messages listlengths 2 2 | tools listlengths 0 0 | source stringclasses 1
value | raw_text stringlengths 780 30.5k | n_tokens int64 181 16.6k | reasoning_len int64 281 25.1k |
|---|---|---|---|---|---|
[
{
"content": "If a coin is tossed ten times, how many different ways are there for obtaining exactly eight heads?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The number of ways to obtain... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
If a coin is tossed ten times, how many different ways are there for obtaining exactly eight heads?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "If a coin is tossed ten times, how many differe... | 227 | 281 |
[
{
"content": "Evaluate the integral $\\int \\frac{3}{5x+2} \\, dx$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To evaluate the integral \\(\\int \\frac{3}{5x+2} \\, dx\\), we can use a ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Evaluate the integral $\int \frac{3}{5x+2} \, dx$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to evaluate the integral ∫ (3/(5x+2)) dx. This is a standard integral that can be solved by substi... | 463 | 304 |
[
{
"content": "Given a Poisson distribution with $\\lambda = 0.7$, how many car crashes can be expected within one week?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The expected value (me... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given a Poisson distribution with $\lambda = 0.7$, how many car crashes can be expected within one week?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given a Poisson distribution with lambda = 0.7. Th... | 181 | 305 |
[
{
"content": "Evaluate the integral $\\int \\frac{1}{6x} \\, dx$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The integral \\(\\int \\frac{1}{6x} \\, dx\\) can be evaluated by factoring ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Evaluate the integral $\int \frac{1}{6x} \, dx$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to evaluate the integral ∫ (1/(6x)) dx.
Step-by-step:
1. Recognize that ∫ (1/(6x)) dx = (1/6) ∫ (1/... | 325 | 314 |
[
{
"content": "In how many different ways can Hailey arrange seven paintings in a row on the wall?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The number of ways to arrange \\(n\\) distin... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
In how many different ways can Hailey arrange seven paintings in a row on the wall?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "In how many different ways can Hailey arrange seven paintings i... | 256 | 328 |
[
{
"content": "How do you find the inverse of a 3 x 3 matrix?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To find the inverse of a \\(3 \\times 3\\) matrix \\(A\\), you can use one of two... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
How do you find the inverse of a 3 x 3 matrix?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We need to explain how to find the inverse of a 3x3 matrix step by step. We'll cover methods: adjugate method (usin... | 994 | 329 |
[
{
"content": "Given the function \\( f(x) = a(x-h)^2 + k \\), where the vertex of the graph of \\( f \\) is at \\( (2,3) \\) and the graph passes through \\( (1,7) \\):\n\na. Write down the value of \\( h \\) and \\( k \\).\n\nb. Find the value of \\( a \\).\nPlease reason step by step, and put your final answe... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given the function \( f(x) = a(x-h)^2 + k \), where the vertex of the graph of \( f \) is at \( (2,3) \) and the graph passes through \( (1,7) \):
a. Write down the value of \( h \) and \( k \).
b. Find the value of \( a \).
Please reason step by step, and put your final... | 448 | 343 |
[
{
"content": "Write the expression $2\\cos^2\\left(\\frac{\\pi}6\\right) - 1$ as a single trigonometric function.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "We use the double-angle iden... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Write the expression $2\cos^2\left(\frac{\pi}6\right) - 1$ as a single trigonometric function.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to write the expression 2 cos^2(π/6) - 1 as a single t... | 316 | 367 |
[
{
"content": "Find $\\lim_{k \\rightarrow \\infty} \\sup a_k$ and $\\lim_{k \\rightarrow \\infty} \\inf a_k$ for the sequence $a_k = \\frac{1}{k}$ where $k \\in \\mathbb{N}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_cal... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find $\lim_{k \rightarrow \infty} \sup a_k$ and $\lim_{k \rightarrow \infty} \inf a_k$ for the sequence $a_k = \frac{1}{k}$ where $k \in \mathbb{N}$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked... | 695 | 400 |
[
{
"content": "What is the total number of possible 10-toss sequences with exactly 3 heads?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The number of sequences of 10 coin tosses with exac... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
What is the total number of possible 10-toss sequences with exactly 3 heads?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "What is the total number of possible 10-toss sequences with exactly 3 ... | 262 | 413 |
[
{
"content": "Given that \\( u_1 \\), \\( u_2 \\), and \\( f \\) are three functions which satisfy \\( L(u_1) = f \\) and \\( L(u_2) = 2f \\), find a solution of the homogeneous wave equation \\( L(u) = 0 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": ""... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given that \( u_1 \), \( u_2 \), and \( f \) are three functions which satisfy \( L(u_1) = f \) and \( L(u_2) = 2f \), find a solution of the homogeneous wave equation \( L(u) = 0 \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_sta... | 466 | 427 |
[
{
"content": "Given the LU decomposition of a matrix \\(A\\) as \\(L\\) and \\(U\\), how can one determine the solution to the system \\(Ax = B\\)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"conte... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given the LU decomposition of a matrix \(A\) as \(L\) and \(U\), how can one determine the solution to the system \(Ax = B\)?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "Given the LU decompos... | 598 | 431 |
[
{
"content": "How many unique ways are there to rearrange the word \"PRIOR\"?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The word \"PRIOR\" has 5 letters: P, R, I, O, R. The letter R ap... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
How many unique ways are there to rearrange the word "PRIOR"?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "How many unique ways are there to rearrange the word 'PRIOR'?" Need to find number of... | 363 | 435 |
[
{
"content": "Given that \\( f'(x) \\) is a differentiable and decreasing function for all \\( x \\), which is larger: \\( f'(5) \\) or \\( f'(6) \\)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"co... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given that \( f'(x) \) is a differentiable and decreasing function for all \( x \), which is larger: \( f'(5) \) or \( f'(6) \)?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given: "Given that f'(x) i... | 312 | 440 |
[
{
"content": "Suppose that $f(t)$ is a (non-random) continuous function on $[0, \\infty)$. Let\n\\[ Z_t = \\int_0^t f(s)\\,dB_s. \\]\nWhat is the mean and variance of $Z_t$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_call... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Suppose that $f(t)$ is a (non-random) continuous function on $[0, \infty)$. Let
\[ Z_t = \int_0^t f(s)\,dB_s. \]
What is the mean and variance of $Z_t$?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are gi... | 478 | 450 |
[
{
"content": "How many square submatrices of order 3 can be formed from a $4 \\times 3$ matrix?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To form a square submatrix of order 3, we need... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
How many square submatrices of order 3 can be formed from a $4 \times 3$ matrix?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "How many square submatrices of order 3 can be formed from a $4 \ti... | 343 | 451 |
[
{
"content": "Give a recursive definition for the sequence \\(a_n = 2^n\\) for \\(n = 2, 3, 4, \\ldots\\) where \\(a_1 = 2\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The sequence is... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Give a recursive definition for the sequence \(a_n = 2^n\) for \(n = 2, 3, 4, \ldots\) where \(a_1 = 2\).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to give a recursive definition for the sequ... | 347 | 455 |
[
{
"content": "Find the limit of \\(a^{\\frac{1}{n}}\\) as \\(n \\to \\infty\\) for \\(0 < a \\leq 1\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The limit \\(\\lim_{n \\to \\infty} a^... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the limit of \(a^{\frac{1}{n}}\) as \(n \to \infty\) for \(0 < a \leq 1\).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to find the limit of a^(1/n) as n -> infinity for 0 < a <= 1.
We nee... | 417 | 459 |
[
{
"content": "Given $\\tan A + \\tan B = 3x$ and $\\tan A \\tan B = 2x^2$, find $\\tan A - \\tan B$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "We are given:\n\\[\n\\tan A + \\tan B = 3... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given $\tan A + \tan B = 3x$ and $\tan A \tan B = 2x^2$, find $\tan A - \tan B$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given:
tan A + tan B = 3x
tan A tan B = 2x^2
We need to find tan A - tan... | 420 | 471 |
[
{
"content": "Given that \\( A \\) is the null set, determine \\( P(A) \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The power set \\(P(A)\\) of a set \\(A\\) is the set of all subset... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given that \( A \) is the null set, determine \( P(A) \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given: "Given that A is the null set, determine P(A)." Here P(A) likely denotes the power set of ... | 283 | 476 |
[
{
"content": "Write an efficient recursive algorithm Pow(a, n) that computes \\(a^n\\) for \\(a \\in \\mathbb{R}\\) and \\(n \\in \\mathbb{Z}\\) where \\(n \\geq 0\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Write an efficient recursive algorithm Pow(a, n) that computes \(a^n\) for \(a \in \mathbb{R}\) and \(n \in \mathbb{Z}\) where \(n \geq 0\).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We need to write an e... | 548 | 476 |
[
{
"content": "Find the domain and range of the equation $y - 3x^2 = 2$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "**Step 1: Rewrite the equation.** \nThe given equation is \\(y - 3x^2... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the domain and range of the equation $y - 3x^2 = 2$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given the equation: y - 3x^2 = 2. We need to find the domain and range.
First, rewrite the equat... | 475 | 479 |
[
{
"content": "Find $\\frac{\\partial z}{\\partial x}$ and $\\frac{\\partial z}{\\partial y}$ for $z=f\\left(\\frac{x}{y}\\right)$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "We are give... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ for $z=f\left(\frac{x}{y}\right)$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given a function z = f(x/y). We need to find th... | 572 | 481 |
[
{
"content": "Solve for $a[1], a[2], a[3]$ in the equation $(a[1]+a[3])t+(a[1]+2a[2])t^2=0$ given that $a[1] = 1$ and the equation is identically 0.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"cont... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Solve for $a[1], a[2], a[3]$ in the equation $(a[1]+a[3])t+(a[1]+2a[2])t^2=0$ given that $a[1] = 1$ and the equation is identically 0.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given the equation: ... | 585 | 485 |
[
{
"content": "Find two vectors $\\mathbf{v}$ and $\\mathbf{w}$ in $\\mathbb{R}^3$ such that their span corresponds to the plane defined by the equation $x + 2y - z = 0$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find two vectors $\mathbf{v}$ and $\mathbf{w}$ in $\mathbb{R}^3$ such that their span corresponds to the plane defined by the equation $x + 2y - z = 0$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We need t... | 445 | 486 |
[
{
"content": "If 5 identical gifts are to be given among 8 children, and no child can receive more than 1 gift, how many ways can this be done?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content":... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
If 5 identical gifts are to be given among 8 children, and no child can receive more than 1 gift, how many ways can this be done?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "If 5 identical gi... | 330 | 497 |
[
{
"content": "Rewrite the exponential expression $e^{(2+3i)}$ in the form $a+bi$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To rewrite \\( e^{(2+3i)} \\) in the form \\( a+bi \\), we u... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Rewrite the exponential expression $e^{(2+3i)}$ in the form $a+bi$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to rewrite the exponential expression e^(2+3i) in the form a+bi.
We know that e^... | 444 | 501 |
[
{
"content": "Given the two quaternion equations:\n\\[ q_1 = 2 - i + j + 3k \\]\n\\[ q_2 = -1 + i + 4j - 2k \\]\nwhere \\(i, j, k\\) belong to the imaginary space, calculate the sum and difference of the two quaternions.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_c... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given the two quaternion equations:
\[ q_1 = 2 - i + j + 3k \]
\[ q_2 = -1 + i + 4j - 2k \]
where \(i, j, k\) belong to the imaginary space, calculate the sum and difference of the two quaternions.
Please reason step by step, and put your final answer within \boxed{}.<|im_... | 583 | 512 |
[
{
"content": "Given the function \\( f(x) = x^3 - x \\), find the critical points by solving \\( \\frac{df}{dx} = 0 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The critical points o... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given the function \( f(x) = x^3 - x \), find the critical points by solving \( \frac{df}{dx} = 0 \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given the function f(x) = x^3 - x. We need to find th... | 452 | 513 |
[
{
"content": "Given $\\sin{x}=\\frac{3}{5}$ and $x \\in \\left[\\frac{\\pi}{2}, \\pi\\right]$, find $\\cos{x}$ and $\\tan{x}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "We are given \\... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given $\sin{x}=\frac{3}{5}$ and $x \in \left[\frac{\pi}{2}, \pi\right]$, find $\cos{x}$ and $\tan{x}$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given sin x = 3/5 and x ∈ [π/2, π] (second quadrant)... | 571 | 513 |
[
{
"content": "Given the equations \\( T = m_1 a \\) and \\( T - m_2 g = -m_2 a \\), express \\( a \\) and \\( T \\) in terms of the masses \\( m_1 \\) and \\( m_2 \\) and the gravitational acceleration \\( g \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content":... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given the equations \( T = m_1 a \) and \( T - m_2 g = -m_2 a \), express \( a \) and \( T \) in terms of the masses \( m_1 \) and \( m_2 \) and the gravitational acceleration \( g \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_st... | 599 | 514 |
[
{
"content": "In how many ways can 10 (identical) dimes be distributed among five children if each child gets at least one dime?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To distribute... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
In how many ways can 10 (identical) dimes be distributed among five children if each child gets at least one dime?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "In how many ways can 10 (identic... | 404 | 515 |
[
{
"content": "Find \\(\\lim_{n\\to \\infty}\\sqrt[n]{a}\\) where \\(0 < a\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To find \\(\\lim_{n\\to \\infty} \\sqrt[n]{a}\\) for \\(0 < a\\)... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find \(\lim_{n\to \infty}\sqrt[n]{a}\) where \(0 < a\).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to find \(\lim_{n\to \infty} \sqrt[n]{a}\) where \(0 < a\).
We need to evaluate the limit as... | 340 | 521 |
[
{
"content": "Choose three positive numbers \\( x, y, \\) and \\( z \\) such that \\( x + y + z = 99 \\) so that the product \\( x \\cdot y \\cdot z \\) is as large as possible.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Choose three positive numbers \( x, y, \) and \( z \) such that \( x + y + z = 99 \) so that the product \( x \cdot y \cdot z \) is as large as possible.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are a... | 561 | 525 |
[
{
"content": "Find the median of the probability density function \\( f(x) = 2x \\) for \\( 0 < x < 1 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The median \\( m \\) of a continuou... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the median of the probability density function \( f(x) = 2x \) for \( 0 < x < 1 \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given a probability density function f(x) = 2x for 0 < x < 1, and ... | 414 | 527 |
[
{
"content": "Given the integers 1, 3, 4, 6 and the operations multiplication (*), division (/), addition (+), and subtraction (-), use each integer exactly once and any number of the operations to obtain the result 24. Brackets are allowed, but no other mathematical operations or concatenation of integers is p... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given the integers 1, 3, 4, 6 and the operations multiplication (*), division (/), addition (+), and subtraction (-), use each integer exactly once and any number of the operations to obtain the result 24. Brackets are allowed, but no other mathematical operations or conca... | 450 | 528 |
[
{
"content": "Find the sum of the finite series:\n$$\\sum_{i=0}^n \\frac{1}{6^n}.$$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The given series is \\(\\sum_{i=0}^n \\frac{1}{6^n}\\). Si... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the sum of the finite series:
$$\sum_{i=0}^n \frac{1}{6^n}.$$
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to find the sum of the finite series: sum_{i=0}^n (1/6^n). Wait, the expression is... | 369 | 532 |
[
{
"content": "Given the function \\( f \\colon \\mathbb{R} \\to \\mathbb{R} \\) defined by \\( f(f(x)) = 3 + 2x \\), find \\( f(3) \\) if \\( f(0) = 3 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given the function \( f \colon \mathbb{R} \to \mathbb{R} \) defined by \( f(f(x)) = 3 + 2x \), find \( f(3) \) if \( f(0) = 3 \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given a function f: R -> ... | 446 | 533 |
[
{
"content": "The side of a square is increasing at a rate of 5 cm/s. At what rate is the area changing when the side is 10 cm long?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The area ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
The side of a square is increasing at a rate of 5 cm/s. At what rate is the area changing when the side is 10 cm long?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given: "The side of a square is incr... | 459 | 542 |
[
{
"content": "Find the general expanded form of \\((x+y+z)^k\\) for \\(k \\in \\mathbb{N}\\). Specifically, determine the coefficients of each term in the expansion where the sum of the powers of \\(x\\), \\(y\\), and \\(z\\) in each term equals \\(k\\).\nPlease reason step by step, and put your final answer wi... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the general expanded form of \((x+y+z)^k\) for \(k \in \mathbb{N}\). Specifically, determine the coefficients of each term in the expansion where the sum of the powers of \(x\), \(y\), and \(z\) in each term equals \(k\).
Please reason step by step, and put your final... | 441 | 545 |
[
{
"content": "Let \\( X \\) have the probability mass function given by \\( P(X=-1)=\\frac{1}{2} \\), \\( P(X=0)=\\frac{1}{3} \\), and \\( P(X=1)=\\frac{1}{6} \\). Find the probability mass function of the random variable \\( Y = |X| \\) and compute \\( E[|X|] \\).\nPlease reason step by step, and put your fina... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Let \( X \) have the probability mass function given by \( P(X=-1)=\frac{1}{2} \), \( P(X=0)=\frac{1}{3} \), and \( P(X=1)=\frac{1}{6} \). Find the probability mass function of the random variable \( Y = |X| \) and compute \( E[|X|] \).
Please reason step by step, and put ... | 617 | 548 |
[
{
"content": "Give an example of a sequence $(x_n)$ of real numbers such that $\\lim_{n\\to+\\infty}|x_n-x_{n+1}|=0$, but $(x_n)$ is not a Cauchy sequence.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Give an example of a sequence $(x_n)$ of real numbers such that $\lim_{n\to+\infty}|x_n-x_{n+1}|=0$, but $(x_n)$ is not a Cauchy sequence.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We need to find a seque... | 396 | 550 |
[
{
"content": "An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with a mean of 800 hours and a standard deviation of 40 hours. Find the probability that a random sample of 16 bulbs will have an average life of less than 775 hours.\nPlease reason s... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with a mean of 800 hours and a standard deviation of 40 hours. Find the probability that a random sample of 16 bulbs will have an average life of less than 77... | 512 | 552 |
[
{
"content": "Find the number of solutions to the equation \\( x_1 + x_2 + x_3 + x_4 = 14 \\) where \\( x_i \\) are nonnegative integers.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the number of solutions to the equation \( x_1 + x_2 + x_3 + x_4 = 14 \) where \( x_i \) are nonnegative integers.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "Find the number of solution... | 482 | 553 |
[
{
"content": "Given that $10 \\equiv 3 \\pmod{7}$, determine the values of $10^2 \\pmod{7}$ and $10^3 \\pmod{7}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "We are given that \\(10 \\eq... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given that $10 \equiv 3 \pmod{7}$, determine the values of $10^2 \pmod{7}$ and $10^3 \pmod{7}$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given: 10 ≡ 3 (mod 7). We need to determine the values of 1... | 638 | 554 |
[
{
"content": "Find a function \\( f: \\mathbb{R} \\to \\mathbb{R} \\) that is order-preserving, i.e., \\( x \\le y \\) implies \\( f(x) \\le f(y) \\) for all \\( x, y \\in \\mathbb{R} \\). Also, find an example of a function that is not order-preserving.\nPlease reason step by step, and put your final answer wi... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find a function \( f: \mathbb{R} \to \mathbb{R} \) that is order-preserving, i.e., \( x \le y \) implies \( f(x) \le f(y) \) for all \( x, y \in \mathbb{R} \). Also, find an example of a function that is not order-preserving.
Please reason step by step, and put your final ... | 610 | 555 |
[
{
"content": "Determine $\\delta$ if $\\varepsilon = 0.06$ for $\\lim_{x \\to 1} (2 - 3x) = -1$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To find \\(\\delta\\) for \\(\\varepsilon = 0... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Determine $\delta$ if $\varepsilon = 0.06$ for $\lim_{x \to 1} (2 - 3x) = -1$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given a limit: lim_{x→1} (2 - 3x) = -1, and we are given ε = 0.06. We need t... | 584 | 556 |
[
{
"content": "What is the probability of getting at least one Head in 10 flips of a fair coin?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The probability of getting at least one Head in... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
What is the probability of getting at least one Head in 10 flips of a fair coin?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "What is the probability of getting at least one Head in 10 flips o... | 393 | 558 |
[
{
"content": "Provide an example of a function \\( f: \\mathbb{R} \\to \\mathbb{R} \\) that is discontinuous at every point \\( x \\in \\mathbb{R} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"c... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Provide an example of a function \( f: \mathbb{R} \to \mathbb{R} \) that is discontinuous at every point \( x \in \mathbb{R} \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We need to provide an example of ... | 636 | 560 |
[
{
"content": "Determine the real and imaginary parts of $\\sin z$ where $z \\in \\Bbb{C}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The real and imaginary parts of \\(\\sin z\\) for \... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Determine the real and imaginary parts of $\sin z$ where $z \in \Bbb{C}$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to determine the real and imaginary parts of sin(z) where z is complex.
Gi... | 370 | 561 |
[
{
"content": "Complete the $f \\times x$ column for the given table.\n$$\n\\begin{array}{c|l}\n\\text{x} & \\text{f} & \\text{fx} \\\\\n\\hline\n5 & 8 & \\\\\n6 & 12 & \\\\\n7 & 15 & \\\\\n8 & 17 & \\\\\n9 & 9 & \\\\\n\\end{array}\n$$\nPlease reason step by step, and put your final answer within \\boxed{}.",
... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Complete the $f \times x$ column for the given table.
$$
\begin{array}{c|l}
\text{x} & \text{f} & \text{fx} \\
\hline
5 & 8 & \\
6 & 12 & \\
7 & 15 & \\
8 & 17 & \\
9 & 9 & \\
\end{array}
$$
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<... | 509 | 564 |
[
{
"content": "Find the integral of the function $\\int \\dfrac{1}{ \\sqrt{ a^2 - x^2 }} \\, dx$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To find the integral \\(\\int \\frac{1}{\\sqr... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the integral of the function $\int \dfrac{1}{ \sqrt{ a^2 - x^2 }} \, dx$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to find the integral of the function ∫ 1/√(a^2 - x^2) dx. We need to r... | 561 | 564 |
[
{
"content": "Consider the sequence $\\{a_n\\}_{n=1}^{\\infty}$ defined by\n\\[ a_n = \\frac{1}{n^2} + \\frac{2}{n^2} + \\cdots + \\frac{n}{n^2}. \\]\nExpress $a_n$ in closed form and calculate $\\lim_{n \\to \\infty} a_n$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasonin... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Consider the sequence $\{a_n\}_{n=1}^{\infty}$ defined by
\[ a_n = \frac{1}{n^2} + \frac{2}{n^2} + \cdots + \frac{n}{n^2}. \]
Express $a_n$ in closed form and calculate $\lim_{n \to \infty} a_n$.
Please reason step by step, and put your final answer within \boxed{}.<|im_en... | 612 | 567 |
[
{
"content": "Find the equation of a circle with center $(\\sqrt{5}, 2\\sqrt{2})$ and radius $\\sqrt{10}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The standard equation of a circle w... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the equation of a circle with center $(\sqrt{5}, 2\sqrt{2})$ and radius $\sqrt{10}$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to find the equation of a circle with center (√5, 2√2) and ... | 411 | 569 |
[
{
"content": "If \\(A\\) and \\(B\\) are both \\(n \\times n\\) matrices, and \\(\\lambda_A\\) and \\(\\lambda_B\\) are the eigenvalues for those matrices with respect to the same eigenvector \\(v\\), then does \\(ABv = BAv\\)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reas... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
If \(A\) and \(B\) are both \(n \times n\) matrices, and \(\lambda_A\) and \(\lambda_B\) are the eigenvalues for those matrices with respect to the same eigenvector \(v\), then does \(ABv = BAv\)?
Please reason step by step, and put your final answer within \boxed{}.<|im_e... | 521 | 571 |
[
{
"content": "What is the integral of $\\frac{1}{1+x}$ with respect to $x$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The integral of \\(\\frac{1}{1+x}\\) with respect to \\(x\\) can b... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
What is the integral of $\frac{1}{1+x}$ with respect to $x$?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to find the integral of 1/(1+x) with respect to x.
Step by step reasoning:
We need to ... | 356 | 574 |
[
{
"content": "Let the random variable $X$ have the $N(0,1)$ distribution with the probability density function:\n$$\nf(x)= \\frac{1}{\\sqrt{2\\pi}}\\exp\\left(-\\frac{x^2}{2}\\right), \\quad -\\infty < x < \\infty.\n$$\nLet $Y = e^X$. Find $E(Y^2)$ and deduce $\\mathrm{Var}(Y)$.\nPlease reason step by step, and... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Let the random variable $X$ have the $N(0,1)$ distribution with the probability density function:
$$
f(x)= \frac{1}{\sqrt{2\pi}}\exp\left(-\frac{x^2}{2}\right), \quad -\infty < x < \infty.
$$
Let $Y = e^X$. Find $E(Y^2)$ and deduce $\mathrm{Var}(Y)$.
Please reason step by ... | 687 | 576 |
[
{
"content": "Find the series representation of the function $\\frac{3}{1 - x^4}$ and determine its convergence radius.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The function \\( f(x) ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the series representation of the function $\frac{3}{1 - x^4}$ and determine its convergence radius.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to find the series representation of the fun... | 472 | 577 |
[
{
"content": "Evaluate the integral \\( K = \\int x (x+3)^{10} \\, dx \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "**Step 1: Use substitution.** \nLet \\( u = x + 3 \\). Then \\( x ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Evaluate the integral \( K = \int x (x+3)^{10} \, dx \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We need to evaluate the indefinite integral K = ∫ x (x+3)^{10} dx.
We can do this by substitution or int... | 702 | 580 |
[
{
"content": "Determine the kernel $Ker(\\phi)$ and the image $Im(\\phi)$ of the function $\\phi: \\mathbb{Z} \\to \\mathbb{Z}_{12}$ defined by $\\phi(x) = x \\mod 12$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": [... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Determine the kernel $Ker(\phi)$ and the image $Im(\phi)$ of the function $\phi: \mathbb{Z} \to \mathbb{Z}_{12}$ defined by $\phi(x) = x \mod 12$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given a ... | 630 | 581 |
[
{
"content": "Solve for \\( x \\) in the equation \\( y = 1.15^{x+2} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To solve the equation \\( y = 1.15^{x+2} \\) for \\( x \\), we can u... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Solve for \( x \) in the equation \( y = 1.15^{x+2} \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given the equation \( y = 1.15^{x+2} \) and need to solve for \( x \). We'll assume \( y > 0 \) (si... | 551 | 582 |
[
{
"content": "Suppose a room contains $n$ people. What is the probability that at least two people share the same birthday?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To calculate the p... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Suppose a room contains $n$ people. What is the probability that at least two people share the same birthday?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "Suppose a room contains n people. Wha... | 619 | 584 |
[
{
"content": "Calculate the integral $\\int_{0}^{i} e^z\\, dz$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The integral is evaluated using the Fundamental Theorem of Calculus for comple... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Calculate the integral $\int_{0}^{i} e^z\, dz$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to calculate the integral ∫_{0}^{i} e^z dz. The function e^z is entire (analytic everywhere in the co... | 362 | 586 |
[
{
"content": "Find $\\cos(x)$ and $\\tan(x)$ if $\\sin(x) = \\frac{3}{5}$ over the interval $[\\pi/2, \\pi]$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "Given \\(\\sin(x) = \\frac{3}{5}... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find $\cos(x)$ and $\tan(x)$ if $\sin(x) = \frac{3}{5}$ over the interval $[\pi/2, \pi]$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given sin(x) = 3/5, and x is in [π/2, π], which is the second qua... | 531 | 588 |
[
{
"content": "Find the shortest distance between the line \\(x + 2y = 1\\) and the origin in the coordinate system.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To find the shortest dista... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the shortest distance between the line \(x + 2y = 1\) and the origin in the coordinate system.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "Find the shortest distance between the line x +... | 548 | 588 |
[
{
"content": "Given the moment generating function of a random variable $Y$ as \\( M_Y(t) = (0.7 + 0.3e^t)^4 \\), find the moment generating function of the random variable \\( W = 2Y - 4 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "us... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given the moment generating function of a random variable $Y$ as \( M_Y(t) = (0.7 + 0.3e^t)^4 \), find the moment generating function of the random variable \( W = 2Y - 4 \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assis... | 596 | 588 |
[
{
"content": "What is the probability of flipping a coin twice and getting heads both times?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The probability of flipping a fair coin and getti... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
What is the probability of flipping a coin twice and getting heads both times?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "What is the probability of flipping a coin twice and getting heads b... | 342 | 589 |
[
{
"content": "Suppose \\( X \\sim \\text{Uniform}(0,1) \\) and \\( Y = X^3 \\). What is the probability density function (pdf) for \\( Y \\)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Suppose \( X \sim \text{Uniform}(0,1) \) and \( Y = X^3 \). What is the probability density function (pdf) for \( Y \)?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given X ~ Uniform(0,1) and Y = X^3.... | 582 | 591 |
[
{
"content": "Find the derivative of $2^{n/100}$ with respect to $n$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The derivative of \\(2^{n/100}\\) with respect to \\(n\\) is found using... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the derivative of $2^{n/100}$ with respect to $n$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to find the derivative of the function f(n) = 2^{n/100} with respect to n. We need to give th... | 508 | 591 |
[
{
"content": "What would be a proper u-substitution for the integral $$\\int(\\sin^{10}x \\cdot \\cos x)\\ dx$$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The integral is \\(\\int \\si... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
What would be a proper u-substitution for the integral $$\int(\sin^{10}x \cdot \cos x)\ dx$$?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "What would be a proper u-substitution for the integra... | 348 | 592 |
[
{
"content": "What is the probability of getting exactly two heads when flipping a coin five times?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The probability of getting exactly two hea... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
What is the probability of getting exactly two heads when flipping a coin five times?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "What is the probability of getting exactly two heads when fli... | 528 | 594 |
[
{
"content": "Suppose \\(\\lim_{n \\to \\infty} (a_n - b_n) = l\\) with \\(l \\in \\mathbb{R}\\), and \\(\\lim_{n \\to \\infty} a_n = \\infty\\). Does \\(b_n\\) converge?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls":... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Suppose \(\lim_{n \to \infty} (a_n - b_n) = l\) with \(l \in \mathbb{R}\), and \(\lim_{n \to \infty} a_n = \infty\). Does \(b_n\) converge?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given:
- lim_{... | 477 | 597 |
[
{
"content": "In the game of Monopoly, what is the probability of not rolling doubles in three consecutive turns? \n\nExplanation: The probability of not rolling doubles on a single turn is \\( \\frac{5}{6} \\), since there are 5 outcomes out of 6 that are not doubles. The probability of not rolling doubles in ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
In the game of Monopoly, what is the probability of not rolling doubles in three consecutive turns?
Explanation: The probability of not rolling doubles on a single turn is \( \frac{5}{6} \), since there are 5 outcomes out of 6 that are not doubles. The probability of not... | 535 | 598 |
[
{
"content": "Find the integral of \\(a^{x+c}\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The integral of \\(a^{x+c}\\) with respect to \\(x\\) (where \\(a > 0\\), \\(a \\neq 1\\), a... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the integral of \(a^{x+c}\).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to find the integral of a^{x+c} with respect to x. The constant c and a are presumably constants, with a > 0, a ≠ 1... | 427 | 599 |
[
{
"content": "Let \\( I = \\int^b_a \\frac{1}{\\log x} \\, dx \\). Find \\(\\frac{dI}{da}\\) and \\(\\frac{dI}{db}\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The integral \\( I \\) ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Let \( I = \int^b_a \frac{1}{\log x} \, dx \). Find \(\frac{dI}{da}\) and \(\frac{dI}{db}\).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given I = ∫_a^b (1 / log x) dx. We need to find dI/da and dI/d... | 474 | 604 |
[
{
"content": "For a random variable \\( X \\) with probability density function \\( p(x) = x^{-2} \\) for \\( x \\ge 1 \\), find the expected value \\( E(X) \\) and the probability \\( P(X \\le 2) \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"r... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
For a random variable \( X \) with probability density function \( p(x) = x^{-2} \) for \( x \ge 1 \), find the expected value \( E(X) \) and the probability \( P(X \le 2) \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assi... | 602 | 605 |
[
{
"content": "What are the equations that relate the internal angles of two corners to the third angle in a triangle?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "In a triangle, the sum o... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
What are the equations that relate the internal angles of two corners to the third angle in a triangle?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "What are the equations that relate the inte... | 427 | 606 |
[
{
"content": "Write $\\mathbf{v}_3'$ and $\\mathbf{v}_4'$ as linear combinations of $\\mathbf{v}_1'$ and $\\mathbf{v}_2'$, where $\\mathbf{v}_1' = \\begin{pmatrix} 1 \\\\ 0 \\\\ 0 \\end{pmatrix}$, $\\mathbf{v}_2' = \\begin{pmatrix} 0 \\\\ 1 \\\\ 0 \\end{pmatrix}$, $\\mathbf{v}_3' = \\begin{pmatrix} -1 \\\\ 2 \\... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Write $\mathbf{v}_3'$ and $\mathbf{v}_4'$ as linear combinations of $\mathbf{v}_1'$ and $\mathbf{v}_2'$, where $\mathbf{v}_1' = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}$, $\mathbf{v}_2' = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}$, $\mathbf{v}_3' = \begin{pmatrix} -1 \\ 2... | 548 | 607 |
[
{
"content": "Find a unit vector perpendicular to the vector \\( v = 2i + 3j \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "A vector perpendicular to \\( v = 2i + 3j \\) can be found b... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find a unit vector perpendicular to the vector \( v = 2i + 3j \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We need to find a unit vector perpendicular to the vector v = 2i + 3j. This is a 2D vector. In 2... | 435 | 608 |
[
{
"content": "Given the function $\\sigma(z) = \\frac{1}{1 + e^{-z}}$, compute $\\frac{\\partial y}{\\partial z}$ where $y = \\sigma(z)$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given the function $\sigma(z) = \frac{1}{1 + e^{-z}}$, compute $\frac{\partial y}{\partial z}$ where $y = \sigma(z)$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given the sigmoid function σ(z) = 1 /... | 590 | 609 |
[
{
"content": "Let \\( G = (\\mathbb{Z}, +) \\) and let \\( n \\) be a positive integer. Let \\( H = n\\mathbb{Z} = \\{na : a \\in \\mathbb{Z}\\} \\). Describe the right cosets of \\( H \\) in \\( G \\) and find \\( |G : H| \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reas... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Let \( G = (\mathbb{Z}, +) \) and let \( n \) be a positive integer. Let \( H = n\mathbb{Z} = \{na : a \in \mathbb{Z}\} \). Describe the right cosets of \( H \) in \( G \) and find \( |G : H| \).
Please reason step by step, and put your final answer within \boxed{}.<|im_en... | 544 | 610 |
[
{
"content": "Given $\\sin(B) = t$ and $0 < B < \\frac{\\pi}{2}$, find $\\cos(B)$ and $\\tan(B)$ in terms of $t$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "Given \\(\\sin(B) = t\\) and... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given $\sin(B) = t$ and $0 < B < \frac{\pi}{2}$, find $\cos(B)$ and $\tan(B)$ in terms of $t$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given sin(B) = t, with 0 < B < π/2, so B is in the first qua... | 477 | 612 |
[
{
"content": "Derive the formula $\\cos(\\theta + \\frac{v\\epsilon^2 \\Omega}{L}+O(\\epsilon^4))-\\cos(\\theta) = -\\epsilon^2\\frac{\\Omega v}{L}\\sin(\\theta)+O(\\epsilon^4)$ using small approximations.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Derive the formula $\cos(\theta + \frac{v\epsilon^2 \Omega}{L}+O(\epsilon^4))-\cos(\theta) = -\epsilon^2\frac{\Omega v}{L}\sin(\theta)+O(\epsilon^4)$ using small approximations.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>as... | 826 | 615 |
[
{
"content": "Find sequences $(a_n)$ and $(b_n)$ such that\n\\[\n\\liminf a_n + \\liminf b_n < \\liminf (a_n + b_n).\n\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "\\boxed{a_n = (-1)^n... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find sequences $(a_n)$ and $(b_n)$ such that
\[
\liminf a_n + \liminf b_n < \liminf (a_n + b_n).
\]
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We need to find sequences (a_n) and (b_n) such that lim inf a_... | 326 | 616 |
[
{
"content": "Find the matrix $S$ of stretch by a factor of $3$ in the $y$-direction and the matrix $S^{-1}$ for mappings from $\\mathbb{R}^2$ to $\\mathbb{R}^2$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the matrix $S$ of stretch by a factor of $3$ in the $y$-direction and the matrix $S^{-1}$ for mappings from $\mathbb{R}^2$ to $\mathbb{R}^2$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to... | 478 | 616 |
[
{
"content": "Give an example of a nonempty subset of $\\mathbb{Z} \\times \\mathbb{Z} \\times \\mathbb{Z}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "**Step-by-step reasoning:**\n1. T... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Give an example of a nonempty subset of $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z}$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "Give an example of a nonempty subset of $\mathbb{Z} \time... | 413 | 619 |
[
{
"content": "Find the derivative $\\displaystyle \\frac{d}{dx}\\int^a_x \\tan(\\tan(t))\\,dt$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The derivative of an integral with a variable ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find the derivative $\displaystyle \frac{d}{dx}\int^a_x \tan(\tan(t))\,dt$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to find the derivative with respect to x of the integral from x to a: ∫_x... | 390 | 623 |
[
{
"content": "For which scalars \\( a \\in \\mathbb{R} \\) is the matrix \\( A = \\begin{bmatrix} a & -1 \\\\ 1 & a \\end{bmatrix} \\) invertible? What is the answer if \\( a \\in \\mathbb{C} \\)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role":... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
For which scalars \( a \in \mathbb{R} \) is the matrix \( A = \begin{bmatrix} a & -1 \\ 1 & a \end{bmatrix} \) invertible? What is the answer if \( a \in \mathbb{C} \)?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<... | 590 | 626 |
[
{
"content": "Simplify the boolean expression $(AB) + (A'C) + (BC)$ to its simplest form.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The expression \\( AB + A'C + BC \\) can be simplifi... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Simplify the boolean expression $(AB) + (A'C) + (BC)$ to its simplest form.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to simplify the boolean expression (AB) + (A'C) + (BC). We need to simpli... | 448 | 626 |
[
{
"content": "Let the random variable \\( X = X(n) \\) have \\( E(X) = u \\) where \\( u \\in \\mathbb{R} \\) and \\( E(X^2) < \\infty \\) such that \\( \\text{VAR}(X) = \\frac{\\sigma^2}{n} \\) where \\( \\sigma^2 > 0 \\) is a fixed positive number and \\( n \\geq 1 \\) is an integer. Write the Chebyshev inequ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Let the random variable \( X = X(n) \) have \( E(X) = u \) where \( u \in \mathbb{R} \) and \( E(X^2) < \infty \) such that \( \text{VAR}(X) = \frac{\sigma^2}{n} \) where \( \sigma^2 > 0 \) is a fixed positive number and \( n \geq 1 \) is an integer. Write the Chebyshev in... | 493 | 627 |
[
{
"content": "Given $\\sin(x) = \\sin(30^\\circ)$, find the general solution for $x$ in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The general solution for \\(\\sin(x) = \\sin(... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Given $\sin(x) = \sin(30^\circ)$, find the general solution for $x$ in degrees.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given the equation sin(x) = sin(30°). We need to find the general solution ... | 510 | 628 |
[
{
"content": "Find \\((f \\circ g)(x)\\) where \\(f(x) = \\frac{1}{x^2 + 3}\\) and \\(g(x) = \\sqrt{x - 2}\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The composition \\((f \\circ g)... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find \((f \circ g)(x)\) where \(f(x) = \frac{1}{x^2 + 3}\) and \(g(x) = \sqrt{x - 2}\).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given two functions:
f(x) = 1/(x^2 + 3)
g(x) = sqrt(x - 2)
We need... | 495 | 629 |
[
{
"content": "How many ways can 5 balls be selected from 30 balls numbered from 1 to 30 such that no two selected balls have consecutive numbers?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
How many ways can 5 balls be selected from 30 balls numbered from 1 to 30 such that no two selected balls have consecutive numbers?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "How many ways c... | 768 | 629 |
[
{
"content": "Write a polynomial of degree 5 that is divisible by \\(x^2 - 2\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To create a polynomial of degree 5 that is divisible by \\(x^... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Write a polynomial of degree 5 that is divisible by \(x^2 - 2\).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We need to write a polynomial of degree 5 that is divisible by x^2 - 2. So we need a polynomial P... | 370 | 630 |
[
{
"content": "How many different license plates can be made using 3 letters followed by 2 digits, if repetition of letters and digits is allowed?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
How many different license plates can be made using 3 letters followed by 2 digits, if repetition of letters and digits is allowed?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "How many differ... | 456 | 635 |
[
{
"content": "Find $\\cos(\\theta)$ and $\\tan(\\theta)$ given $\\sin(\\theta) = -\\frac{7}{25}$ and $270^\\circ < \\theta < 360^\\circ$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Find $\cos(\theta)$ and $\tan(\theta)$ given $\sin(\theta) = -\frac{7}{25}$ and $270^\circ < \theta < 360^\circ$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given sin(θ) = -7/25 and 270° < θ < 360°.... | 644 | 637 |
[
{
"content": "Express the equation $log_9(y)=\\frac{x+4}{2}$ in the form $y=k \\cdot a^x$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To express \\( \\log_9(y) = \\frac{x+4}{2} \\) in t... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Express the equation $log_9(y)=\frac{x+4}{2}$ in the form $y=k \cdot a^x$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are given the equation: log_9(y) = (x+4)/2.
We need to express it in the form y = k... | 574 | 638 |
[
{
"content": "Evaluate the integral $\\int{\\dfrac{\\cos{x}}{2+\\sin{x}}} dx$ using the substitution $u = 2 + \\sin{x}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "To evaluate the integ... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Evaluate the integral $\int{\dfrac{\cos{x}}{2+\sin{x}}} dx$ using the substitution $u = 2 + \sin{x}$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked to evaluate the integral ∫ (cos x)/(2 + sin x) ... | 567 | 640 |
[
{
"content": "Give an example of a sequence with subsequences converging to 1, 2, and 3.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "We can construct a simple sequence by repeating the p... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
Give an example of a sequence with subsequences converging to 1, 2, and 3.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We need to give an example of a sequence of real numbers that has subsequences convergi... | 590 | 643 |
[
{
"content": "What is the sum of the first $m$ natural numbers, both even and odd?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"reasoning_content": "",
"role": "user",
"tool_calls": []
},
{
"content": "The first \\(m\\) natural numbers are \\(1, 2, 3, \\dots, m... | [] | nvidia/Nemotron-SFT-Math-v4::train | <|im_start|>system
<|im_end|>
<|im_start|>user
What is the sum of the first $m$ natural numbers, both even and odd?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
We are asked: "What is the sum of the first m natural numbers, both even and odd?" I need to ... | 352 | 644 |
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