher_vllm_clean_v4_conceptual | math | "Find $53\\cdot\\left(3\\frac{1}{5} - 4\\frac{1}{2}\\right) \\div \\left(2\\frac{3}{4} + 1\\frac{2}{(...TRUNCATED) | -15\frac{3}{5} | "<｜begin▁of▁sentence｜><｜User｜>Find $53\\cdot\\left(3\\frac{1}{5} - 4\\frac{1}{2}\\right)(...TRUNCATED) | "<think>\nOkay, so I have this math problem here: 53 multiplied by (3 and 1/5 minus 4 and 1/2), then(...TRUNCATED) | official | v4_conceptual | 19,301 | 2,754 | 8027e69ef8ec6f0b | -15 \dfrac{3}{5} | true | 1 | [{"content":"Please reason step by step, and put your final answer within \\boxed{}.","role":"system(...TRUNCATED) | 2,767 |
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